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# Media and Technology
## Introduction
When a celebrity announces that they are quitting social media, it’s big news (especially on social media). Depending on the star’s status and their reason for leaving, the decision is met with a blend of astonishment, dismay, concern for the individual or others they affect, and discussion about larger problems like bullying or online toxicity.
Why do they quit? Their reasons vary, and many eventually return. Lizzo left Twitter after claiming there were “too many trolls.” Lorde indicated that the stress of continual updates, “having front-row seats to the hellfire” necessitated a break (Kirkpatrick 2020). Other artists, like Coldplay, never formally deactivated their accounts, but went for long periods of inactivity. Rhianna took a six month hiatus; Justin Bieber and Adele also went without for some time. No matter what the reason, if a popular artist quits social media, a slew of articles and interviews will focus on the decision and the reasons behind it.
What makes these decisions newsworthy? A person deciding not to use a particular app doesn’t affect our day-to-day life. Or does it? What if that person shared intimate aspects of their life, offering a sense of connection to their followers? What if the singer provided continual updates on the progress of their new album, or gave their followers a better chance of meeting them? What if that singer posted or liked new remixes or playlists of their material, giving their fans new music to try?
Beyond the relationship with the artist, the social media presence gives fans a sense of community. Recall the discussion of groups. In traditional terms, a musician’s fanbase would be a secondary group: The group creates community, but the members aren’t close and are unlikely to serve expressive functions. But social media can easily turn that secondary group into a primary one. Follow a Reddit thread about a new video, and you’ll see dozens of people who seem to know each other well, who affirm or argue with each other along familiar lines, as if they’re cousins reuniting over a dinner table. They’ve never met in person and probably never will, but they may know intimate details about each other's lives; they’ve shared ups and downs in the manner similar to a local, close-knit group.
Selena Gomez has had a complicated relationship with social media. She has announced several times that she is quitting, and went through periods of regular downtime. She’s indicated that many of her updates are posted from friends’ devices. “As soon as I became the most followed person on Instagram,” she said, “I sort of freaked out. It had become so consuming to me. It’s what I woke up to and went to sleep to. I was an addict, and it felt like I was seeing things I didn’t want to see, like it was putting things in my head that I didn’t want to care about” (Haskell 2017).
This chapter will further explore the relationships, opportunities, and issues related to media and technology. While the specific products and platforms may quickly grow out of date, consider the larger implications of group dynamics, culture, socialization, and stratification as they relate to the ways we communicate and connect, and the old and new technologies that are meant to help us.
### References
Haskell, Rob. 2017. “Selena Gomez on Instagram Fatigue, Good Mental Health, and Stepping Back From the Limelight.” Vogue. (https://www.vogue.com/article/selena-gomez-april-cover-interview-mental-health-instagram)
Kirkpatrick, Emily. 2020. “Lorde Explains Why She Stepped Back from Social Media in 2018.” Vanity Fair. (https://www.vanityfair.com/style/2020/11/lorde-explains-no-instagram-twitter-cazzie-david-interview) |
# Media and Technology
## Technology Today
It is easy to look at the latest virtual reality headset and think technology is a recent addition to our world. But from the steam engine to the most cutting-edge robotic surgery tools, technology has described the application of science to address the problems of daily life. We might roll our eyes at enormous and clunky computers of the 1970s that had far less storage than a free thumb drive. But chances are, twenty years from now our skinny laptops and pocket-filling phones will look just as archaic.
### What Is Technology?
If someone asked your instructor what instructional technology they used, your instructor would likely assume the questioner was referring to courseware platforms, classroom response offerings, or presentation software. But if your instructor simply responded with, “pencil and paper,” they’d still be accurately describing technology. Modern paper and writing devices would have been considered fantastical creations in ancient times. And the fact that they endure, even as many other potential replacements have come into play, shows how effective those technologies are.
Just as the availability of digital technology shapes how we live today, the creation of stone tools changed how premodern humans lived and how well they ate. From the first calculator, invented in 2400 BCE Babylon in the form of an abacus, to the predecessor of the modern computer, created in 1882 by Charles Babbage, all of our technological innovations are advancements on previous iterations. And indeed, all aspects of our lives are influenced by technology. In agriculture, the introduction of machines that can till, thresh, plant, and harvest greatly reduced the need for manual labor, which in turn meant there were fewer rural jobs. This led to the urbanization of society, as well as lowered birth rates because there was less need for large families to work the farms. In the criminal justice system, the ability to ascertain innocence through DNA testing has saved the lives of people on death row. The examples are endless: technology plays a role in absolutely every aspect of our lives.
### Technological Inequality
As with any improvement to human society, not everyone has equal access. Technology, in particular, often creates changes that lead to ever greater inequalities. In short, the gap gets wider faster. This technological stratification has led to a new focus on ensuring better access for all.
There are two forms of technological stratification. The first is differential class-based access to technology in the form of the digital divide. This digital divide has led to the second form, a knowledge gap, which is, as it sounds, an ongoing and increasing gap in information for those who have less access to technology. Simply put, students in well-funded schools receive more exposure to technology than students in poorly funded schools. Those students with more exposure gain more proficiency, which makes them far more marketable in an increasingly technology-based job market and leaves our society divided into those with technological knowledge and those without. Even as we improve access, we have failed to address an increasingly evident gap in e-readiness—the ability to sort through, interpret, and process knowledge (Sciadas 2003).
Since the beginning of the millennium, social science researchers have tried to bring attention to the digital divide, the uneven access to technology among different races, classes, and geographic areas. The term became part of the common lexicon in 1996, when then Vice President Al Gore used it in a speech. This was the point when personal computer use shifted dramatically, from 300,000 users in 1991 to more than 10 million users by 1996 (Rappaport 2009). In part, the issue of the digital divide had to do with communities that received infrastructure upgrades that enabled high-speed Internet access, upgrades that largely went to affluent urban and suburban areas, leaving out large swaths of the country.
At the end of the twentieth century, technology access was also a big part of the school experience for those whose communities could afford it. Early in the millennium, poorer communities had little or no technology access, while well-off families had personal computers at home and wired classrooms in their schools. In the 2000s, however, the prices for low-end computers dropped considerably, and it appeared the digital divide was naturally ending. Research demonstrates that technology use and Internet access still vary a great deal by race, class, and age in the United States, though most studies agree that there is minimal difference in Internet use by adult men and adult women.
Data from the Pew Research Center (Perrin 2019) suggests the emergence of yet another divide. Larger percentages of groups such as Latinos and African Americans use their phones rather than traditional computers to connect to the Internet and undertake related activities. Roughly eight in ten White people reported owning computers, in contrast to roughly six in ten Black and Hispanic people owning them. White people were also more likely to have broadband (high-speed Internet) in their homes. But approximately one in four Black and Hispanic people reported being smartphone-only Internet users, a number that far outpaces White people's reliance on the devices. While it might seem that the Internet is the Internet, regardless of how you get there, there’s a notable difference. Tasks like updating a résumé or filling out a job application are much harder on a cell phone than on a large-screen computer in the home. As a result, the digital divide might mean no access to computers or the Internet, but could mean access to the kind of online technology that allows for empowerment, not just entertainment (Washington 2011).
Another aspect of the digital divide is present in the type of community one lives in. Census data released in 2018 showed that in the study period of 2013 to 2017, 78 percent of U.S. households had Internet access, but that homes in rural and low-income areas were below that national average by 13 percent. The data was collected by county, and showed that "mostly urban" counties significantly outpaced "mostly rural" counties. "Completely rural," lower-income counties had the lowest rates of home Internet adoption, at about 60 percent (Martin 2019).
One potential outcome of reduced home Internet and computer access can be the relatively low representation of certain populations in computing courses, computing majors, and computing careers. Some school districts, often with the help of government grants or corporate sponsorships, aim to address this aspect of the digital divide by providing computers to those who need them, either at a low cost or at no charge. A number of organizations, such as Code.org, Black Girls Code, and Black Boys Code, work to overcome the disparity by offering computer science education programs and camps, collaborative instruction programs with local school districts, and (perhaps most impactful in the long term) teacher training programs. As a result, the number of Black and Hispanic students in courses like Advanced Placement Computer Science has increased dramatically in recent years, as has the number of college majors from the same populations.
As a whole, the digital divide brings some level of controversy. Some question why it still exists after having been identified more than twenty years ago. Others question whether or not it exists at all, and offer data to support the claim that it does not exist (American Press Institute 2015). However, most experts agree that the COVID-19 pandemic revealed that the digital divide has persisted, particularly in education. While millions of students were confined to home and remote instruction, they were divided by their Internet access, their familiarity with computer hardware and software, and their ability to solve their own technology issues (PRB 2020). Even when governments and educational institutions implemented improvements to the access and technology situation, there remained the qualitative aspect of unplanned remote education: Many instructors and students are not as effective while communicating only through computer screens. When considering education, policymakers faced arduous decision-making processes and contentious debates as they tried the balance the issues of safety, educational quality, teacher safety, student mental health, and the overall changing landscape of the pandemic.
### Constant Contact and Replaced Relationships
How often do you check your phone for new messages or alerts? If you're typical, it might be over 100 times a day. (The number is difficult to cite with confidence, because every few months, organizations or companies release new studies claiming to have updated statistics.) What happens to your phone when you are sleeping? In 2012, researchers reported that “44% of cell phone owners have slept with their phone next to their bed because they wanted to make sure they didn’t miss any calls, text messages, or other updates during the night, and 29% of cell owners describe their cell phone as ‘something they can’t imagine living without’” (Smith 2012). Just three years later, a frequently cited report by Bank of America indicated the number of phone-accompanied sleepers was at 71 percent (Kooser 2015). A more recent survey of 500 people found it to be 66 percent, but that survey only included adults (Abbott 2020). However, these surveys and the reaction to them might be a factor of selective memory: Prior to the rise of cell phones, many people had telephones in their rooms, often within arm's reach of their bed.
While people report that cell phones make it easier to stay in touch, simplify planning, and increase their productivity, those are not the only impacts of constant device usage in the United States. Smith also reports that “roughly one in five cell owners say that their phone has made it at least somewhat harder to forget about work at home or on the weekends; to give people their undivided attention; or to focus on a single task without being distracted” (Smith 2012). As mentioned in the opening of this chapter, even celebrities who have perhaps benefitted the most from increased communication and social media report stress and concern about their online presence and its related outcomes.
With so many people using social media both in the United States and abroad, it is no surprise that social media is a powerful force for social change or political expression. For example, McKenna Pope, a thirteen-year-old girl, used the Internet to successfully petition Hasbro to fight gender stereotypes by creating a gender-neutral Easy-Bake Oven instead of using only the traditional pink color (Kumar 2014). Movements such as MeToo and Black Lives Matter gained prominence partly through what is sometimes referred to as "hashtag activism." More recently, TikTok users who actively opposed Donald Trump's re-election registered for nearly all the seats at a major rally. When they did not attend, the arena was nearly empty, after the campaign had predicted it would be overflowing. Later, Trump supporters used the social media site Parler in their own rally planning and coordination.
Such consistent and impactful usage leads to unavoidable results: Newer communication methods are replacing older ones. Speaking by phone seems archaic and almost intrusive for some people, who greatly prefer non-voice messaging apps or texts. Media observers, etiquette commentators, and friends and family may lament people beginning and ending relationships by text message, but those methods have proven more comfortable, especially for young people.
What are the effects? There have not been studies on every type of relationship, but research into romantic relationships shows interesting results. First, consider the elements of a relationship. One is attachment, or the bond that people form with each other. Research has shown that constant communication via messaging significantly increases the level of attachment. That fact seems intuitive: people who continually check in on each other, report their whereabouts, and offer support or affirmation will build a stronger bond. The same study, however, found that the respondents rated the overall quality of the relationship as weaker or less satisfying when it was dominated by text messaging instead of voice conversation (Luo 2014).
Many of us have experienced another aspect of relationships: reliance or imbalance. Researchers have found that close friends who are heavily reliant on mobile devices and associated messaging may have more issues regarding overdependence on the relationship and differing expectations regarding communication. Friendships that do not rely on mobile devices may have far less frequent contact. Research found elements of guilt and pressure to respond (called entrapment) in mobile-dependent relationships, which led to overall dissatisfaction (Hall 2012).
### Online Privacy, Security, and Control
As we increase our footprints on the web by going online more often to connect socially, share material, conduct business, and store information, we also increase our vulnerability to those with negative intent. Most Americans seem to accept that increased usage of online and related tools brings risks, but their perceptions of those risks are evolving. For example, people have different viewpoints on risks associated with individuals, companies, and the government. The Pew Research Center conducts frequent surveys on these topics. A recent publication indicated the following:
1. 81 percent of people felt they had little control over the data collected by companies; 84 percent felt they had little control over data collected by the government.
2. 62 percent felt that it was not possible to go through the day without having data collected about them by companies; 63% felt it wasn't possible to go through a day without data collection by the government.
3. 79 percent were concerned about that data use by companies; 64 percent were concerned about data use by the government.
Other elements of the research demonstrate that older Americans felt more concern than younger ones, and that Black and Hispanic people were more likely than White people to believe the government was tracking them (Auxier 2019).
These attitudes may be revealed by practices or attitudes toward privacy efforts and safeguards. One person may be annoyed every time a privacy notice interrupts them, and they may simply sign the statement without thinking much about it. Another person may read every word of the agreement and carefully deliberate over whether to proceed.
Online privacy concerns also extend from individuals to their dependents. In accordance with the Child Online Privacy Protection Act, school districts must consider and control certain elements of privacy on behalf of students, meaning they cannot require or encourage students under age thirteen to provide personal information. Likewise, online platforms such as Instagram do not let children under the age of thirteen register for their sites. And where children are registered by their parents, sites like YouTube and, more recently, TikTok issue controls to prevent inappropriate portrayals by children or inappropriate behavior by other members. For example, YouTube often disables comments on videos produced by children (Moreno 2020). TikTok added privacy and protection methods in 2020, but in early 2021 was hit with allegations of violating child safety and privacy guidelines.
Although schools and companies are required to take steps to lower risks to children, parents and guardians are free to make their own choices on behalf of their children. Some parents avoid showing their children on social media; they do not post pictures, and ask family members to refrain from doing so (Levy, 2019). On the other end of the spectrum, some parents run social media accounts for their children. Sometimes referred to as "sharents," they may share entertaining videos, promote products through demos or try-ons, or post professionally produced photos on behalf of clothing companies or equipment makers. A child's (even a toddler's) role as an influencer can be financially lucrative, and companies making everything from helmets to dancewear have taken notice (Allchin 2012).
### Net Neutrality
The issue of net neutrality, the principle that all Internet data should be treated equally by Internet service providers, is part of the national debate about Internet access and the digital divide. On one side of this debate is the belief that those who provide Internet service, like those who provide electricity and water, should be treated as common carriers, legally prohibited from discriminating based on the customer or nature of the goods. Supporters of net neutrality suggest that without such legal protections, the Internet could be divided into “fast” and “slow” lanes. A conflict perspective theorist might suggest that this discrimination would allow bigger corporations, such as Amazon, to pay Internet providers a premium for faster service, which could lead to gaining an advantage that would drive small, local competitors out of business.
The other side of the debate holds the belief that designating Internet service providers as common carriers would constitute an unreasonable regulatory burden and limit the ability of telecommunication companies to operate profitably. A functional perspective theorist might point out that, without profits, companies would not invest in making improvements to their Internet service or expanding those services to underserved areas. The final decision rests with the Federal Communications Commission and the federal government, which must decide how to fairly regulate broadband providers without dividing the Internet into haves and have-nots.
### Summary
Technology is the application of science to address the problems of daily life. The fast pace of technological advancement means the advancements are continuous, but that not everyone has equal access. The gap created by this unequal access has been termed the digital divide. The knowledge gap refers to an effect of the digital divide: the lack of knowledge or information that keeps those who were not exposed to technology from gaining marketable skills
### Section Quiz
### Short Answer
### Further Research
To learn more about the digital divide and why it matters, check out this website with research on the digital divide.
To find out more about Internet privacy and security, check out this website on privacy rights.
### References
Abbott, Tyler. 2020. “America's Love Affair With Their Phones.” Reviews.org. (https://www.reviews.org/mobile/cell-phone-addiction/#Smart_Phone_Addiction_Stats)
Allchin, Josie. 2012. “New guidance for brands using child ambassadors.” Marketing Week. (https://www.marketingweek.com/new-guidance-for-brands-using-child-ambassadors/)
American Press Institute. 2015. “Race and ethnicity, device usage, and connectivity.” (https://www.americanpressinstitute.org/publications/reports/survey-research/race-ethnicity-device-usage-connectivity/)
Auxier, Brooke and Rainie, Lee. 2019. “Americans and Privacy.” Pew Research Center. (https://www.pewresearch.org/internet/2019/11/15/americans-and-privacy-concerned-confused-and-feeling-lack-of-control-over-their-personal-information/)
Guillén, M.F., and S.L. Suárez. 2005. “Explaining the Global Digital Divide: Economic, Political and Sociological Drivers of Cross-National Internet Use.” Social Forces 84:681–708.
Hall, J. A., & Baym, N. K. (2012). “Calling and texting (too much): Mobile maintenance expectations, (over) dependence, entrapment, and friendship satisfaction.” New Media and Society, 14, 316–331.
Kooser, Amanda. 2015. “Sleep with your smartphone in hand? You're not alone.” CNET. (https://www.cnet.com/news/americans-like-to-snooze-with-their-smartphones-says-survey/)
Levy, Sara. 2019. “No, I Won't Post A Picture of My Kid on Social Media.” Glamour. (https://www.glamour.com/story/mom-wont-post-childs-photo-on-social-media)
Luo, Shanhong. 2014. “Effects of Texting on Satisfaction in Romantic Relationships: The Role of Attachment.” Computers in Human Behavior. April 2014. (10.1016/j.chb.2014.01.014)
Lewis, Dave. 2014. “ICloud Data Breach: Hacking and Celebrity Photos.” Forbes.com. Forbes. Retrieved October 6, 2014 (https://www.forbes.com/sites/davelewis/2014/09/02/icloud-data-breach-hacking-and-nude-celebrity-photos/?sh=735a2af22de7).
Liff, Sondra, and Adrian Shepherd. 2004. “An Evolving Gender Digital Divide.” Oxford Internet Institute, Internet Issue Brief No. 2. Retrieved January 11, 2012 (https://educ.ubc.ca/faculty/bryson/565/genderdigdiv.pdf).
Martin, Michael J. R. 2019. “Rural and Lower Income Counties Lag Nation in Internet Subscription.” (https://www.census.gov/library/stories/2018/12/rural-and-lower-income-counties-lag-nation-internet-subscription.html)
McChesney, Robert. 1999. Rich Media, Poor Democracy: Communication Politics in Dubious Times. Urbana and Chicago: University of Illinois Press.
Moreno, Johan. 2020. “YouTube Disables Personalized Ads, Commnts on Children's Videos.” Forbes. (https://www.forbes.com/sites/johanmoreno/2020/01/06/youtube-disables-personalized-ads-comments-on-childrens-videos/?sh=202ef7695bf0)
Mossberger, Karen, Caroline Tolbert, and Michele Gilbert. 2006. “Race, Place, and Information Technology.” Urban Affairs Review 41:583–620.
Perrin, Andrew and Turner, Erica. 2019. “Smartphones help blacks, Hispanics bridge some – but not all – digital gaps with whites.” Pew Research Cener. (https://www.pewresearch.org/fact-tank/2019/08/20/smartphones-help-blacks-hispanics-bridge-some-but-not-all-digital-gaps-with-whites/)
“Planned Obsolescence.” 2009. The Economist, March 23. Retrieved January 12, 2012 (http://www.economist.com/node/13354332).
Population Reference Bureau. 2020. “Children, Coronavirus, and the Digital Divide: Native American, Black, and Hispanic Students at Greater Educational Risk During Pandemic. (https://www.prb.org/coronavirus-digital-divide-education/)
Rainie, Lee, Sara Kiesler, Ruogo Kang, and Mary Madden. 2013. "Anonymity, Privacy, and Security Online." Pew Research Centers Internet American Life Project RSS. Pew Research Center. Retrieved October 5, 2014 (http://www.pewinternet.org/2013/09/05/anonymity-privacy-and-security-online/).
Rappaport, Richard. 2009. “A Short History of the Digital Divide.” Edutopia, October 27. Retrieved January 10, 2012 (http://www.edutopia.org/digital-generation-divide-connectivity).
Sciadas, George. 2003. “Monitoring the Digital Divide … and Beyond.” World Bank Group. Retrieved January 22, 2012 (http://www.infodev.org/en/Publication.20.html).
Smith, Aaron. 2012. "The Best (and Worst) of Mobile Connectivity." Pew Research Internet Project. Retrieved December 19, 2014 (http://www.pewinternet.org/2012/11/30/the-best-and-worst-of-mobile-connectivity/).
Time.com. 2014. "Rankings." Fortune. Time.com. Retrieved October 1, 2014 (http://fortune.com/rankings/).
Washington, Jesse. 2011. “For Minorities, New ‘Digital Divide’ Seen.” Pew Internet and American Life Project, January 10. Retrieved January 12, 2012 (http://www.pewinternet.org/Media-Mentions/2011/For-minorities-new-digital-divide-seen.aspx). |
# Media and Technology
## Media and Technology in Society
Technology and the media are interwoven, and neither can be separated from contemporary society in most core and semi-peripheral nations. Media is a term that refers to all print, digital, and electronic means of communication. From the time the printing press was created (and even before), technology has influenced how and where information is shared. Today, it is impossible to discuss media and the ways societies communicate without addressing the fast-moving pace of technology change. Twenty years ago, if you wanted to share news of your baby’s birth or a job promotion, you phoned or wrote letters. You might tell a handful of people, but you probably wouldn’t call up several hundred, including your old high school chemistry teacher, to let them know. Now, you might join an online community of parents-to-be even before you announce your pregnancy via a staged Instagram picture. The circle of communication is wider than ever, and when we talk about how societies engage with technology, we must take media into account, and vice versa.
Technology creates media. The comic book you bought your daughter is a form of media, as is the movie you streamed for family night, the web site you used to order takeout, the billboard you passed on the way to pick up your food, and the newspaper you read while you were waiting for it. Without technology, media would not exist, but remember, technology is more than just the media we are exposed to.
### Categorizing Technology
There is no one way of dividing technology into categories. Whereas once it might have been simple to classify innovations such as machine-based or drug-based or the like, the interconnected strands of technological development mean that advancement in one area might be replicated in dozens of others. For simplicity’s sake, we will look at how the U.S. Patent Office, which receives patent applications for nearly all major innovations worldwide, addresses patents. This regulatory body will patent three types of innovation. Utility patents are the first type. These are granted for the invention or discovery of any new and useful process, product, or machine, or for a significant improvement to existing technologies. The second type of patent is a design patent. Commonly conferred in architecture and industrial design, this means someone has invented a new and original design for a manufactured product. Plant patents, the final type, recognize the discovery of new plant types that can be asexually reproduced. While genetically modified food is the hot-button issue within this category, farmers have long been creating new hybrids and patenting them. A more modern example might be food giant Monsanto, which patents corn with built-in pesticide (U.S. Patent and Trademark Office 2011).
Anderson and Tushman (1990) suggest an evolutionary model of technological change, in which a breakthrough in one form of technology leads to a number of variations. Once those are assessed, a prototype emerges, and then a period of slight adjustments to the technology, interrupted by a breakthrough. For example, in terms of portable data storage, the first mainstream device was a floppy disk–a square, plastic object larger than a playing card, which in its final iteration held 1.4 megabytes of data (or less than a single high-resolution photo). Until the early 2000s, these were common formats, and students and professionals would regularly carry several of them. Floppy disks were improved and upgraded, then replaced by higher-capacity Zip and Jaz disks, which were then replaced by flash drives. This is essentially a generational model for categorizing technology, in which first-generation technology is a relatively unsophisticated jumping-off point that leads to an improved second generation, and so on.
Another type of evolution involves disruptive technology (or disruptive innovation), which is a product, service, or process that has a major effect on the operation of an entire industry, and/or may create new industries or new markets. In the example above, a disruptive technology might be the advent of cloud-based storage platforms like Google Drive and iCloud, which have significantly reduced the need for physical portable storage. Disruptive technology can create and destroy entire industries, sometimes in a rapid manner rather than in an evolutionary one. In one of the most famous examples, the advent of digital photography rendered film-based cameras obsolete; the change came quickly, and many companies could not adjust. In a similar manner, ride-sharing services have had a massive impact on the taxi and limousine industry. Emerging technologies such as blockchain, additive manufacturing (3D printing), and augmented reality are likely to have similar impacts. For example, if companies decide that it is more efficient to 3D print many products or components close to their destinations instead of shipping them from distant manufacturing plants and warehouses, the entire shipping industry may be affected.
The sociological impact of disruptive technology can be sudden. Digital photography, for example, resulted in the rapid decline of companies like Kodak, which had been stalwarts of the American economy and a major employer. Layoffs devastated cities like Rochester, New York. The advent of online music purchasing and subscription services resulted in the closure of thousands of record stores, both small businesses and large chains like Tower Records. Beyond the economic impact, these stores were often parts of the fabric of communities, places for fans to gather to explore and share music. Automation has likewise changed manufacturing and mining, resulting in severe job loss and drastic alterations in regions such as the Great Lakes, where many towns went from being part of the Manufacturing Belt to being part of the Rust Belt.
### Types of Media and Technology
Media and technology have evolved hand in hand, from early print to modern publications, from radio to television to film. New media emerge constantly, such as we see in the online world.
### Newspaper
Early forms of print media, found in ancient Rome, were hand-copied onto boards and carried around to keep the citizenry informed. With the invention of the printing press, the way that people shared ideas changed, as information could be mass produced and stored. For the first time, there was a way to spread knowledge and information more efficiently; many credit this development as leading to the Renaissance and ultimately the Age of Enlightenment. This is not to say that newspapers of old were more trustworthy than the Weekly World News and National Enquirer are today. Sensationalism abounded, as did censorship that forbade any subjects that would incite the populace.
The invention of the telegraph, in the mid-1800s, changed print media almost as much as the printing press. Suddenly information could be transmitted in minutes. As the nineteenth century became the twentieth, U.S. publishers such as Hearst redefined the world of print media and wielded an enormous amount of power to socially construct national and world events. Of course, even as the media empires of William Randolph Hearst and Joseph Pulitzer were growing, print media also allowed for the dissemination of countercultural or revolutionary materials. Internationally, Vladimir Lenin’s Irksa (The Spark) newspaper was published in 1900 and played a role in Russia’s growing communist movement (World Association of Newspapers 2004).
With the invention and widespread use of television in the mid-twentieth century, newspaper circulation steadily dropped off, and in the 21st century, circulation has dropped further as more people turn to internet news sites and other forms of new media to stay informed. According to the Pew Research Center, 2009 saw an unprecedented drop in newspaper circulation––down 10.6 percent from the year before (Pew 2010).
This shift away from newspapers as a source of information has profound effects on societies. When the news is given to a large diverse conglomerate of people, it must maintain some level of broad-based reporting and balance in order to appeal to a broad audience and keep them subscribing. As newspapers decline, news sources become more fractured, so each segment of the audience can choose specifically what it wants to hear and what it wants to avoid. Increasingly, newspapers are shifting online in an attempt to remain relevant. It is hard to tell what impact new media platforms will have on the way we receive and process information.
It is hard to tell what impact new media platforms will have on the way we receive and process information. The Pew Research Center’s Project for Excellence in Journalism (2013) reported that audiences for all the major news magazines declined in 2012, though digital ad revenue increased. The same report suggested that, while newspaper circulation is holding steady at around $10 billion after years of decline, it is digital pay plans that allow newspapers to keep their heads above water, and the digital ad revenue that is increasing for news magazines is not enough to compensate for print revenue loss in newspapers.
A 2014 report suggested that U.S. adults read a median of five books per year in 2013, which is about average. But are they reading traditional print or e-books? About 69 percent of people said they had read at least one printed book in the past year, versus 28 percent who said they’d read an e-book (DeSilver 2014). Is print more effective at conveying information? In recent study, Mangen, Walgermo, and Bronnick (2013) found that students who read on paper performed slightly better than those who read an e-book on an open-book reading comprehension exam of multiple-choice and short-answer questions. While a meta-analysis of research by Andrews (1992) seemed to confirm that people read more slowly and comprehend less when reading from screens, a meta-analysis of more recent research on this topic does not show anything definite (Noyes and Garland 2008).
### Television and Radio
Radio programming obviously preceded television, but both shaped people’s lives in much the same way. In both cases, information (and entertainment) could be enjoyed at home, with a kind of immediacy and community that newspapers could not offer. For instance, many people in the United States might remember when they saw on television or heard on the radio that the Twin Towers in New York City had been attacked in 2001. Even though people were in their own homes, media allowed them to share these moments in real time. This same kind of separate-but-communal approach occurred with entertainment too. School-aged children and office workers gathered to discuss the previous night’s installment of a serial television or radio show.
Right up through the 1970s, U.S. television was dominated by three major networks (ABC, CBS, and NBC) that competed for ratings and advertising dollars. The networks also exerted a lot of control over what people watched. Public television, in contrast, offered an educational nonprofit alternative to the sensationalization of news spurred by the network competition for viewers and advertising dollars. Those sources—PBS (Public Broadcasting Service), the BBC (British Broadcasting Company), and CBC (Canadian Broadcasting Company)—garnered a worldwide reputation for high-quality programming and a global perspective. Al Jazeera, the Arabic independent news station, has joined this group as a similar media force that broadcasts to people worldwide.
The impact of television on U.S. society is hard to overstate. By the late 1990s, 98 percent of U.S. homes had at least one television set, and the average person watched between two and a half and five hours of television daily. All this television has a powerful socializing effect, providing reference groups while reinforcing social norms, values, and beliefs.
### Film
The film industry took off in the 1930s, when color and sound were first integrated into feature films. Like television, early films were unifying for society: as people gathered in theaters to watch new releases, they would laugh, cry, and be scared together. Movies also act as time capsules or cultural touchstones for society. From Westerns starring the tough-talking Clint Eastwood to the biopic of Facebook founder and Harvard dropout Mark Zuckerberg, movies illustrate society’s dreams, fears, and experiences. While many consider Hollywood the epicenter of moviemaking, India’s Bollywood actually produces more films per year, speaking to the cultural aspirations and norms of Indian society. The film industry, like other media formats, has gone through substantial change as a result of streaming services, online privacy, and the new competition for people's entertainment dollars. Because the mainstream movie industry has been so reliant on ticket sales at live theaters, the COVID-19 pandemic affected it more dramatically than most other media categories. Highly anticipated movies slated for 2020 and 2021 releases were delayed or shifted to streaming distribution, reducing revenue. And some companies made lasting decisions regarding their future offerings.
### New Media and Online Environments
New media encompasses all interactive forms of information exchange. These include social networking sites, blogs, podcasts, wikis, and virtual worlds. Many are not "new" in the sense that they were developed in the past few years (some may be older than you), but they are newer than the media mentioned above, and they rely on types of technologies that were not available until about thirty years ago. Many are ways disruptive to traditional media or to companies that rely on those other formats. Clearly, the list of new media grows almost daily, and you might feel we are missing some. In fact, the immediacy of new media coupled with the lack of oversight means we must be more careful than ever to ensure that we are making good decisions about the accuracy, ethics, and cultural responsiveness of these formats.
### Product Advertising and the Attention Economy
Companies use advertising to sell to us, but the way they reach us is changing. Naomi Klein identified the destructive impact of corporate branding her 1999 text, No Logo, an antiglobalization treatise that focused on sweatshops, corporate power, and anticonsumerist social movements. In the post-millennial society, synergistic advertising practices ensure you are receiving the same message from a variety of sources and on a variety of platforms. For example, you may see billboards for Miller beer on your way to a stadium, sit down to watch a game preceded by a Miller commercial on the big screen, and watch a halftime ad in which people are shown holding up the trademark bottles. Chances are you can guess which brand of beer is for sale at the concession stand.
Advertising has changed, as technology and media have allowed consumers to bypass traditional advertising venues. From the invention of the remote control, which allows us to skip television advertising without leaving our seats, to recording devices that let us watch programs but skip the ads, conventional television advertising is on the wane. And print media is no different. Advertising revenue in newspapers and on television has fallen significantly, which shows that companies need new ways of getting their messages to consumers.
Brand ambassadorships can also be powerful tools for advertisers. For example, companies hire college students to be their on-campus representatives, and they may target for students engaged in high-profile activities like sports, fraternities, and music. (This practice is slightly different from sponsorships, and note that some students, particularly athletes, need to follow strict guidelines about accepting money or products.) The marketing team is betting that if we buy perfume because Beyoncé tells us to, we’ll also choose our workout gear, clothing, or make-up brand if another student encourages that choice. Tens of thousands of brand ambassadors or brand evangelists work on college campuses, and such marketing approaches are seen as highly effective investments for companies. The numbers make it clear: Ambassador-referred customers provide sixteen percent higher value to companies than other customers, and over ninety percent of people indicate that people trust referrals from people they know (On-Campus Advertising, 2017).
Social media has made such influencer and ambassador marketing a near constant. Some formal ambassadors are sponsored by companies to show or use their products. In some cases, compensation arrives only in the form of the free products and whatever monetization the ambassador receives from the site, such as YouTube. Influencers are usually less formally engaged with companies than are ambassadors, relying mostly on site revenue to reward their efforts. Some influencers may overstate their popularity in order to get free products or services. For example, luxury hotels report that they are barraged by influencers (some with very few followers, and therefore questionable influence) who expect free stays in exchange for creating posts promoting the location (Locker 2019).
One ethical and perhaps relationship-oriented question is whether paid ambassadors should be required to disclose their relationship with a company, and how that works in online versus face-to-face interactions. In this case, online presence may be more "truthful" than in-person relationships. A video can formally include sponsorship information, and some ambassadors list partners or sponsors on their profiles. But in day-to-day, in-person conversations, it might be awkward for a classmate or colleague to mention that they are wearing a particular brand or using gear based on a financial relationship. In other words, the person sitting next to you with the great bag may be paid to carry it, and you may never know.
### Homogenization and Fragmentation
Despite the variety of media at hand, the mainstream news and entertainment you enjoy are increasingly homogenized. Research by McManus (1995) suggests that different news outlets all tell the same stories, using the same sources, resulting in the same message, presented with only slight variations. So whether you are reading the New York Times or the CNN’s web site, the coverage of national events like a major court case or political issue will likely be the same.
Simultaneously with this homogenization among the major news outlets, the opposite process is occurring in the newer media streams. With so many choices, people increasingly customize their news experience, minimizing their opportunity to encounter information that does not jive with their worldview (Prior 2005). For instance, those who are staunchly Republican can avoid centrist or liberal-leaning cable news shows and web sites that would show Democrats in a favorable light. They know to seek out Fox News over MSNBC, just as Democrats know to do the opposite. Further, people who want to avoid politics completely can choose to visit web sites that deal only with entertainment or that will keep them up to date on sports scores. They have an easy way to avoid information they do not wish to hear. Americans seem to view this phenomenon with great concern, indicating that the impact of customized or personalized news delivers worse news. Yet, they still engage with the platforms that deliver news in that manner.
The fragmentation of the news has led to an increased amount of digital tribalism. Tribalism in this sense is the state or tendency to gather and reinforce ideas belonging to a group, and to do so out of a sense of strong loyalty. Digital tribalism, then, is the tendency to do so online, and also to forge new tribes purely based on online personas or ideologies. Instead of basing these groups on the classic bonds of ethnic, religious, or geographic ideologies, they are based on politics, emotions, lifestyles or lifestyle goals, or even brands (Taute & Sierra 2014). Digital tribes can lead people to a greater sense of belonging, and can also be heavily exploited for commercial or power-attaining interests.
### Summary
Media and technology have been interwoven from the earliest days of human communication. The printing press, the telegraph, and the Internet are all examples of their intersection. Mass media have allowed for more shared social experiences, but new media now create a seemingly endless amount of airtime for any and every voice that wants to be heard. Advertising has also changed with technology. New media allow consumers to bypass traditional advertising venues and cause companies to be more innovative and intrusive as they try to gain our attention.
### Section Quiz
### Short Answer
### Further Research
To get a sense of the timeline of technology. Check out this website with a technology timeline.
To learn more about new media, check out the New Media Institute
To understand how independent media coverage differs from major corporate affiliated news outlets, review material from the Democracy Now! website.
### References
Anderson, C.A., and B.J. Bushman. 2001. “Effects of Violent Video Games on Aggressive Behavior, Aggressive Cognition, Aggressive Affect, Physiological Arousal, and Prosocial Behavior: A Meta-Analytic Review of the Scientific Literature.” Psychological Science 12:353–359.
Anderson, Craig. 2003. “Violent Video Games: Myths, Facts and Unanswered Questions.” American Psychological Association, October. Retrieved January 13, 2012 (http://www.apa.org/science/about/psa/2003/10/anderson.aspx).
Anderson, Philip, and Michael Tushman. 1990. “Technological Discontinuities and Dominant Designs: A Cyclical Model of Technological Change.” Administrative Science Quarterly 35:604–633.
CNBC, 2020. “Apple, US States Reach $113 million settlement on iPhone throttling.” (https://www.cnbc.com/2020/11/18/apple-us-states-reach-113-million-settlement-on-iphone-throttling.html)
Dillon, Andrew. 1992. “Reading From Paper Versus Screens: A Critical Review of the Empirical Literature.” Ergonomics 35(10): 1297–1326.
DeSilver, Drew. 2014. “Overall Book Readership Stable, But e-Books Becoming More Popular.” Pew Research Center. Retrieved December 5, 2014 (http://www.pewresearch.org/fact-tank/2014/01/21/overall-book-readership-stable-but-e-books-becoming-more-popular/).
Duggan, Maeve, and Aaron Smith. "Social Media Update 2013." Pew Research Centers Internet American Life Project RSS. Pew Research Center. Retrieved October 2, 2014 (http://www.pewinternet.org/2013/12/30/social-media-update-2013/).
International Telecommunication Unions. 2014. “The World in 2014: ICT Facts and Figures.” United Nations. Retrieved December 5, 2014 (http://www.itu.int/en/ITU-D/Statistics/Documents/facts/ICTFactsFigures2014-e.pdf).
Jansen, Jim. "Use of the Internet in Higher-income Households." Pew Research Centers Internet American Life Project RSS. Pew Research Center. Retrieved October 1, 2014 (http://www.pewinternet.org/2010/11/24/use-of-the-internet-in-higher-income-households).
Kumar, Ravi. 2014. "Social Media and Social Change: How Young People Are Tapping into Technology." Youthink! N.p. Retrieved October 3, 2014 (http://blogs.worldbank.org/youthink/social-media-and-social-change-how-young-people-are-tapping-technology).
Lievrouw, Leah A., and Sonia Livingstone, eds. 2006. Handbook of New Media: Social Shaping and Social Consequences. London : SAGE Publications.
Locker, Melissa. 2019. “Don’t expect free stuff just because you have 2,000 Instagram followers.” Fast Company. (https://www.fastcompany.com/90330182/instagram-influencers-face-backlash-after-asking-for-free-hotels-and-travel-perks)
McManus, John. 1995. “A Market-Based Model of News Production.” Communication Theory 5:301–338.
Mangen, A., B.R. Walgermo, and K. Bronnick. 2013. “Reading Linear Texts on Paper Versus Computer Screen: Effects on Reading Comprehension.” International Journal of Educational Research 58 :61–68.
Nielsen. 2013. “'Bingeing’ in the New Viewing for Over-the-Top-Streamers.” Retrieved December 5, 2014 (http://www.nielsen.com/us/en/insights/news/2013/binging-is-the-new-viewing-for-over-the-top-streamers.html).
Noyes, Jan, and Kate J. Garland. 2008. “Computer- Vs. Paper-Based Tasks: Are They Equivalent?” Ergonomics 51(9): 1352–1375.
On Campus Advertising. 2017. “These Statistics Show Why College Brand Ambassadors Are So Important.” (https://oncampusadvertising.com/college-brand-ambassadors-important/)
Pew Research Center. 2010. “State of the News Media 2010.” Pew Research Center Publications, March 15. Retrieved January 24, 2012 (http://pewresearch.org/pubs/1523/state-of-the-news-media-2010).
Pew Research Center’s Project for Excellence in Journalism. 2013. “The State of the News Media 2013.” Pew Research Center Publications. Retrieved December 5, 2014 (http://www.stateofthemedia.org/2013/overview-5/key-findings/).
Prior, Markus. 2005. “News vs. Entertainment: How Increasing Media Choice Widens Gaps in Political Knowledge and Turnout.” American Journal of Political Science 49(3):577–592.
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Singer, Natasha. 2011. “On Campus, It’s One Big Commercial.” New York Times, September 10. Retrieved February 10, 2012 (http://www.nytimes.com/2011/09/11/business/at-colleges-the-marketers-are-everywhere.html?pagewanted=1&_r=1&ref=education).
Smith, Aaron. 2012. "The Best (and Worst) of Mobile Connectivity." Pew Research Centers Internet American Life Project RSS. Pew Research Center. Retrieved October 3, 2014 (http://www.pewinternet.org/2012/11/30/the-best-and-worst-of-mobile-connectivity/).
Smith, Aaron. 2014a. "African Americans and Technology Use." Pew Research Centers Internet American Life Project RSS. Pew Research Center. Retrieved October 1, 2014 (http://www.pewinternet.org/2014/01/06/african-americans-and-technology-use/).
Smith, Aaron. 2014b. "Older Adults and Technology Use." Pew Research Centers Internet American Life Project RSS. Pew Reserch Center. Retrieved October 2, 2014 (http://www.pewinternet.org/2014/04/03/older-adults-and-technology-use/).
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World Association of Newspapers. 2004. “Newspapers: A Brief History.” Retrieved January 12, 2012 (http://www.wan-press.org/article.php3?id_article=2821). |
# Media and Technology
## Global Implications of Media and Technology
Technology, and increasingly media, has always driven globalization. In a landmark book, Thomas Friedman (2005), identified several ways in which technology “flattened” the globe and contributed to our global economy. The first edition of The World Is Flat, written in 2005, posits that core economic concepts were changed by personal computing and high-speed Internet. Access to these two technological shifts has allowed core-nation corporations to recruit workers in call centers located in China or India. Using examples like a Midwestern U.S. woman who runs a business from her home via the call centers of Bangalore, India, Friedman warns that this new world order will exist whether core-nation businesses are ready or not, and that in order to keep its key economic role in the world, the United States will need to pay attention to how it prepares workers of the twenty-first century for this dynamic.
Of course not everyone agrees with Friedman’s theory. Many economists pointed out that in reality innovation, economic activity, and population still gather in geographically attractive areas, and they continue to create economic peaks and valleys, which are by no means flattened out to mean equality for all. China’s hugely innovative and powerful cities of Shanghai and Beijing are worlds away from the rural squalor of the country’s poorest denizens.
It is worth noting that Friedman is an economist, not a sociologist. His work focuses on the economic gains and risks this new world order entails. In this section, we will look more closely at how media globalization and technological globalization play out in a sociological perspective. As the names suggest, media globalization is the worldwide integration of media through the cross-cultural exchange of ideas, while technological globalization refers to the cross-cultural development and exchange of technology.
### Media Globalization
Lyons (2005) suggests that multinational corporations are the primary vehicle of media globalization, and these corporations control global mass-media content and distribution (Compaine 2005). It is true, when looking at who controls which media outlets, that there are fewer independent news sources as larger and larger conglomerates develop. In the early 2000s, the United States offered about 1,500 newspapers, 2,800 book publishers, plus 6,000 magazines and a whopping 10,000 radio outlets (Bagdikian 2004). By 2019, some of those numbers had changed: There were only 1,000 newspapers, but over 7,000 magazines (note that both newspapers and magazines count as such even if they publish largely online) (BBC 2019). The number of book publishers and radio outlets has generally remained static, which may seem surprising.
On the surface, there is endless opportunity to find diverse media outlets. But the numbers are misleading. Media consolidation is a process in which fewer and fewer owners control the majority of media outlets. This creates an oligopoly in which a few firms dominate the media marketplace. In 1983, a mere 50 corporations owned the bulk of mass-media outlets. Today in the United States just five companies control 90 percent of media outlets (McChesney 1999). Ranked by 2014 company revenue, Comcast is the biggest, followed by the Disney Corporation, Time Warner, CBS, and Viacom (Time.com 2014). What impact does this consolidation have on the type of information to which the U.S. public is exposed? Does media consolidation deprive the public of multiple viewpoints and limit its discourse to the information and opinions shared by a few sources? Why does it matter?
Monopolies matter because less competition typically means consumers are less well served since dissenting opinions or diverse viewpoints are less likely to be found. Media consolidation results in the following dysfunctions. First, consolidated media owes more to its stockholders than to the public. Publicly traded Fortune 500 companies must pay more attention to their profitability and to government regulators than to the public's right to know. The few companies that control most of the media, because they are owned by the power elite, represent the political and social interests of only a small minority. In an oligopoly there are fewer incentives to innovate, improve services, or decrease prices.
While some social scientists predicted that the increase in media forms would create a global village (McLuhan 1964), current research suggests that the public sphere accessing the global village will tend to be rich, Caucasoid, and English-speaking (Jan 2009). As shown by the spring 2011 uprisings throughout the Arab world, technology really does offer a window into the news of the world. For example, here in the United States we saw internet updates of Egyptian events in real time, with people tweeting, posting, and blogging on the ground in Tahrir Square.
Still, there is no question that the exchange of technology from core nations to peripheral and semi-peripheral ones leads to a number of complex issues. For instance, someone using a conflict theorist approach might focus on how much political ideology and cultural colonialism occurs with technological growth. In theory at least, technological innovations are ideology-free; a fiber optic cable is the same in a Muslim country as a secular one, a communist country or a capitalist one. But those who bring technology to less-developed nations—whether they are nongovernment organizations, businesses, or governments—usually have an agenda. A functionalist, in contrast, might focus on the ways technology creates new means to share information about successful crop-growing programs, or on the economic benefits of opening a new market for cell phone use. Either way, cultural and societal assumptions and norms are being delivered along with those high-speed wires.
Cultural and ideological bias are not the only risks of media globalization. In addition to the risk of cultural imperialism and the loss of local culture, other problems come with the benefits of a more interconnected globe. One risk is the potential for censoring by national governments that let in only the information and media they feel serve their message, as is occurring in China. In addition, core nations such as the United States risk the use of international media by criminals to circumvent local laws against socially deviant and dangerous behaviors such as gambling, child pornography, and the sex trade. Offshore or international web sites allow U.S. citizens (and others) to seek out whatever illegal or illicit information they want, from twenty-four hour online gambling sites that do not require proof of age, to sites that sell child pornography. These examples illustrate the societal risks of unfettered information flow.
### Technological Globalization
Technological globalization is speeded in large part by technological diffusion, the spread of technology across borders. In the last two decades, there has been rapid improvement in the spread of technology to peripheral and semi-peripheral nations, and a 2008 World Bank report discusses both the benefits and ongoing challenges of this diffusion. In general, the report found that technological progress and economic growth rates were linked, and that the rise in technological progress has helped improve the situations of many living in absolute poverty (World Bank 2008). The report recognizes that rural and low-tech products such as corn can benefit from new technological innovations, and that, conversely, technologies like mobile banking can aid those whose rural existence consists of low-tech market vending. In addition, technological advances in areas like mobile phones can lead to competition, lowered prices, and concurrent improvements in related areas such as mobile banking and information sharing.
However, the same patterns of social inequality that create a digital divide in the United States also create digital divides within peripheral and semi-peripheral nations. While the growth of technology use among countries has increased dramatically over the past several decades, the spread of technology within countries is significantly slower among peripheral and semi-peripheral nations. In these countries, far fewer people have the training and skills to take advantage of new technology, let alone access it. Technological access tends to be clustered around urban areas and leaves out vast swaths of peripheral-nation citizens. While the diffusion of information technologies has the potential to resolve many global social problems, it is often the population most in need that is most affected by the digital divide. For example, technology to purify water could save many lives, but the villages in peripheral nations most in need of water purification don’t have access to the technology, the funds to purchase it, or the technological comfort level to introduce it as a solution.
### Summary
Technology drives globalization, but what that means can be hard to decipher. While some economists see technological advances leading to a more level playing field where anyone anywhere can be a global contender, the reality is that opportunity still clusters in geographically advantaged areas. Still, technological diffusion has led to the spread of more and more technology across borders into peripheral and semi-peripheral nations. However, true technological global equality is a long way off.
### Section Quiz
### Short Answer
### Further Research
Check out more in this article about the global digital divide. http://openstax.org/l/Global_Digital_Divide
### References
Acker, Jenny C., and Isaac M. Mbiti. 2010. “Mobile Phones and Economic Development in Africa.” Journal of Economic Perspectives 24(3):207–232. Retrieved January 12, 2012 (pubs.aeaweb.org/doi/pdf/10.1257/jep.24.3.207).
Bagdikian, Ben H. 2004. The New Media Monopoly. Boston, MA: Beacon Press Books.
Bristow, Michael. 2011. “Can China Control Social Media Revolution?” BBC News China, November 2. Retrieved January 14, 2012 (http://www.bbc.co.uk/news/world-asia-pacific-15383756).
Compaine, B. 2005. “Global Media.” Pp. 97-101 in Living in the Information Age: A New Media Reader Belmont: Wadsworth Thomson Learning.
Friedman, Thomas. 2005. The World Is Flat: A Brief History of the Twenty-First Century. New York: Farrar, Straus, and Giroux.
ITU News. 2009. “ITU Telecom World 2009: Special Report: Reflecting New Needs and Realities.” November. Retrieved January 14, 2012 (http://www.itu.int/net/itunews/issues/2009/09/26.aspx).
Jan, Mirza. 2009. “Globalization of Media: Key Issues and Dimensions.” European Journal of Scientific Research 29:66–75.
Katine Chronicles Blog. 2010. “Are Mobile Phones Africa’s Silver Bullet?” The Guardian, January 14. Retrieved January 12, 2012 (http://www.guardian.co.uk/katine/katine-chronicles-blog?page=6).
Ma, Damien. 2011. “2011: When Chinese Social Media Found Its Legs.” The Atlantic, December 18. Retrieved January 15, 2012 (http://www.theatlantic.com/international/archive/2011/12/2011-when-chinese-social-media-found-its-legs/250083/).
McLuhan, Marshall. 1964. Understanding Media: The Extensions of Man. New York: McGraw-Hill.
Pierson, David. 2012. “Number of Web Users in China Hits 513 Million.” Los Angeles Times, January 16. Retrieved January 16, 2012 (http://latimesblogs.latimes.com/technology/2012/01/chinese-web-users-grow-to-513-million.html).
The World Bank. 2008. “Global Economic Prospects 2008: Technology Diffusion in the Developing World.” World Bank. Retrieved January 24, 2012 (http://siteresources.worldbank.org/INTGEP2008/Resources/GEP_ove_001-016.pdf). |
# Media and Technology
## Theoretical Perspectives on Media and Technology
It is difficult to conceive of any one theory or theoretical perspective that can explain the variety of ways in which people interact with technology and the media. Technology runs the gamut from the match you strike to light a candle all the way up to sophisticated nuclear power plants that might power the factory where that candle was made. Media could refer to the television you watch, the ads wrapping the bus you take to work or school, or the magazines you flip through in a dentist's waiting room, not to mention all the forms of new media, including Instagram, Facebook, blogs, YouTube, and the like. Are media and technology critical to the forward march of humanity? Are they pernicious capitalist tools that lead to the exploitation of workers worldwide? Are they the magic bullet the world has been waiting for to level the playing field and raise the world’s poor out of extreme poverty? Choose any opinion and you will find studies and scholars who agree with you––and those who disagree.
### Functionalism
Because functionalism focuses on how media and technology contribute to the smooth functioning of society, a good place to begin understanding this perspective is to write a list of functions you perceive media and technology to perform. Your list might include the ability to find information on the Internet, television’s entertainment value, or how advertising and product placement contribute to social norms.
### Commercial Function
As you might guess, with nearly every U.S. household possessing a television, and the 250 billion hours of television watched annually by people in the United States, companies that wish to connect with consumers find television an irresistible platform to promote their goods and services (Nielsen 2012). Television advertising is a highly functional way to meet a market demographic where it lives. Sponsors can use the sophisticated data gathered by network and cable television companies regarding their viewers and target their advertising accordingly. Whether you are watching cartoons on Nick Jr. or a cooking show on Telemundo, chances are advertisers have a plan to reach you.
And it certainly doesn’t stop with television. Commercial advertising precedes movies in theaters and shows up on and inside public transportation, as well as on the sides of building and roadways. Major corporations such as Coca-Cola bring their advertising into public schools, by sponsoring sports fields or tournaments, as well as filling the halls and cafeterias of those schools with vending machines hawking their goods. With rising concerns about childhood obesity and attendant diseases, the era of soda machines in schools may be numbered. In fact, as part of the United States Department of Agriculture's Healthy, Hunger Free Kids Act and Michelle Obama's Let's Move! Initiative, a ban on junk food in school began in July 2014.
### Entertainment Function
An obvious manifest function of media is its entertainment value. Most people, when asked why they watch television or go to the movies, would answer that they enjoy it. And the numbers certainly illustrate that. While 2012 Nielsen research shows a slight reduction of U.S. homes with televisions, the reach of television is still vast. And the amount of time spent watching is equally large. Clearly, enjoyment is paramount. On the technology side, as well, there is a clear entertainment factor to the use of new innovations. From online gaming to chatting with friends on Facebook, technology offers new and more exciting ways for people to entertain themselves.
### Social Norm Functions
Even while the media is selling us goods and entertaining us, it also serves to socialize us, helping us pass along norms, values, and beliefs to the next generation. In fact, we are socialized and resocialized by media throughout our whole lives. All forms of media teach us what is good and desirable, how we should speak, how we should behave, and how we should react to events. Media also provide us with cultural touchstones during events of national significance. How many of your older relatives can recall watching the explosion of the space shuttle Challenger on television? How many of those reading this textbook followed the events of September 11 or Hurricane Katrina on television or the Internet?
Just as in Anderson and Bushman's (2011) evidence in the Violence in Media and Video Games: Does It Matter? feature, debate still exists over the extent and impact of media socialization. One recent study (Krahe et al. 2011) demonstrated that violent media content does have a desensitizing affect and is correlated with aggressive thoughts. Another group of scholars (Gentile, Mathieson, and Crick 2011) found that among children exposure to media violence led to an increase in both physical and relational aggression. Yet, a meta-analysis study covering four decades of research (Savage 2003) could not establish a definitive link between viewing violence and committing criminal violence.
It is clear from watching people emulate the styles of dress and talk that appear in media that media has a socializing influence. What is not clear, despite nearly fifty years of empirical research, is how much socializing influence the media has when compared to other agents of socialization, which include any social institution that passes along norms, values, and beliefs (such as peers, family, religious institutions, and the like).
### Life-Changing Functions
Like media, many forms of technology do indeed entertain us, provide a venue for commercialization, and socialize us. For example, some studies suggest the rising obesity rate is correlated with the decrease in physical activity caused by an increase in use of some forms of technology, a latent function of the prevalence of media in society (Kautiainen et al. 2011). Without a doubt, a manifest function of technology is to change our lives, sometimes for the better and sometimes for the worse. Think of how the digital age has improved the ways we communicate. Have you ever used Skype or another webcast to talk to a friend or family member far away? Or maybe you have organized a fund drive, raising thousands of dollars, all from your desk chair.
Of course, the downside to this ongoing information flow is the near impossibility of disconnecting from technology that leads to an expectation of constant convenient access to information and people. Such a fast-paced dynamic is not always to our benefit. Some sociologists assert that this level of media exposure leads to narcotizing dysfunction, a result in which people are too overwhelmed with media input to really care about the issue, so their involvement becomes defined by awareness instead of by action (Lazerfeld and Merton 1948).
### Conflict Perspective
In contrast to theories in the functional perspective, the conflict perspective focuses on the creation and reproduction of inequality—social processes that tend to disrupt society rather than contribute to its smooth operation. When we take a conflict perspective, one major focus is the differential access to media and technology embodied in the digital divide. Conflict theorists also look at who controls the media, and how media promotes the norms of upper-middle-class White people in the United States while minimizing the presence of the working class, especially people of color.
### Control of Media and Technology
Powerful individuals and social institutions have a great deal of influence over which forms of technology are released, when and where they are released, and what kind of media is available for our consumption, which is a form of gatekeeping. Shoemaker and Vos (2009) define gatekeeping as the sorting process by which thousands of possible messages are shaped into a mass media-appropriate form and reduced to a manageable amount. In other words, the people in charge of the media decide what the public is exposed to, which, as C. Wright Mills (1956) famously noted, is the heart of media’s power. Take a moment to think of the way “new media” evolve and replace traditional forms of hegemonic media. With hegemonic media, a culturally diverse society can be dominated by one race, gender, or class that manipulates the media to impose its worldview as a societal norm. New media weakens the gatekeeper role in information distribution. Popular sites such as YouTube and Facebook not only allow more people to freely share information but also engage in a form of self-policing. Users are encouraged to report inappropriate behavior that moderators will then address.
In addition, some conflict theorists suggest that the way U.S. media are generated results in an unbalanced political arena. Those with the most money can buy the most media exposure, run smear campaigns against their competitors, and maximize their visual presence. Almost a year before the 2012 U.S. presidential election, the candidates––Barack Obama for the Democrats and numerous Republican contenders––had raised more than $186 million (Carmi et al. 2012). Some would say that the Citizens United vs. Federal Election Committee is a major contributing factor to our unbalanced political arena. In Citizens United, the Supreme Court affirmed the right of outside groups, including Super Political Action Committees (SuperPACs) with undisclosed donor lists, to spend unlimited amounts of money on political ads as long as they don't coordinate with the candidate's campaign or specifically advocate for a candidate. What do you think a conflict perspective theorist would suggest about the potential for the non-rich to be heard in politics, especially when SuperPACs ensure that the richest groups have the most say?
### Technological Social Control and Digital Surveillance
Social scientists take the idea of the surveillance society so seriously that there is an entire journal devoted to its study, Surveillance and Society. The panoptic surveillance envisioned by Jeremy Bentham, depicted in the form of an all-powerful, all-seeing government by George Orwell in 1984, and later analyzed by Michel Foucault (1975) is increasingly realized in the form of technology used to monitor our every move. This surveillance was imagined as a form of constant monitoring in which the observation posts are decentralized and the observed is never communicated with directly. Today, digital security cameras capture our movements, observers can track us through our cell phones, and police forces around the world use facial-recognition software.
### Feminist Perspective
Take a look at popular television shows, advertising campaigns, and online game sites. In most, women are portrayed in a particular set of parameters and tend to have a uniform look that society recognizes as attractive. Most are thin, White or light-skinned, beautiful, and young. Why does this matter? Feminist perspective theorists believe this idealized image is crucial in creating and reinforcing stereotypes. For example, Fox and Bailenson (2009) found that online female avatars conforming to gender stereotypes enhance negative attitudes toward women, and Brasted (2010) found that media (advertising in particular) promotes gender stereotypes. As early as 1990, Ms. magazine instituted a policy to publish without any commercial advertising.
The gender gap in tech-related fields (science, technology, engineering, and math) is no secret. A 2011 U.S. Department of Commerce Report suggested that gender stereotyping is one reason for this gap which acknowledges the bias toward men as keepers of technological knowledge (US Department of Commerce 2011). But gender stereotypes go far beyond the use of technology. Press coverage in the media reinforces stereotypes that subordinate women; it gives airtime to looks over skills, and coverage disparages women who defy accepted norms.
Recent research in new media has offered a mixed picture of its potential to equalize the status of men and women in the arenas of technology and public discourse. A European agency, the Advisory Committee on Equal Opportunities for Men and Women (2010), issued an opinion report suggesting that while there is the potential for new media forms to perpetuate gender stereotypes and the gender gap in technology and media access, at the same time new media could offer alternative forums for feminist groups and the exchange of feminist ideas. Still, the committee warned against the relatively unregulated environment of new media and the potential for antifeminist activities, from pornography to human trafficking, to flourish there.
Increasingly prominent in the discussion of new media and feminism is cyberfeminism, the application to, and promotion of, feminism online. Research on cyberfeminism runs the gamut from the liberating use of blogs by women living in Iraq during the second Gulf War (Peirce 2011) to an investigation of the Suicide Girls web site (Magnet 2007).
### Symbolic Interactionism
Technology itself may act as a symbol for many. The kind of computer you own, the kind of car you drive, your ability to afford the latest Apple product—these serve as a social indicator of wealth and status. Neo-Luddites are people who see technology as symbolizing the coldness and alienation of modern life. But for technophiles, technology symbolizes the potential for a brighter future. For those adopting an ideological middle ground, technology might symbolize status (in the form of a massive flat-screen television) or failure (ownership of a basic old mobile phone with no bells or whistles).
### Social Construction of Reality
Meanwhile, media create and spread symbols that become the basis for our shared understanding of society. Theorists working in the interactionist perspective focus on this social construction of reality, an ongoing process in which people subjectively create and understand reality. Media constructs our reality in a number of ways. For some, the people they watch on a screen can become a primary group, meaning the small informal groups of people who are closest to them. For many others, media becomes a reference group: a group that influences an individual and to which an individual compares himself or herself, and by which we judge our successes and failures. We might do very well without the latest smartphone, until we see characters using it on our favorite television show or our classmates whipping it out between classes.
While media may indeed be the medium to spread the message of rich White men, Gamson, Croteau, Hoynes, and Sasson (1992) point out that some forms of media discourse allow competing constructions of reality to appear. For example, advertisers find new and creative ways to sell us products we don’t need and probably wouldn’t want without their prompting, but some networking sites such as Freecycle offer a commercial-free way of requesting and trading items that would otherwise be discarded. The web is also full of blogs chronicling lives lived “off the grid,” or without participation in the commercial economy.
### Social Networking and Social Construction
While Tumblr and Facebook encourage us to check in and provide details of our day through online social networks, corporations can just as easily promote their products on these sites. Even supposedly crowd-sourced sites like Yelp (which aggregates local reviews) are not immune to corporate shenanigans. That is, we think we are reading objective observations when in reality we may be buying into one more form of advertising.
Facebook, which started as a free social network for college students, is increasingly a monetized business, selling you goods and services in subtle ways. But chances are you don’t think of Facebook as one big online advertisement. What started out as a symbol of coolness and insider status, unavailable to parents and corporate shills, now promotes consumerism in the form of games and fandom. For example, think of all the money spent to upgrade popular Facebook games like Candy Crush. And notice that whenever you become a “fan,” you likely receive product updates and special deals that promote online and real-world consumerism. It is unlikely that millions of people want to be “friends” with Pampers. But if it means a weekly coupon, they will, in essence, rent out space on their Facebook pages for Pampers to appear. Thus, we develop both new ways to spend money and brand loyalties that will last even after Facebook is considered outdated and obsolete.
### Summary
There are myriad theories about how society, technology, and media will progress. Functionalism sees the contribution that technology and media provide to the stability of society, from facilitating leisure time to increasing productivity. Conflict theorists are more concerned with how technology reinforces inequalities among communities, both within and among countries. They also look at how media typically give voice to the most powerful, and how new media might offer tools to help those who are disenfranchised. Symbolic interactionists see the symbolic uses of technology as signs of everything from a sterile futuristic world to a successful professional life.
### Section Quiz
### Short Answer
### Further Research
To learn more about cyberfeminism, check out the interdisciplinary artist collective, subRosa.
To explore the implications of panoptic surveillance, review some surveillance studies at the free, open source Surveillance and Society site.
Read an example of socialist media from .
### References
A. Taute, H., & Sierra, J. (2014). Brand tribalism: an anthropological perspective. Journal of Product & Brand Management, 23(1), 2–15. http://doi.org/10.1108/JPBM-06-2013-0340
BBC News. 2019. “United States Profile--Media.” (https://www.bbc.com/news/world-us-canada-16757497)
Brasted, Monica. 2010. “Care Bears vs. Transformers: Gender Stereotypes in Advertisements.” Retrieved January 10, 2012 (http://www.sociology.org/media-studies/care-bears-vs-transformers-gender-stereotypes-in-advertisements).
Carmi, Evan, Matthew Ericson, David Nolen, Kevin Quealy, Michael Strickland, Jeremy White, and Derek Willis. 2012. “The 2012 Money Race: Compare the Candidates.” New York Times. Retrieved January 15, 2012 (http://elections.nytimes.com/2012/campaign-finance).
Foucault, Michel. 1975. Discipline and Punish: The Birth of the Prison. New York: Vintage Books.
Fox, Jesse, and Jeremy Bailenson. 2009. “Virtual Virgins and Vamps: The Effects of Exposure to Female Characters’ Sexualized Appearance and Gaze in an Immersive Virtual Environment.” Sex Roles 61:147–157.
Gamson, William, David Croteau, William Hoynes, and Theodore Sasson. 1992. “Media Images and the Social Construction of Reality.” Annual Review of Sociology 18:373–393.
Gentile, Douglas, Lindsay Mathieson, and Nikki Crick. 2011. “Media Violence Associations with the Form and Function of Aggression among Elementary School Children.” Social Development 20:213–232.
Kautiainen, S., L. Koivusilta, T. Lintonen, S. M. Virtanen, and A. Rimpelä. 2005. “Use of Information and Communication Technology and Prevalence of Overweight and Obesity Among Adolescents.” International Journal of Obesity 29:925–933
Krahe, Barbara, Ingrid Moller, L. Huesmann, Lucyna Kirwil, Julianec Felber, and Anja Berger. 2011. “Desensitization to Media Violence: Links With Habitual Media Violence
Exposure, Aggressive Cognitions, and Aggressive Behavior.” Journal of Personality and Social Psychology 100:630–646.
Lazerfeld, Paul F. and Robert K. Merton. 1948. “Mass Communication, Popular Taste, and Organized Social Action.” The Communication of Ideas. New York: Harper & Bros.
Magnet, Shoshana. 2007. “Feminist Sexualities, Race, and The Internet: An Investigation of suicidegirls.com.” New Media & Society 9:577-602.
Mills, C. Wright. 2000 [1956]. The Power Elite. New York: Oxford University Press.
NielsenWire. 2011. “Nielsen Estimates Number of U.S. Television Homes to be 114.7 Million.” May 3. Retrieved January 15, 2012 (http://blog.nielsen.com/nielsenwire/media_entertainment/nielsen-estimates-number-of-u-s-television-homes-to-be-114-7-million/).
Pierce, Tess. 2011. “Singing at the Digital Well: Blogs as Cyberfeminist Sites of Resistance.” Feminist Formations 23:196–209.
Savage, Joanne. 2003. “Does Viewing Violent Media Really Cause Criminal Violence? A Methodological Review.” Aggression and Violent Behavior 10:99–128.
Shoemaker, Pamela and Tim Vos. 2009. “Media Gatekeeping.” Pp. 75–89 in An Integrated Approach to Communication Theory and Research, 2nd ed., edited by D. Stacks and M. Salwen. New York: Routledge.
U.S. Department of Commerce. 2011. “Women in STEM: A Gender Gap to Innovation.” August. Retrieved February 22, 2012 (http://www.esa.doc.gov/sites/default/files/reports/documents/womeninstemagaptoinnovation8311.pdf/). |
# Social Stratification in the United States
## Introduction
Jarrett grew up on a farm in rural Ohio, left home to serve in the Army, and returned a few years later to take over the family farm. He moved into his family house, and eighteen months later married Eric, with whom he had maintained a long-distance relationship for several years. Eric had two children from a previous marriage. They quickly realized the income from the farm was no longer sufficient to meet their needs. Jarrett, with little experience beyond the farm, took on a job at a grocery store to supplement his income. This part-time job shifted the direction of their family’s life.
One of the managers at the store liked Jarrett, his attitude, and his work ethic. He began to groom Jarrett for advancement at the store, and encouraged him to take a few classes at a local college. Despite knowing he'd receive financial support from the military, this was the first time Jarrett had seriously thought about college. Could he be successful, Jarrett wondered? Could he actually become the first in his family to earn a degree? Fortunately, Eric also believed in him. Jarrett kept his college enrollment a secret from his mother, his brothers, and his friends. He did not want others to know about it, in case he failed.
Jarrett was nervous on his first day of class. He was older than the other students, and he had never considered himself college material. When he earned only a C- on his first test, he thought his fears were being realized, and that it was perhaps not a fit for him. But his instructor strongly recommended that Jarrett pay a visit to the academic success center. After a few sessions, he utilized a better study schedule and got a B- on the next exam. He was successful in that class, and enrolled in two more the next semester.
Unfortunately, life took a difficult turn when Jarrett's and Eric's daughter became ill; he couldn't focus on his studies and he dropped all of his classes. With his momentum slowed, Jarrett wasn't sure he was ready to resume after his daughter recovered. His daughter, though, set him straight. One day after telling her to start her homework, she was reluctant and said, "You're not doing your homework anymore; I shouldn’t have to do mine." A bit annoyed, Jarrett and Eric explained the difference between being an adult with work and family obligations and being a child in middle school. But Jarrett realized he was most upset at himself for using her illness as an excuse. He thought he wasn't living up to the example he wanted to set for her. The next day, he called his academic advisor and re-enrolled.
Just under two years later, Jarrett was walking across the stage to receive a Bachelor’s degree with a special certificate for peer support. The ceremony seemed surreal to Jarrett. He'd earned medals and other recognition in the military, but he always felt those accomplishments were shared among his team. While he'd had a lot of help with college, he felt that graduating was a milestone that was more closely tied to himself.
Stories like this permeate American society and may sound familiar, yet this quest to achieve the American Dream is often hard for many Americans to achieve, even with hard work. After all, nearly one in three first-year college students is a first-generation college student and many are not as successful as Jarrett. According to the Center for Student Opportunity, a national nonprofit, 89% of first-generation students will not earn an undergraduate degree within six years of starting their studies. In fact, these students “drop out of college at four times the rate of peers whose parents have postsecondary degrees” (Center for Student Opportunity quoted in Huot 2014).
Why do students with parents who have completed college tend to graduate more often than those students whose parents do not hold degrees? That question and many others will be answered as we explore social stratification.
### References
Huot, Anne E. 2014. "A Commitment to Making College Accessible to First-Generation College Students." Huffington Post. Retrieved March 25, 2021 from https://www.huffpost.com/entry/first-generation-college-students_b_6081958. -s. |
# Social Stratification in the United States
## What Is Social Stratification?
Sociologists use the term social stratification to describe the system of social standing. Social stratification refers to a society’s categorization of its people into rankings based on factors like wealth, income, education, family background, and power.
Geologists also use the word “stratification” to describe the distinct vertical layers found in rock. Typically, society’s layers, made of people, represent the uneven distribution of society’s resources. Society views the people with more resources as the top layer of the social structure of stratification. Other groups of people, with fewer and fewer resources, represent the lower layers. An individual’s place within this stratification is called socioeconomic status (SES).
Most people and institutions in the United States indicate that they value equality, a belief that everyone has an equal chance at success. In other words, hard work and talent—not inherited wealth, prejudicial treatment, institutional racism, or societal values—determine social mobility. This emphasis on choice, motivation, and self-effort perpetuates the American belief that people control their own social standing.
However, sociologists recognize social stratification as a society-wide system that makes inequalities apparent. While inequalities exist between individuals, sociologists are interested in larger social patterns. Sociologists look to see if individuals with similar backgrounds, group memberships, identities, and location in the country share the same social stratification. No individual, rich or poor, can be blamed for social inequalities, but instead all participate in a system where some rise and others fall. Most Americans believe the rising and falling is based on individual choices. But sociologists see how the structure of society affects a person's social standing and therefore is created and supported by society.
Factors that define stratification vary in different societies. In most societies, stratification is an economic system, based on wealth, the net value of money and assets a person has, and income, a person’s wages or investment dividends. While people are regularly categorized based on how rich or poor they are, other important factors influence social standing. For example, in some cultures, prestige is valued, and people who have them are revered more than those who don’t. In some cultures, the elderly are esteemed, while in others, the elderly are disparaged or overlooked. Societies’ cultural beliefs often reinforce stratification.
One key determinant of social standing is our parents. Parents tend to pass their social position on to their children. People inherit not only social standing but also the cultural norms, values, and beliefs that accompany a certain lifestyle. They share these with a network of friends and family members that provide resources and support. This is one of the reasons first-generation college students do not fare as well as other students. They lack access to the resources and support commonly provided to those whose parents have gone to college.
Other determinants are found in a society’s occupational structure. Teachers, for example, often have high levels of education but receive relatively low pay. Many believe that teaching is a noble profession, so teachers should do their jobs for love of their profession and the good of their students—not for money. Yet, the same attitude is not applied to professional athletes, executives, or those working in corporate world. Cultural attitudes and beliefs like these support and perpetuate social and economic inequalities.
### Systems of Stratification
Sociologists distinguish between two types of systems of stratification. Closed systems accommodate little change in social position. They do not allow people to shift levels and do not permit social relationships between levels. Closed systems include estate, slavery, and caste systems. Open systems are based on achievement and allow for movement and interaction between layers and classes. How different systems operate reflect, emphasize, and foster specific cultural values, shaping individual beliefs. In this section, we’ll review class and caste stratification systems, plus discuss the ideal system of meritocracy.
### The Caste System
Caste systems are closed stratification systems where people can do little or nothing to change the social standing of their birth. The caste system determines all aspects of an individual’s life: occupations, marriage partners, and housing. Individual talents, interests, or potential do not provide opportunities to improve a person's social position.
In the Hindu caste tradition, people expect to work in an occupation and to enter into a marriage based on their caste. Accepting this social standing is considered a moral duty and people are socialized to accept their social standing. Cultural values reinforced the system. Caste systems promote beliefs in fate, destiny, and the will of a higher power, rather than promoting individual freedom as a value. This belief system is an ideology. Every culture has an ideology that supports its system of stratification.
The caste system in India has been officially dismantled, but is still deeply embedded in Indian society, particularly in rural areas. In India’s larger cities, people now have more opportunities to choose their own career paths and marriage partners. As a global center of employment, corporations have introduced merit-based hiring and employment to the nation shifting the cultural expectations of the caste system.
### The Class System
A class system is based on both social factors and individual achievement. A class consists of a set of people who share similar status based on factors like wealth, income, education, family background, and occupation. Unlike caste systems, class systems are open. People may move to a different level (vertical movement) of education or employment status than their parents. Though family and other societal models help guide a person toward a career, personal choice and opportunity play a role.
They can also socialize with and marry members of other classes. People have the option to form an exogamous marriage, a union of spouses from different social categories. Exogamous marriages often focus on values such as love and compatibility. Though social conformities still exist that encourage people to choose partners within their own class, called an endogamous marriage, people are not as pressured to choose marriage partners based solely on their social location.
### Meritocracy
Meritocracy is a hypothetical system in which social stratification is determined by personal effort and merit. The concept of meritocracy is an ideal because no society has ever existed where social standing was based entirely on merit. Rather, multiple factors influence social standing, including processes like socialization and the realities of inequality within economic systems. While a meritocracy has never existed, sociologists see aspects of meritocracies in modern societies when they study the role of academic and job performance and the systems in place for evaluating and rewarding achievement in these areas.
The differences between an open and closed system are explored further in the example below.
### Status Consistency
Sociologists use the term status consistency to describe the consistency, or lack thereof, of an individual’s rank across the factors that determine social stratification within a lifetime. Caste systems correlate with high status consistency, due to the inability to move out of a class, whereas the more flexible class system demonstrates lower status consistency.
To illustrate, let’s consider Serena. Serena earned her high school diploma but did not go to college. Completing high school but not college is a trait more common to the lower-middle class. After high school, she began landscaping, which, as manual labor, tracks with lower-middle class or even lower class. However, over time, Serena started her own company. She hired employees. She won larger contracts. Serena became a business owner and earned more money. Those traits represent the upper-middle class. Inconsistencies between Serena’s educational level, her occupation, and income show Serena’s flexibility in her social status, giving her low status consistency. In a class system, hard work, new opportunities, coupled with a lower education status still allow a person movement into middle or upper class, whereas in a caste system, that would not be possible. In a class system, low status consistency correlates with having more choices and opportunities.
### Summary
Stratification systems, where people are ranked based on their wealth, power, and status within society, are either closed, meaning they allow little change in social position, or open, meaning they allow movement and interaction between the layers. A caste system is one in which social standing is based on ascribed status or birth. Class systems are open, with achievement playing a role in social position. People fall into classes based on factors like wealth, income, education, and occupation. A meritocracy is an ideal system of social stratification that confers standing based on solely on personal worth, rewarding effort. A pure meritocracy has never existed. Stratification is reinforced and shaped by cultural beliefs and values, called an ideology.
### Section Quiz
### Short Answer
### Further Research
The New Press provides an interactive helpful in exploring social stratification. Within the relatively straightforward graphic activity, you can select two demographic categories and illustrate the quantity those populations by income level.
### References
Köhler, Nicholas. 2010. “An Uncommon Princess.” Maclean’s, November 22. Retrieved March 25, 2021 from https://www.macleans.ca/news/world/an-uncommon-princess/.
McKee, Victoria. 1996. “Blue Blood and the Color of Money.” New York Times, June 9.
Marquand, Robert. 2011. “What Kate Middleton’s Wedding to Prince William Could Do for Britain.” Christian Science Monitor, April 15. Retrieved January 9, 2012 (http://www.csmonitor.com/World/Europe/2011/0415/What-Kate-Middleton-s-wedding-to-Prince-William-could-do-for-Britain).
Wong, Grace. 2011. "Kate Middleton: A Family Business That Built a Princess." CNN Money. Retrieved December 22, 2014 (http://money.cnn.com/2011/04/14/smallbusiness/kate-middleton-party-pieces/). |
# Social Stratification in the United States
## Social Stratification and Mobility in the United States
How does social stratification affect your ability to move up or down the social classes? What is a standard of living? What factors matter in rising up or becoming more successful in the eyes of those around you? Does being in a social class dictate your style, behavior, or opportunities?
### Social Classes in the United States
For sociologists, categorizing social class is a fluid science. Sociologists generally identify three levels of class in the United States: upper, middle, and lower class. Within each class, there are many subcategories. Wealth is the most significant way of distinguishing classes, because wealth can be transferred to one’s children and perpetuate the class structure. One economist, J.D. Foster, defines the 20 percent of U.S. citizens’ highest earners as “upper income,” and the lower 20 percent as “lower income.” The remaining 60 percent of the population make up the middle class (Mason 2010). With that distinction, economists can describe the range in annual household incomes for the middle-class, but they cannot show how the range of all incomes vary and how they change over time. For this reason, the Pew Center defines classes based on the median household income. The lower class includes those whose income is two-thirds of the national median, the middle class includes those whose income falls between two-thirds and twice the median, and the upper class includes those whose income is above twice the national median (Kochhar 2015). Though median income levels vary from state to state, at the national level you would be considered in the middle-class if you earned between $48,500 to $145,500 in 2018 U.S. dollars (Bennett 2000).
One sociological perspective distinguishes the classes, in part, according to their relative power and control over their lives. Members of the upper class not only have power and control over their own lives, but their social status gives them power and control over others’ lives. The middle class doesn’t generally control other strata of society, but its members do exert control over their own lives. In contrast, the lower class has little control over their work or lives. Below, we will explore the major divisions of U.S. social class and their key subcategories.
### Upper Class
The upper class is considered the top, and only the powerful elite get to see the view from there. In the United States, people with extreme wealth make up one percent of the population, and they own roughly one-third of the country’s wealth (Beeghley 2008).
Money provides not just access to material goods, but also access to a lot of power. As corporate leaders, members of the upper class make decisions that affect the job status of millions of people. As media owners, they influence the collective identity of the nation. They run the major network television stations, radio broadcasts, newspapers, magazines, publishing houses, and sports franchises. As board members of the most influential colleges and universities, they influence cultural attitudes and values. As philanthropists, they establish foundations to support social causes they believe in. As campaign contributors and legislation drivers, they fund political campaigns to sway policymakers, sometimes to protect their own economic interests and at other times to support or promote a cause. (The methods, effectiveness, and impact of these political efforts are discussed in the Politics and Government chapter.)
U.S. society has historically distinguished between “old money” (inherited wealth passed from one generation to the next) and “new money” (wealth you have earned and built yourself). While both types may have equal net worth, they have traditionally held different social standings. People of old money, firmly situated in the upper class for generations, have held high prestige. Their families have socialized them to know the customs, norms, and expectations that come with wealth. Often, the very wealthy don’t work for wages. Some study business or become lawyers in order to manage the family fortune. Others, such as Paris Hilton and Kim Kardashian, capitalize on being a rich socialite and transform that into celebrity status, flaunting a wealthy lifestyle.
However, new-money members of the upper class are not oriented to the customs and mores of the elite. They haven’t gone to the most exclusive schools. They have not established old-money social ties. People with new money might flaunt their wealth, buying sports cars and mansions, but they might still exhibit behaviors attributed to the middle and lower classes.
### The Middle Class
Many people consider themselves middle class, but there are differing ideas about what that means. People with annual incomes of $150,000 call themselves middle class, as do people who annually earn $30,000. That helps explain why, in the United States, the middle class is broken into upper and lower subcategories.
Lower-middle class members tend to complete a two-year associate’s degrees from community or technical colleges or a four-year bachelor’s degree. Upper-middle class people tend to continue on to postgraduate degrees. They’ve studied subjects such as business, management, law, or medicine.
Middle-class people work hard and live fairly comfortable lives. Upper-middle-class people tend to pursue careers, own their homes, and travel on vacation. Their children receive high-quality education and healthcare (Gilbert 2010). Parents can support more specialized needs and interests of their children, such as more extensive tutoring, arts lessons, and athletic efforts, which can lead to more social mobility for the next generation. Families within the middle class may have access to some wealth, but also must work for an income to maintain this lifestyle.
In the lower middle class, people hold jobs supervised by members of the upper middle class. They fill technical, lower- level management or administrative support positions. Compared to lower-class work, lower-middle-class jobs carry more prestige and come with slightly higher paychecks. With these incomes, people can afford a decent, mainstream lifestyle, but they struggle to maintain it. They generally don’t have enough income to build significant savings. In addition, their grip on class status is more precarious than those in the upper tiers of the class system. When companies need to save money, lower-middle class people are often the ones to lose their jobs.
### The Lower Class
The lower class is also referred to as the working class. Just like the middle and upper classes, the lower class can be divided into subsets: the working class, the working poor, and the underclass. Compared to the lower middle class, people from the lower economic class have less formal education and earn smaller incomes. They work jobs that require less training or experience than middle-class occupations and often do routine tasks under close supervision.
Working-class people, the highest subcategory of the lower class, often land steady jobs. The work is hands-on and often physically demanding, such as landscaping, cooking, cleaning, or building.
Beneath the working class is the working poor. They have unskilled, low-paying employment. However, their jobs rarely offer benefits such as healthcare or retirement planning, and their positions are often seasonal or temporary. They work as migrant farm workers, housecleaners, and day laborers. Education is limited. Some lack a high school diploma.
How can people work full-time and still be poor? Even working full-time, millions of the working poor earn incomes too meager to support a family. The government requires employers pay a minimum wage that varies from state to state, and often leave individuals and families below the poverty line. In addition to low wages, the value of the wage has not kept pace with inflation. “The real value of the federal minimum wage has dropped 17% since 2009 and 31% since 1968 (Cooper, Gould, & Zipperer, 2019). Furthermore, the living wage, the amount necessary to meet minimum standards, differs across the country because the cost of living differs. Therefore, the amount of income necessary to survive in an area such as New York City differs dramatically from small town in Oklahoma (Glasmeier, 2020).
The underclass is the United States’ lowest tier. The term itself and its classification of people have been questioned, and some prominent sociologists (including a former president of the American Sociological Association), believe its use is either overgeneralizing or incorrect (Gans 1991). But many economists, sociologists government agencies, and advocacy groups recognize the growth of the underclass. Members of the underclass live mainly in inner cities. Many are unemployed or underemployed. Those who do hold jobs typically perform menial tasks for little pay. Some of the underclass are homeless. Many rely on welfare systems to provide food, medical care, and housing assistance, which often does not cover all their basic needs. The underclass have more stress, poorer health, and suffer crises fairly regularly.
### Class Traits
Does a person’s appearance indicate class? Can you tell a person’s education level based on their clothing? Do you know a person’s income by the car they drive? Class traits, also called class markers, are the typical behaviors, customs, and norms that define each class. Class traits indicate the level of exposure a person has to a wide range of cultures. Class traits also indicate the amount of resources a person has to spend on items like hobbies, vacations, and leisure activities.
People may associate the upper class with enjoyment of costly, refined, or highly cultivated tastes—expensive clothing, luxury cars, high-end fund-raisers, and frequent or expensive vacations. People may also believe that the middle and lower classes are more likely to enjoy camping, fishing, or hunting, shopping at large retailers, and participating in community activities. While these descriptions may identify class traits, they are stereotypes. Moreover, just as class distinctions have blurred in recent decades, so too have class traits. A factory worker could be a skilled French cook. A billionaire might dress in ripped jeans, and a low-income student might own designer shoes.
For famous wealthy people, making choices that do not seem to align with their economic status can often lead to public commentary. Jennifer Lopez being spotted in a dress that cost less than $30 and Zac Efron shopping at thrift stores have made the news. Others, like Halle Berry and Keanu Reeves, are known for frequent use of public transportation and relatively modest living (at least when considering to their net worth). When questioned, most point to nothing more than practicality. Lady Gaga tweeted " why do people look at me like I'm crazy when i use coupons at grocery or try bargaining at retail..." (2012). And in dense, crowded cities such as Washington, Chicago, and New York, riding the trains is often faster and easier than taking a car.
### Social Mobility
People are often inspired and amazed at people's ability to overcome extremely difficult upbringings. Mariano Rivera, acknowledged to be the best relief pitcher in history, made a baseball glove out of cardboard and tape because his family could not afford a real one. Alice Coachman grew up with few resources and was denied access to training facilities because of her race; she ran barefoot and built her own high jump equipment before becoming the first Black athlete (and one of the first American track and field athletes) to win an Olympic Gold. Pelé, perhaps the most transformative figure in soccer, learned the game while using a rag-stuffed sock for a ball. These are some of the stories told in documentaries or biographies meant to inspire and share the challenges of unequal upbringings. Relative to the overall population, the number of people who rise from poverty to become very successful is small, and the number that become wealthy is even smaller. Systemic barriers like unequal education, discrimination, and lack of opportunity can slow or diminish one's ability to move up. Still, people who earn a college degree, get a job promotion, or marry someone with a good income may move up socially.
Social mobility refers to the ability of individuals to change positions within a social stratification system. When people improve or diminish their economic status in a way that affects social class, they experience social mobility. Individuals can experience upward or downward social mobility for a variety of reasons. Upward mobility refers to an increase—or upward shift—when they move from a lower to a higher socioeconomical class. In contrast, individuals experience downward mobility when they move from higher socioeconomic class to a lower one. Some people move downward because of business setbacks, unemployment, or illness. Dropping out of school, losing a job, or getting a divorce may result in a loss of income or status and, therefore, downward social mobility.
It is not uncommon for different generations of a family to belong to varying social classes. This is known as intergenerational mobility. For example, an upper-class executive may have parents who belonged to the middle class. In turn, those parents may have been raised in the lower class. Patterns of intergenerational mobility can reflect long-term societal changes.
On the other hand, intragenerational mobility refers to changes in a person's social mobility over the course of their lifetime. For example, the wealth and prestige experienced by one person may be quite different from that of their siblings.
Structural mobility happens when societal changes enable a whole group of people to move up or down the social class ladder. Structural mobility is attributable to changes in society as a whole. In the first half of the twentieth century, industrialization expanded the U.S. economy, raising the standard of living and leading to upward structural mobility for almost everyone. In the decade and a half of the twenty-first century, recessions and the outsourcing of jobs overseas have contributed to the withdrawal of Americans from the workforce (BLS 2021). Many people experienced economic setbacks, creating a wave of downward structural mobility.
When analyzing the trends and movements in social mobility, sociologists consider all modes of mobility. Scholars recognize that mobility is not as common or easy to achieve as many people think.
### Stratification of Socioeconomic Classes
In the last century, the United States has seen a steady rise in its standard of living, the level of wealth available to acquire the material necessities and comforts to maintain a specific lifestyle. The country’s standard of living is based on factors such as income, employment, class, literacy rates, mortality rates, poverty rates, and housing affordability. A country with a high standard of living will often reflect a high quality of life, which in the United States means residents can afford a home, own a car, and take vacations. Ultimately, standard of living is shaped by the wealth and distribution of wealth in a country and the expectations its citizens have for their lifestyle.
Wealth is not evenly distributed in most countries. In the United States, a small portion of the population has the means to the highest standard of living. The wealthiest one percent of the population holds one-third of our nation’s wealth while the bottom 50 percent of Americans hold only 2 percent. Those in-between, the top 50 to 90 percent hold almost two-thirds of the nation’s wealth (The Federal Reserve, 2021).
Many people think of the United States as a “middle-class society.” They think a few people are rich, a few are poor, and most are fairly well off, existing in the middle of the social strata. Rising from lower classes into the middle-class is to achieve the American Dream. For this reason, scholars are particularly worried by the shrinking of the middle class. Although the middle class is still significantly larger than the lower and upper classes, it shrank from 69 percent in 1971 to 51 percent in 2020. Arguably the most significant threat to the U.S.’s relatively high standard of living is the decline of the middle class. The wealth of the middle class has also been declining in recent decades. Its share of the wealth fell from 32 percent in 1983 to 16 percent in 2016 (Horowitz, Igielnik, & Kochhar 2020).
People with wealth often receive the most and best schooling, access better health care, and consume the most goods and services. In addition, wealthy people also wield decision-making power over their daily life because money gives them access to better resources. By contrasts, many lower-income individuals receive less education and inadequate health care and have less influence over the circumstances of their everyday lives.
Additionally, tens of millions of women and men struggle to pay rent, buy food, find work, and afford basic medical care. Women who are single heads of household tend to have a lower income and lower standard of living than their married or single male counterparts. This is a worldwide phenomenon known as the “feminization of poverty”—which acknowledges that women disproportionately make up the majority of individuals in poverty across the globe and have a lower standard of living. In the United States, women make up approximately 56 percent of Americans living in poverty. One reason for this difference is the struggle of single mothers to provide for their children. One in four unmarried mothers lives in poverty (Bleiweis, 2020). The wage gap, discussed extensively in the Work and the Economy chapter, also contributes to the gender-disparity in poverty.
In the United States, poverty is most often referred to as a relative rather than absolute measurement. Absolute poverty is an economic condition in which a family or individual cannot afford basic necessities, such as food and shelter, so that day-to-day survival is in jeopardy. Relative poverty is an economic condition in which a family or individuals have 50% income less than the average median income. This income is sometimes called the poverty level or the poverty line. In 2021, for example, the poverty for a single individual was set at $12,880 for one individual, $17,420 for a couple, and $26,500 for a family of four (ASPE 2021).
As a wealthy developed country, the United States invests in resources to provide the basic necessities to those in need through a series of federal and state social welfare programs. These programs provide food, medical, and cash assistance. Temporary Assistance for Needy Families (TANF) provides cash assistance. The goal of TANF is to help families with children achieve economic self-sufficiency. Adults who receive assistance must fall under a specific income level, usually half the poverty level, set by the state. TANF funding goes to childcare, support for parents who are working or training a required number of hours a week, and other services. TANF is time-limited. Most states only provide assistance for a maximum of 5 years (CBPP).
One of the best-known programs is the Supplemental Nutrition Assistance Program (SNAP), administered by the United States Department of Agriculture and formerly known as the Food Stamp Program. This program began in the Great Depression, when unmarketable or surplus food was distributed to the hungry. It was not formalized until 1961, when President John F. Kennedy initiated a food stamp pilot program. His successor Lyndon B. Johnson was instrumental in the passage of the Food Stamp Act in 1964. In 1965, more than 500,000 individuals received food assistance. During the height of the pandemic in 2020, participation reached 43 million people.
### Summary
The United States has a high standard of living, where individuals expect to own property and have the ability to travel. Even so, the United States struggles with economic inequality, with a small number of citizens with a large amount of wealth and a larger number of people falling into relative poverty. There are three main classes in the United States: upper, middle, and lower class. Social mobility describes a shift from one social class to another. Class traits, also called class markers, are the typical behaviors, customs, and norms that define each class, but have become less definitive in assigning class to a specific individual.
### Section Quiz
### Short Answer
### Further Research
The Pew Research Center Created an income calculator to determine people's socioeconomic classification according to state and income.
### References
Civilian labor force participation rate, U.S. Bureau of Labor Statistics, https://www.bls.gov/charts/employment-situation/civilian-labor-force-participation-rate.htm accessed March 15, 2021.
Distribution of Household Wealth in the U.S. since 1989. (n.d.) The Federal Reserve. Retrieved March 21, 2021 from https://www.federalreserve.gov/releases/z1/dataviz/dfa/distribute/chart/#quarter:124;series:Net%20worth;demographic:networth;population:7;units:shares;range:2005.4,2020.4.
Policy Basics: Temporary Assistance for Needy Families. (February 6, 2020). Center on Budget and Policy Priorities (CBPP). https://www.cbpp.org/research/family-income-support/temporary-assistance-for-needy-families
HHS Poverty Guidelines for 2021. (January 13, 2021). Office of the Assistant Secretary for Planning and Evaluation (ASPE). https://aspe.hhs.gov/poverty-guidelines.
Beeghley, Leonard. 2008. The Structure of Social Stratification in the United States. Upper Saddle River, NJ: Prentice Hall.
Bennett, J.; Fry, R.; and Kochhar, R. (July 23, 2000). Are you in the American middle class? Find out with our income calculator. Pew Research Center. https://www.pewresearch.org/fact-tank/2020/07/23/are-you-in-the-american-middle-class/.
Bleiweis, R; Boesch, D.; & Gaines, A. C. (August 3, 2020). The Basic Facts About Women in Poverty. Center for American Progress. Center for American Progress. https://www.americanprogress.org/issues/women/reports/2020/08/03/488536/basic-facts-women-poverty/
Cooper, Gould, & Zipperer, 2019. Low-wage workers are suffering from a decline in the real value of the federal minimum wage. Economic Policy Institute. Retrieved November 22, 2020. https://files.epi.org/pdf/172974.pdf
DeVine, Christine. 2005. Class in Turn-of-the-Century Novels of Gissing, James, Hardy and Wells. London: Ashgate Publishing Co.
Gilbert, Dennis. 2010. The American Class Structure in an Age of Growing Inequality. Newbury Park, CA: Pine Forge Press.
Glasmeier, Amy K. Living Wage Calculator. 2020. Massachusetts Institute of Technology. livingwage.mit.edu.
Horowitz, J. M.; Igielnik, R.; and Kochhar, R. (2020, January 9). Trends in income and wealth inequality. Pew Research Center. https://www.pewresearch.org/social-trends/2020/01/09/trends-in-income-and-wealth-inequality/
Kochhar, R. and Fry, R. (December 10, 2015). 5 takeaways about the American middle class. Pew Research Center. https://www.pewresearch.org/fact-tank/2015/12/10/5-takeaways-about-the-american-middle-class/.
Popken, Ben. "CEO Pay Up 298%, Average Worker's? 4.3% (1995-2005)," 2007, The Consumerist. Retrieved on December 31, 2014 (http://consumerist.com/2007/04/09/ceo-pay-up-298-average-workers-43-1995-2005/)
United States Department of Labor. 2014. “Wage and Hour Division: Minimum Wage Laws in the States—September 1, 2014.” Retrieved January 10, 2012 (http://www.dol.gov/whd/minwage/america.htm).
United States Department of Agriculture (USDA). (November, 2020). Food and Nutrition Service Research and Data. Retrieved March 21, 2021 from https://www.fns.usda.gov/data-research.
Williams, Raymond. 1984 [1976]. Keywords: A Vocabulary of Culture and Society. New York: Oxford University Press. |
# Social Stratification in the United States
## Global Stratification and Inequality
Global stratification compares the wealth, status, power, and economic stability of countries across the world. Global stratification highlights worldwide patterns of social inequality.
In the early years of civilization, hunter-gatherer and agrarian societies lived off the earth and rarely interacted with other societies. When explorers began traveling, societies began trading goods, as well as ideas and customs.
In the nineteenth century, the Industrial Revolution created unprecedented wealth in Western Europe and North America. Due to mechanical inventions and new means of production, people began working in factories—not only men, but women and children as well. By the late nineteenth and early twentieth centuries, industrial technology had gradually raised the standard of living for many people in the United States and Europe.
The Industrial Revolution also saw the rise of vast inequalities between countries that were industrialized and those that were not. As some nations embraced technology and saw increased wealth and goods, the non-industrialized nations fell behind economically, and the gap widened.
Sociologists studying global stratification analyze economic comparisons between nations. Income, purchasing power, and wealth are used to calculate global stratification. Global stratification also compares the quality of life that a country’s population can have. Poverty levels have been shown to vary greatly across countries. Yet all countries struggle to support the lower classes.
### Models of Global Stratification
In order to determine the stratification or ranking of a country, economists created various models of global stratification. All of these models have one thing in common: they rank countries according to their economic status, often ranked by gross national product (GNP). The GNP is the value of goods and services produced by a nation’s citizens both within its boarders and abroad.
Another system of global classification defines countries based on the gross domestic product (GDP), a country’s national wealth. The GDP calculated annually either totals the income of all people living within its borders or the value of all goods and services produced in the country during the year. It also includes government spending. Because the GDP indicates a country’s productivity and performance, comparing GDP rates helps establish a country’s economic health in relation to other countries, with some countries rising to the top and others falling to the bottom. The chapter on Work and the Economy (specifically the section on Globalization and the Economy) shows the differences in GDP among various countries.
Traditional models, now considered outdated, used labels, such as “first world”, “second world,” and “third world” to describe the stratification of the different areas of the world. First and second world described industrialized nations, while third world referred to “undeveloped” countries (Henslin 2004). When researching existing historical sources, you may still encounter these terms, and even today people still refer to some nations as the “third world.” This model, however, is outdated because it lumps countries together that are quite different in terms of wealth, power, prestige, and economic stability.
Another model separates countries into two groups: more developed and less developed. More-developed nations have higher wealth, such as Canada, Japan, and Australia. Less-developed nations have less wealth to distribute among populations, including many countries in central Africa, South America, and some island nations.
GNP and GDP are used to gain insight into global stratification based on a country’s standard of living. According to this analysis, a GDP standard of a middle-income nation represents a global average. In low-income countries, most people are poor relative to people in other countries. Citizens have little access to amenities such as electricity, plumbing, and clean water. People in low-income countries are not guaranteed education, and many are illiterate. The life expectancy of citizens is lower than in high-income countries. Therefore, the different expectations in lifestyle and access to resources varies.
### Summary
Global stratification compares the wealth, status, power, and economic stability, of countries and ranks the countries. By comparing income and productivity between nations, researchers can better identify global financial and econommic leaders as well as inequalities within and among nations.
### Section Quiz
### Short Answer
### Further Research
Our World in Data's Global Economic Inequality page a wide range of data sources, narratives, and charts. While the sources should be verified before citing them in papers, the presentation offers a multifaceted picture of global inequality : .
### References
Nationsonline.org. “Countries by Gross National Income (GNI).” Retrieved January 9, 2012 (http://www.nationsonline.org/oneworld/GNI_PPP_of_countries.htm).
PRB.org. “GNI PPP Per Capita (US$).” PRB 2011 World Population Data Sheet. 2011 Population Reference Bureau. Retrieved January 10, 2012 (http://www.prb.org/DataFinder/Topic/Rankings.aspx?ind=61).
Rostow, Walt W. 1960. The Stages of Economic Growth: A Non-Communist Manifesto. Cambridge, MA: Cambridge University Press.
Landler, Mark, and David E. Sanger. 2009. “World Leaders Pledge $1.1 Trillion for Crisis.” New York Times, April 3. Retrieved January 9, 2012 (http://www.nytimes.com/2009/04/03/world/europe/03summit.html). |
# Social Stratification in the United States
## Theoretical Perspectives on Social Stratification
Basketball is one of the highest-paying professional sports and stratification exists even among teams in the NBA. For example, the Toronto Raptors hands out the lowest annual payroll, while the New York Knicks reportedly pays the highest. Stephen Curry, a Golden State Warriors guard, is one of the highest paid athletes in the NBA, earning around $43 million a year (Sports Illustrated 2020), whereas the lowest paid player earns just over $200,000 (ESPN 2021). Even within specific fields, layers are stratified, members are ranked, and inequality exists.
In sociology, even an issue such as NBA salaries can be seen from various points of view. Functionalists will examine the purpose of such high salaries, conflict theorists will study the exorbitant salaries as an unfair distribution of money, and symbolic interactionists will describe how players display that wealth. Social stratification takes on new meanings when it is examined from different sociological perspectives—functionalism, conflict theory, and symbolic interactionism.
### Functionalism
In sociology, the functionalist perspective examines how society’s parts operate. According to functionalism, different aspects of society exist because they serve a vital purpose. What is the function of social stratification?
In 1945, sociologists Kingsley Davis and Wilbert Moore published the Davis-Moore thesis, which argued that the greater the functional importance of a social role, the greater must be the reward. The theory posits that social stratification represents the inherently unequal value of different work. Certain tasks in society are more valuable than others (for example, doctors or lawyers). Qualified people who fill those positions are rewarded more than others.
According to Davis and Moore, a firefighter’s job is more important than, for instance, a grocery store cashier’s job. The cashier position does not require similar skill and training level as firefighting. Without the incentive of higher pay, better benefits, and increased respect, why would someone be willing to rush into burning buildings? If pay levels were the same, the firefighter might as well work as a grocery store cashier and avoid the risk of firefighting. Davis and Moore believed that rewarding more important work with higher levels of income, prestige, and power encourages people to work harder and longer.
Davis and Moore stated that, in most cases, the degree of skill required for a job determines that job’s importance. They noted that the more skill required for a job, the fewer qualified people there would be to do that job. Certain jobs, such as cleaning hallways or answering phones, do not require much skill. Therefore, most people would be qualified for these positions. Other work, like designing a highway system or delivering a baby, requires immense skill limiting the number of people qualified to take on this type of work.
Many scholars have criticized the Davis-Moore thesis. In 1953, Melvin Tumin argued that it does not explain inequalities in the education system or inequalities due to race or gender. Tumin believed social stratification prevented qualified people from attempting to fill roles (Tumin 1953).
### Conflict Theory
Conflict theorists are deeply critical of social stratification, asserting that it benefits only some people, not all of society. For instance, to a conflict theorist, it seems wrong that a basketball player is paid millions for an annual contract while a public school teacher may earn $35,000 a year. Stratification, conflict theorists believe, perpetuates inequality. Conflict theorists try to bring awareness to inequalities, such as how a rich society can have so many poor members.
Many conflict theorists draw on the work of Karl Marx. During the nineteenth-century era of industrialization, Marx believed social stratification resulted from people’s relationship to production. People were divided into two main groups: they either owned factories or worked in them. In Marx’s time, bourgeois capitalists owned high-producing businesses, factories, and land, as they still do today. Proletariats were the workers who performed the manual labor to produce goods. Upper-class capitalists raked in profits and got rich, while working-class proletariats earned skimpy wages and struggled to survive. With such opposing interests, the two groups were divided by differences of wealth and power. Marx believed workers experience deep alienation, isolation and misery resulting from powerless status levels (Marx 1848). Marx argued that proletariats were oppressed by the bourgeoisie.
Today, while working conditions have improved, conflict theorists believe that the strained working relationship between employers and employees still exists. Capitalists own the means of production, and a system is in place to make business owners rich and keep workers poor. According to conflict theorists, the resulting stratification creates class conflict.
### Symbolic Interactionism
Symbolic interactionism uses everyday interactions of individuals to explain society as a whole. Symbolic interactionism examines stratification from a micro-level perspective. This analysis strives to explain how people’s social standing affects their everyday interactions.
In most communities, people interact primarily with others who share the same social standing. It is precisely because of social stratification that people tend to live, work, and associate with others like themselves, people who share their same income level, educational background, class traits and even tastes in food, music, and clothing. The built-in system of social stratification groups people together. This is one of the reasons why it was rare for a royal prince like England’s Prince William to marry a commoner.
Symbolic interactionists also note that people’s appearance reflects their perceived social standing. As discussed above, class traits seen through housing, clothing, and transportation indicate social status, as do hairstyles, taste in accessories, and personal style. Symbolic interactionists also analyze how individuals think of themselves or others interpretation of themselves based on these class traits.
To symbolically communicate social standing, people often engage in conspicuous consumption, which is the purchase and use of certain products to make a social statement about status. Carrying pricey but eco-friendly water bottles could indicate a person’s social standing, or what they would like others to believe their social standing is. Some people buy expensive trendy sneakers even though they will never wear them to jog or play sports. A $17,000 car provides transportation as easily as a $100,000 vehicle, but the luxury car makes a social statement that the less expensive car can’t live up to. All these symbols of stratification are worthy of examination by an interactionist.
### Summary
Social stratification can be examined from different sociological perspectives—functionalism, conflict theory, and symbolic interactionism. The functionalist perspective states that systems exist in society for good reasons, such as incentives and rewards for those who demonstrate high skill and complete a high-level of education or training. Conflict theorists observe that stratification promotes inequality, such as different opportunities and success of rich business owners and their lower paid workers. Symbolic interactionists examine stratification from a micro-level perspective. They observe how social standing affects people’s everyday interactions and how the concept of “social class” is constructed and maintained through everyday interactions.
### Section Quiz
### Short Answer
### References
NBA Player Salaries - 2020-2021. ESPN. Retrieved March 23, 2021 from http://www.espn.com/nba/salaries/_/page/14.
Davis, Kingsley, and Wilbert E. Moore. “Some Principles of Stratification.” American Sociological Review 10(2):242–249. Retrieved January 9, 2012 (http://www.jstor.org/stable/2085643).
Marx, Karl. 1848. Manifesto of the Communist Party. Retrieved January 9, 2012 (http://www.marxists.org/archive/marx/works/1848/communist-manifesto/).
Sports Illustrated 2020 SI.com LLC. 2020. “Here Are The Five NBA Players Whose 2019-2020 Salaries Top LeBron James”. Retrieved November 13, 020. (https://www.si.com/nba/lakers/news/here-are-the-five-nba-players-whose-2019-2020-salaries-top-lebron-james).
Tumin, M. (1953). Some Principles of Stratification: A Critical Analysis. American Sociological Review, 18(4), 387-394. Retrieved March 24, 2021, from http://www.jstor.org/stable/2087551 |
# Global Inequality
## Introduction
The April 24, 2013 collapse of the Rana Plaza in Dhaka, Bangladesh that killed over 1,100 people, was the deadliest garment factory accident in history, and it was preventable (International Labour Organization, Department of Communication 2014).
In addition to garment factories employing about 5,000 people, the building contained a bank, apartments, childcare facilities, and a variety of shops. Many of these closed the day before the collapse when cracks were discovered in the building walls. When some of the garment workers refused to enter the building, they were threatened with the loss of a month’s pay. Most were young women, aged twenty or younger. They typically worked over thirteen hours a day, with two days off each month. For this work, they took home between twelve and twenty-two cents an hour, or $10.56 to $12.48 a week. Without that pay, most would have been unable to feed their children. In contrast, the U.S. federal minimum wage is $7.25 an hour, and workers receive wages at time-and-a-half rates for work in excess of forty hours a week.
32 percent of the clothing made in the collapsed Rana Plaza building was intended for U.S., Canadian, and European stores. Walmart jeans were made on the fifth floor. Clothing for The Children’s Place was produced in the building, as well. Afterward, Walmart and The Children’s Place pledged $1 million and $450,000 (respectively) to the Rana Plaza Trust Fund, but fifteen other companies with clothing made in the building chose not to (Institute for Global Labour and Human Rights 2014).
While you read this chapter, think about the global system that allows U.S. companies to outsource their manufacturing to peripheral nations, where many women and children work in conditions that some characterize as slave labor. Do people in the United States have a responsibility to foreign workers? Should U.S. corporations be held accountable for what happens to garment factory workers who make their clothing? What can you do as a consumer to help such workers?
### References
Butler, Sarah. 2013. “Bangladeshi Factory Deaths Spark Action among High-Street Clothing Chains.” The Guardian. Retrieved November 7, 2014 (http://www.theguardian.com/world/2013/jun/23/rana-plaza-factory-disaster-bangladesh-primark).
Institute for Global Labour and Human Rights. 2014. "Rana Plaza: A Look Back and Forward." Global Labour Rights. Retrieved November 7, 2014 (http://www.globallabourrights.org/campaigns/factory-collapse-in-bangladesh).
International Labour Organization, Department of Communication. 2014. "Post Rana Plaza: A Vision for the Future." Working Conditions: International Labour Organization. Retrieved November 7, 2014 (http://www.ilo.org/global/about-the-ilo/who-we-are/ilo-director-general/statements-and-speeches/WCMS_240382/lang--en/index.htm).
Korzeniewicz, Robert, and Timothy Patrick Moran. 2009. Unveiling Inequality: A World Historical Perspective. New York, NY: Russell Sage Foundation. |
# Global Inequality
## Global Stratification and Classification
Just as the United States' wealth is increasingly concentrated among its richest citizens, global inequality concentrates resources within certain nations and among certain people.
Measuring the financial resource of the world's richest people is generally easier than measuring the resources of people living in poverty (Matthews 2019), but researchers and advocates have created some tools to evaluate and understand economic conditions and outcomes.
One straightforward method is to compare the ratio of income of the richest 10 percent to the income of the poorest 10 percent. (The same method is sometime used with the richest 20 percent and the poorest 20 percent.) This method does not always provide a full picture of income inequality (it literally leaves out the middle), but it can certain provide insight.
The Human Development Index expresses the capabilities of people's potential achievement. The index is calculated using data regarding people's lifespan, education, and income. By using both financial and non-financial factors, it paints a deeper picture of the lives and issues in a region. For example, a nation with high income but low education will still have difficulty in overall opportunity. This approach was developed by Pakistani economist Mahbub ul Haq, who produced the first annual Human Development report, which captures and illustrates development issues and changes each year.
Another measure of inequality is Gini Coefficient, named after the Italian sociologist and statistician Corrado Gini. (Be sure not to confuse this with GNI, which is the gross national income.) It is is calculated using a number of financial indicators, and is expressed as either a decimal or a percentage. A country in which every resident has the same income would have a Gini coefficient of 0 (or 0 percent). A country in which one resident earned all the income, while everyone else earned nothing, would have an income Gini coefficient of 1 (or 100 percent). Thus, the higher the number (the closer to that one person having all the income or wealth), the more inequality there is.
Other gauges are a bit more direct: To indicate the level of poverty within a nation or region, researchers calculate the percentage of the population living beneath various poverty thresholds. A common measure is to consider the percentage of a nation's population living on less than $1.90 per day, which is commonly known as the International Poverty Line. (Note that United States dollars are often used as a global standard in these types of measurement.) The table in the next sub-section uses this method.
These are just a few of the ways that sociologists, economists, governments, and others try to understand levels of income inequality and poverty. Changes in these indicators would alert policymakers that something is affecting the population. No changes might tell people that, for example, a new financial assistance program for the poor is not working.
With these analytical elements in mind, let’s consider how the three major sociological perspectives might contribute to our understanding of global inequality.
The functionalist perspective is a macroanalytical view that focuses on the way that all aspects of society are integral to the continued health and viability of the whole. A functionalist might focus on why we have global inequality and what social purposes it serves. This view might assert, for example, that we have global inequality because some nations are better than others at adapting to new technologies and profiting from a globalized economy, and that when core nation companies locate in peripheral nations, they expand the local economy and benefit the workers.
Conflict theory focuses on the creation and reproduction of inequality. A conflict theorist would likely address the systematic inequality created when core nations exploit the resources of peripheral nations. For example, how many U.S. companies take advantage of overseas workers who lack the constitutional protection and guaranteed minimum wages that exist in the United States? Doing so allows them to maximize profits, but at what cost?
The symbolic interaction perspective studies the day-to-day impact of global inequality, the meanings individuals attach to global stratification, and the subjective nature of poverty. Someone applying this view to global inequality would probably focus on understanding the difference between what someone living in a core nation defines as poverty (relative poverty, defined as being unable to live the lifestyle of the average person in your country) and what someone living in a peripheral nation defines as poverty (extreme poverty, defined as being barely able, or unable, to afford basic necessities, such as food).
### Global Stratification
While stratification in the United States refers to the unequal distribution of resources among individuals, global stratification refers to this unequal distribution among nations. There are two dimensions to this stratification: gaps between nations and gaps within nations. When it comes to global inequality, both economic inequality and social inequality may concentrate the burden of poverty among certain segments of the earth’s population (Myrdal 1970).
As mentioned earlier, one way to evaluate stratification is to consider how many people are living in poverty, and particularly extreme poverty, which is often defined as needing to survive on less than $1.90 per day. Fortunately, until the COVID-19 pandemic impacted economies in 2020, the extreme poverty rate had been on a 20-year decline. In 2015, 10.1 percent of the world's population was living in extreme poverty; in 2017, that number had dropped an entire percentage point to 9.2 percent. While a positive, that 9.2 percent is equivalent to 689 million people living on less than $1.90 a day. The same year, 24.1 percent of the world lived on less than $3.20 per day and 43.6 percent on less than $5.50 per day in 2017 (World Bank 2020). The table below makes the differences in poverty very clear.
Most of us are accustomed to thinking of global stratification as economic inequality. For example, we can compare the United States’ average worker’s wage to America’s average wage. Social inequality, however, is just as harmful as economic discrepancies. Prejudice and discrimination—whether against a certain race, ethnicity, religion, or the like—can create and aggravate conditions of economic equality, both within and between nations. Think about the inequity that existed for decades within the nation of South Africa. Apartheid, one of the most extreme cases of institutionalized and legal racism, created a social inequality that earned it the world’s condemnation.
Gender inequity is another global concern. Consider the controversy surrounding female genital mutilation. Nations that practice this female circumcision procedure defend it as a longstanding cultural tradition in certain tribes and argue that the West shouldn’t interfere. Western nations, however, decry the practice and are working to stop it.
Inequalities based on sexual orientation and gender identity exist around the globe. According to Amnesty International, a number of crimes are committed against individuals who do not conform to traditional gender roles or sexual orientations (however those are culturally defined). From culturally sanctioned rape to state-sanctioned executions, the abuses are serious. These legalized and culturally accepted forms of prejudice and discrimination exist everywhere—from the United States to Somalia to Tibet—restricting the freedom of individuals and often putting their lives at risk (Amnesty International 2012).
### Global Classification
A major concern when discussing global inequality is how to avoid an ethnocentric bias implying that less-developed nations want to be like those who’ve attained post-industrial global power. Terms such as developing (nonindustrialized) and developed (industrialized) imply that unindustrialized countries are somehow inferior, and must improve to participate successfully in the global economy, a label indicating that all aspects of the economy cross national borders. We must take care how we delineate different countries. Over time, terminology has shifted to make way for a more inclusive view of the world.
Global classification methods are not only important in understanding economic differences among countries, but also in providing ways to classify countries and identify trends in other areas. The classifications discussed below will be used in other chapters, such as the chapter on health and medicine.
### Cold War Terminology
Cold War terminology was developed during the Cold War era (1945–1980). Familiar and still used by many, it classifies countries into first world, second world, and third world nations based on their respective economic development and standards of living. When this nomenclature was developed, capitalistic democracies such as the United States and Japan were considered part of the first world. The poorest, most undeveloped countries were referred to as the third world and included most of sub-Saharan Africa, Latin America, and Asia. The second world was the in-between category: nations not as limited in development as the third world, but not as well off as the first world, having moderate economies and standard of living, such as China or Cuba. Later, sociologist Manual Castells (1998) added the term fourth world to refer to stigmatized minority groups that were denied a political voice all over the globe (indigenous minority populations, prisoners, and the homeless, for example).
Also during the Cold War, global inequality was described in terms of economic development. Along with developing and developed nations, the terms less-developed nation and underdeveloped nation were used. This was the era when the idea of noblesse oblige (first-world responsibility) took root, suggesting that the so-termed developed nations should provide foreign aid to the less-developed and underdeveloped nations in order to raise their standard of living.
### Immanuel Wallerstein: World Systems Approach
Immanuel Wallerstein’s (1979) world systems approach uses an economic basis to understand global inequality. Wallerstein conceived of the global economy as a complex system that supports an economic hierarchy that placed some nations in positions of power with numerous resources and other nations in a state of economic subordination. Those that were in a state of subordination faced significant obstacles to mobilization.
Core nations are dominant capitalist countries, highly industrialized, technological, and urbanized. For example, Wallerstein contends that the United States is an economic powerhouse that can support or deny support to important economic legislation with far-reaching implications, thus exerting control over every aspect of the global economy and exploiting both semi-peripheral and peripheral nations. We can look at free trade agreements such as the North American Free Trade Agreement (NAFTA) as an example of how a core nation is able to leverage its power to gain the most advantageous position in the matter of global trade.
Peripheral nations have very little industrialization; what they do have often represents the outdated castoffs of core nations or the factories and means of production owned by core nations. They typically have unstable governments, inadequate social programs, and are economically dependent on core nations for jobs and aid. There are abundant examples of countries in this category, such as Vietnam and Cuba. We can be sure the workers in a Cuban cigar factory, for example, which are owned or leased by global core nation companies, are not enjoying the same privileges and rights as U.S. workers.
Semi-peripheral nations are in-between nations, not powerful enough to dictate policy but nevertheless acting as a major source for raw material and an expanding middle-class marketplace for core nations, while also exploiting peripheral nations. Mexico is an example, providing abundant cheap agricultural labor to the U.S., and supplying goods to the United States market at a rate dictated by the U.S. without the constitutional protections offered to United States workers.
### World Bank Economic Classification by Income
While the World Bank is often criticized, both for its policies and its method of calculating data, it is still a common source for global economic data. Along with tracking the economy, the World Bank tracks demographics and environmental health to provide a complete picture of whether a nation is high income, middle income, or low income.
### High-Income Nations
The World Bank defines high-income nations as having a gross national income of at least $12,536 per capita. in 2019 (World Bank 2021). (Note that the classifications will always lag by a couple of years so that analysts can evaluate the true income of the nations.) Examples include Belgium, Canada, Japan, Oman, Puerto Rico, and the United States.
High-income countries face two major issues: capital flight and deindustrialization. Capital flight refers to the movement (flight) of capital from one nation to another, as when General Motors automotive company closed U.S. factories in Michigan and opened factories in Mexico.
Deindustrialization, a related issue, occurs as a consequence of capital flight, as no new companies open to replace jobs lost to foreign nations. As expected, global companies move their industrial processes to the places where they can get the most production with the least cost, including the building of infrastructure, training of workers, shipping of goods, and, of course, paying employee wages. This means that as emerging economies create their own industrial zones, global companies see the opportunity for existing infrastructure and much lower costs. Those opportunities lead to businesses closing the factories that provide jobs to the middle class within core nations and moving their industrial production to peripheral and semi-peripheral nations.
### Middle-Income Nations
The World Bank divides middle-income economies into two categories. Lower middle income areas are those with a GNI per capita of more than $1,036 but less than $4,045. Upper middle income areas are those with A GNI per capita between $4,046 and $12,535. Democratic Republic of Congo, Tunisia, Philippines, El Salvador, and Nepal are are examples of lower-middle-income countries. And Argentina, Mexico, China, Iran, Turkey, and Namibia are examples of upper-middle-income nations (World Bank 2021).
Perhaps the most pressing issue for middle-income nations is the problem of debt accumulation. As the name suggests, debt accumulation is the buildup of external debt, wherein countries borrow money from other nations to fund their expansion or growth goals. As the uncertainties of the global economy make repaying these debts, or even paying the interest on them, more challenging, nations can find themselves in trouble. Once global markets have reduced the value of a country’s goods, it can be very difficult to ever manage the debt burden. Such issues have plagued middle-income countries in Latin America and the Caribbean, as well as East Asian and Pacific nations (Dogruel and Dogruel 2007).
### Low-Income Nations
The World Bank defines low-income countries as nations whose per capita GNI was $1,035 per capita or less in 2019. For example, Afghanistan, Ethiopia, and Yemen are considered low-income countries. Low-income economies are primarily found in Asia and Africa (World Bank 2021), where most of the world’s population lives. There are two major challenges that these countries face: women are disproportionately affected by poverty (in a trend toward a global feminization of poverty) and much of the population lives in absolute poverty.
Nations' classifications often change as their economies evolve and, sometimes, when their political positions change. Nepal, Indonesia, and Romania all moved up to a higher status based on improved economies. While Sudan, Algeria, and Sri Lanka moved down a level. A few years ago, Myanmar was a low-income nation, but now it has moved into the middle-income area. With Myanmar's 2021 coup, the massive citizen response, and the military's killing of protesters, its economy may go through a downturn again, returning it to the low-income nation status.
### Summary
Stratification refers to the gaps in resources both between nations and within nations. While economic equality is of great concern, so is social equality, like the discrimination stemming from race, ethnicity, gender, religion, and/or sexual orientation. While global inequality is nothing new, several factors make it more relevant than ever, like the global marketplace and the pace of information sharing. Researchers try to understand global inequality by classifying it according to factors such as how industrialized a nation is, whether a country serves as a means of production or as an owner, and what income a nation produces.
### Section Quiz
### Short Answer
### Further Research
To learn more about the United Nations Millennium Development Goals, look here.
To learn more about the existence and impact of global poverty, peruse the poverty and equity data portal here.
### References
Amnesty International. 2012. “Sexual Orientation and Gender Identity.” Retrieved January 3, 2012 (http://www.amnesty.org/en/sexual-orientation-and-gender-identity).
Castells, Manuel. 1998. End of Millennium. Malden, MA: Blackwell.
Central Intelligence Agency. 2012. “The World Factbook.” Retrieved January 5, 2012 (https://www.cia.gov/library/publications/the-world-factbook/wfbExt/region_noa.html).
Central Intelligence Agency. 2014. “Country Comparison: Infant Mortality Rate.” Retrieved November 7, 2014 (https://www.cia.gov/library/publications/the-worldfactbook/rankorder/2091rank.html?countryname=Canada&countrycode=ca®ionCode=noa&rank=182#ca).
Dogruel, Fatma, and A. Suut Dogruel. 2007. “Foreign Debt Dynamics in Middle Income Countries.” Paper presented January 4, 2007 at Middle East Economic Association Meeting, Allied Social Science Associations, Chicago, IL.
Moghadam, Valentine M. 2005. “The Feminization of Poverty and Women’s Human Rights.” Gender Equality and Development Section UNESCO, July. Paris, France.
Myrdal, Gunnar. 1970. The Challenge of World Poverty: A World Anti-Poverty Program in Outline. New York: Pantheon.
Oxfam. 2014. “Working for the Few: Political Capture and Economic Inequality.” Oxfam.org. Retrieved November 7, 2014 (http://www.oxfam.org/sites/www.oxfam.org/files/bp-working-for-few-political-capture-economic-inequality-200114-summ-en.pdf).
United Nations. 2013. "Millennium Development Goals." Retrieved November 7, 2014 (http://www.un.org/millenniumgoals/bkgd.shtml).
Wallerstein, Immanuel. 1979. The Capitalist World Economy. Cambridge, England: Cambridge World Press.
World Bank. 2014a. “Gender Overview.” Retrieved November 7, 2014 (http://www.worldbank.org/en/topic/gender/overview#1).
World Bank. 2014b. “High Income: OECD: Data.” Retrieved November 7, 2014 (http://data.worldbank.org/income-level/OEC).
World Bank. 2014c. “Low Income: Data.” Retrieved November 7, 2014 (http://data.worldbank.org/income-level/LIC).
World Bank. 2014d. “Upper Middle Income: Data.” Retrieved November 7, 2014 (http://data.worldbank.org/income-level/UMC).
World Bank. 2020. "Understanding Poverty: Poverty Overview." Retrieved April 3 2021. (https://www.worldbank.org/en/topic/poverty/overview)
World Bank. 2021. "World Bank Country and Lending Groups." Retrieved April 3 2021. (https://datahelpdesk.worldbank.org/knowledgebase/articles/906519-world-bank-country-and-lending-groups) |
# Global Inequality
## Global Wealth and Poverty
What does it mean to be poor? Does it mean being a single mother with two kids in New York City, waiting for the next paycheck in order to buy groceries? Does it mean living with almost no furniture in your apartment because your income doesn’t allow for extras like beds or chairs? Or does it mean having to live with the distended bellies of the chronically malnourished throughout the peripheral nations of Sub-Saharan Africa and South Asia? Poverty has a thousand faces and a thousand gradations; there is no single definition that pulls together every part of the spectrum. You might feel you are poor if you can’t afford cable television or buy your own car. Every time you see a fellow student with a new laptop and smartphone you might feel that you, with your ten-year-old desktop computer, are barely keeping up. However, someone else might look at the clothes you wear and the calories you consume and consider you rich.
### Types of Poverty
Social scientists define global poverty in different ways and take into account the complexities and the issues of relativism described above. Relative poverty is a state of living where people can afford necessities but are unable to meet their society’s average standard of living. People often disparage “keeping up with the Joneses”—the idea that you must keep up with the neighbors’ standard of living to not feel deprived. But it is true that you might feel ”poor” if you are living without a car to drive to and from work, without any money for a safety net should a family member fall ill, and without any “extras” beyond just making ends meet.
Contrary to relative poverty, people who live in extreme poverty lack even the basic necessities, which typically include adequate food, clean water, safe housing, and access to healthcare. Extreme poverty occurs when someone lives on less than 1.90 U.S dollars per day.
In prior years, the World Bank—the primary organization analyzing these trends––focused heavily on the number of people under that extreme poverty level of $1.90 per day. (The previous term was "absolute poverty.") In 2018, the World Bank added two more measures to consider: people living on less than $3.20 and people living on less than $5.50. As the number of people in that extreme category continues to decline, these two new categories will be important to recognize the population that lives above the $1.90 line, but still remains vulnerable to extreme poverty. Someone who begins to earn enough to live on more than $1.90 is still in severe poverty and should be considered as such (Schoch 2020).
If you were forced to live on $1.90 a day, or even $5.50, how would you do it? What would you deem worthy of spending money on, and what could you do without? How would you manage the necessities—and how would you make up the gap between what you need to live and what you can afford?
Subjective poverty describes poverty that is composed of many dimensions; it is subjectively present when your actual income does not meet your expectations and perceptions. With the concept of subjective poverty, the poor themselves have a greater say in recognizing when it is present. In short, subjective poverty has more to do with how a person or a family defines themselves. This means that a family subsisting on a few dollars a day in Nepal might think of themselves as doing well, within their perception of normal. However, a westerner traveling to Nepal might visit the same family and see extreme need.
### Who Are the Impoverished?
Who are the impoverished? Who is living in absolute poverty? The truth that most of us would guess is that the richest countries are often those with the least people. Compare the United States, which possesses a relatively small slice of the population pie and owns by far the largest slice of the wealth pie, with India. These disparities have the expected consequence. The poorest people in the world are women and those in peripheral and semi-peripheral nations. For women, the rate of poverty is particularly worsened by the pressure on their time. In general, time is one of the few luxuries the very poor have, but study after study has shown that women in poverty, who are responsible for all family comforts as well as any earnings they can make, have less of it. The result is that women are suffering more in terms of overall wellbeing (Buvinic 1997). It is harder for females to get credit to expand businesses, to take the time to learn a new skill, or to spend extra hours improving their craft so as to be able to earn at a higher rate.
### Global Feminization of Poverty
In almost all societies, women have higher rates of poverty than men. More women and girls live in poor conditions, receive inadequate healthcare, bear the brunt of malnutrition and inadequate drinking water, and so on. This situation goes back decades, and led University of Michigan sociologist Diana Pearce to coin the term "feminization of poverty" in 1978. Throughout the 1990s, data indicated that while overall poverty rates were rising, especially in peripheral nations, the rates of impoverishment increased for women nearly 20 percent more than for men (Mogadham 2005). More recently, as extreme poverty rates continue to fall, women still make up a disproportionate amount of the world's poor. Gender differences are sometimes difficult to discern in international poverty data, but researchers have undertaken efforts to define the makeup of those affected by poverty. Of people aged 25-34, the world has 122 women living in poverty for every 100 men living in poverty. The world's elderly below the poverty line are also more likely to be women (World Bank 2018).
Why is this happening? While myriad variables affect women's poverty, research specializing in this issue identifies three causes (Mogadham 2005):
While women are living longer and healthier lives today compared to ten years ago, around the world many women are denied basic rights, particularly in the workplace. In peripheral nations, they accumulate fewer assets, farm less land, make less money, and face restricted civil rights and liberties. Women can stimulate the economic growth of peripheral nations, but they are often undereducated and lack access to credit needed to start small businesses. When women are able to attain higher levels of education, they account for significant economic growth within their nations (OECD 2012).
A wide range of organizations undertake programs or provide support in order to improve opportunity, safety, education, equality, and financial outcomes for women. Some of these efforts involve diplomacy, such as one government (or a coalition) working to secure greater rights and improve circumstances of women in other countries. Key areas of focus are reducing institutional and cultural discrimination, ending domestic violence, providing women more agency in decision making, and increasing education for children (Scott 2012). Other programs focus on more immediate needs and opportunities. Microcredit and women's collective savings accounts are ways to provide financial resources for women and families to make important investments, such as building a well at their home to improve health and reduce time spent obtaining clean water. Other uses may involve starting a business, paying a debt, or buying an important appliance or equipment. Unfortunately, these microfinance programs don't have a track record of alleviating poverty, and in some cases they can lead to negative outcomes such as trapping women in a cycle of debt, or increasing domestic violence. Collective savings programs—where local people pool their resources and extend credit within their group—have shown some more positive outcomes (Aizenman 2016 and Niner 2018). The UN has emphasized that microfinance and cultural empowerment would both be more successful if they were used in concert with each other (Scott 2012).
### Africa
The majority of the poorest countries in the world are in Africa. That is not to say there is not diversity within the countries of that continent; countries like South Africa and Egypt have much lower rates of poverty than Angola and Ethiopia, for instance. Overall, African income levels have been dropping relative to the rest of the world, meaning that Africa as a whole is getting relatively poorer. Making the problem worse, 2014 saw an outbreak of the Ebola virus in western Africa, leading to a public health crisis and an economic downturn due to loss of workers and tourist dollars.
Why is Africa in such dire straits? Much of the continent’s poverty can be traced to the availability of land, especially arable land (land that can be farmed). Centuries of struggle over land ownership have meant that much useable land has been ruined or left unfarmed, while many countries with inadequate rainfall have never set up an infrastructure to irrigate. Many of Africa’s natural resources were long ago taken by colonial forces, leaving little agricultural and mineral wealth on the continent.
Further, African poverty is worsened by civil wars and inadequate governance that are the result of a continent re-imagined with artificial colonial borders and leaders. Consider the example of Rwanda. There, two ethnic groups cohabitated with their own system of hierarchy and management until Belgians took control of the country in 1915 and rigidly confined members of the population into two unequal ethnic groups. While, historically, members of the Tutsi group held positions of power, the involvement of Belgians led to the Hutu seizing power during a 1960s revolt. This ultimately led to a repressive government and genocide against Tutsis that left hundreds of thousands of Rwandans dead or living in diaspora (U.S. Department of State 2011c). The painful rebirth of a self-ruled Africa has meant many countries bear ongoing scars as they try to see their way towards the future (World Poverty 2012a). In 2020, armed conflicts were underway in regions of nations including the Tigray conflict in Ethiopia, the Kamwina Nsapo rebellion in Democratic Republic of Congo, the Boko Haram insurgency in Nigeria and neighboring countries, and several more. While most of the ongoing conflicts are considered minor, they are both dangerous and disruptive to the people living in those regions, and several have included ethnic cleansing, mass kidnapping, extensive sexual violence, and use of child soldiers.
### Asia
While the majority of the world’s poorest countries are in Africa, the majority of the world’s poorest people are in Asia. As in Africa, Asia finds itself with disparity in the distribution of poverty, with Japan and South Korea holding much more wealth than India and Cambodia. In fact, most poverty is concentrated in South Asia. One of the most pressing causes of poverty in Asia is simply the pressure that the size of the population puts on its resources. Unlike Africa, many people living in poverty reside in urban areas, often in crowded, unhygenic conditions with limited access to water and resources. Estimates indicate that Asia has 60 percent of the world's people who live in slums (WorldVision 2019). Those who find work often do so in garment factories or other manufacturing facilities, where pay is very low and the demands are incredibly high. (See the feature below on sweatshop labor.) Children are sent to work in these conditions as well.
Asia is also frequently impacted by natural disasters. Countries like India, Bangladesh, Vietnam, Thailand, and the Philippines experience frequent typhoons (hurricanes) and flooding. For those living in insecure structures —often constructed from various leftover materials and not subject to any type of building codes—such events can leave entire swaths of the population homeless and vulnerable to disease or injury (WorldVision 2019).
### MENA
The Middle East and North Africa region (MENA) includes oil-rich countries in the Gulf, such as Iran, Iraq, and Kuwait, but also countries that are relatively resource-poor in relationship to their populations, such as Morocco and Yemen. These countries are predominately Islamic. For the last quarter-century, economic growth was slower in MENA than in other developing economies, and almost a quarter of the 300 million people who make up the population live on less than $2.00 a day (World Bank 2013).
The International Labour Organization tracks the way income inequality influences social unrest. The two regions with the highest risk of social unrest are Sub-Saharan Africa and the Middle East-North Africa region (International Labour Organization 2012). Increasing unemployment and high socioeconomic inequality in MENA were major factors in the Arab Spring, which—beginning in 2010—toppled dictatorships throughout the Middle East in favor of democratically elected government. Unemployment and income inequalities are still being blamed on immigrants, foreign nationals, and ethnic/religious minorities.
### Consequences of Poverty
Not surprisingly, the consequences of poverty are often also causes. The poor often experience inadequate healthcare, limited education, and the inaccessibility of birth control. But those born into these conditions are incredibly challenged in their efforts to break out since these consequences of poverty are also causes of poverty, perpetuating a cycle of disadvantage.
According to sociologists Neckerman and Torche (2007) in their analysis of global inequality studies, the consequences of poverty are many. Neckerman and Torche have divided them into three areas. The first, termed “the sedimentation of global inequality,” relates to the fact that once poverty becomes entrenched in an area, it is typically very difficult to reverse. As mentioned above, poverty exists in a cycle where the consequences and causes are intertwined. The second consequence of poverty is its effect on physical and mental health. Poor people face physical health challenges, including malnutrition and high infant mortality rates. Mental health is also detrimentally affected by the emotional stresses of poverty, with relative deprivation carrying the most robust effect. Again, as with the ongoing inequality, the effects of poverty on mental and physical health become more entrenched as time goes on. Neckerman and Torche’s third consequence of poverty is the prevalence of crime. Cross-nationally, crime rates are higher, particularly for violent crime, in countries with higher levels of income inequality (Fajnzylber 2002).
### Slavery
While most of us are accustomed to thinking of slavery in terms of the antebellum South, modern day slavery goes hand-in-hand with global inequality. In short, slavery refers to any situation in which people are sold, treated as property, or forced to work for little or no pay. Just as in the pre-Civil War United States, these humans are at the mercy of their employers. Chattel slavery, the form of slavery once practiced in the American South, occurs when one person owns another as property. Child slavery, which may include child prostitution, is a form of chattel slavery. In debt bondage, or bonded labor, the poor pledge themselves as servants in exchange for the cost of basic necessities like transportation, room, and board. In this scenario, people are paid less than they are charged for room and board. When travel is required, they can arrive in debt for their travel expenses and be unable to work their way free, since their wages do not allow them to ever get ahead.
The global watchdog group Anti-Slavery International recognizes other forms of slavery: human trafficking (in which people are moved away from their communities and forced to work against their will), child domestic work and child labor, and certain forms of servile marriage, in which women are little more than enslaved people (Anti-Slavery International 2012).
### Summary
When looking at the world’s poor, we first have to define the difference between relative poverty, absolute poverty, and subjective poverty. While those in relative poverty might not have enough to live at their country’s standard of living, those in absolute poverty do not have, or barely have, basic necessities such as food. Subjective poverty has more to do with one’s perception of one’s situation. North America and Europe are home to fewer of the world’s poor than Africa, which has most poor countries, or Asia, which has the most people living in poverty. Poverty has numerous negative consequences, from increased crime rates to a detrimental impact on physical and mental health.
### Section Quiz
### Short Answer
### Further Research
Students often think that the United States is immune to the atrocity of human trafficking. Check out this website to learn more about trafficking in the United States.
For more information about the ongoing practices of slavery in the modern world take a look at the Anti-Slavery International website.
### References
Aizenman, Nurith. 2016. "You Asked, We Answer: Can Microloans Lift Women Out of Poverty?" NPR. November 1 2016. (https://www.npr.org/sections/goatsandsoda/2016/11/01/500093608/you-asked-we-answer-can-tiny-loans-lift-women-out-of-poverty)
Anti-Slavery International. 2012. “What Is Modern Slavery?” Retrieved January 1, 2012 (http://www.antislavery.org/english/slavery_today/what_is_modern_slavery.aspx).
Barta, Patrick. 2009. “The Rise of the Underground.” Wall Street Journal, March 14. Retrieved January 1, 2012 (http://online.wsj.com/article/SB123698646833925567.html).
Buvinić, M. 1997. “Women in Poverty: A New Global Underclass.” Foreign Policy, Fall (108):1–7.
Chan, Emily. "Why Do We Still Know So Little About How Our Clothes Are Made?" Vogue. December 18 2019. (https://www.vogue.co.uk/fashion/article/how-are-our-clothes-actually-made)
Chen, Martha. 2001. “Women in the Informal Sector: A Global Picture, the Global Movement.” The SAIS Review 21:71–82
Chronicle of Higher Education. 2006. “Nearly Nude Penn State Students Protest Sweatshop Labor.” March 26. Retrieved January 4, 2012 (http://chronicle.com/article/Nearly-Nude-Penn-Staters/36772).
Fajnzylber, Pablo, Daniel Lederman, and Norman Loayza. 2002. “Inequality and Violent Crime.” Journal of Law and Economics 45:1–40.
International Labour Organization. 2012. “High Unemployment and Growing Inequality Fuel Social Unrest around the World.” Retrieved November 7, 2014 (http://www.ilo.org/global/about-the-ilo/newsroom/comment-analysis/WCMS_179430/lang--en/index.htm).
Karim, Naimul. 2020. "Fashion brands accused of exploiting workers at risk of layoffs." Thomson Reuters Foundation News. October 16 2020. (https://news.trust.org/item/20201015230800-amzjn
Neckerman, Kathryn, and Florencia Torche. 2007. “Inequality: Causes and Consequences.” Annual Review of Sociology 33:335–357.
Niner, Sara. 2018. "Why microfinance as aid isn't enugh to empower women." The Conversation. May 23, 2018. (https://theconversation.com/why-microfinance-as-aid-isnt-enough-to-empower-women-96632)
OECD. 2012. "Gender equality in education, employment and entrepreneurship." Meeting of the OECD Council at Ministerial Level, Paris: 1–252.
Schoch, Marta and Lakner, Christopher and Freije-Rodrigues, Samuel. 2020. " Monitoring poverty at the US$3.20 and US$5.50 lines: differences and similarities with extreme poverty trends." World Bank Blogs. November 19 2020. (https://blogs.worldbank.org/opendata/monitoring-poverty-us320-and-us550-lines-differences-and-similarities-extreme-poverty)
Scott, Lucy. 2012. "Female Empowerment and Extreme Poverty Reduction." United Nations University. June 6 2012. (https://unu.edu/publications/articles/female-empowerment-and-extreme-poverty-reduction.html#info)
Shah, Anup. 2011. “Poverty around the World.” Global Issues. Retrieved January 17, 2012 (http://www.globalissues.org/print/article/4).
U.S. Department of State. 2011a. “Background Note: Argentina.” Retrieved January 3, 2012 (http://www.state.gov/r/pa/ei/bgn/26516.htm).
U.S. Department of State. 2011b. “Background Note: China.” Retrieved January 3, 2012 (http://www.state.gov/r/pa/ei/bgn/18902.htm#econ).
U.S. Department of State. 2011c. “Background Note: Rwanda.” Retrieved January 3, 2012 (http://www.state.gov/r/pa/ei/bgn/2861.htm#econ).
USAS. 2021. “What is USAS.” August. Retrieved April 3, 2021 (http://usas.org/about).
World Bank. 2013. “Middle East and North Africa." Retrieved November 7, 2014 (http://web.worldbank.org/WBSITE/EXTERNAL/COUNTRIES/MENAEXT/0,,menuPK:247619~pagePK:146748~piPK:146812~theSitePK:256299,00.html).
World Bank. 2014e. “Poverty Overview.” Retrieved November 7, 2014 (http://www.worldbank.org/en/topic/poverty/overview).
World Poverty. 2012a. “Poverty in Africa, Famine and Disease.” Retrieved January 2, 2012 (http://world-poverty.org/povertyinafrica.aspx).
World Poverty. 2012b “Poverty in Asia, Caste and Progress.” Retrieved January 2, 2012 (http://world-poverty.org/povertyinasia.aspx).
World Poverty. 2012c. “Poverty in Latin America, Foreign Aid Debt Burdens.” Retrieved January 2, 2012 (http://world-poverty.org/povertyinlatinamerica.aspx).
World Bank. 2018 "Gender difference in poverty and household composition through the life- cycle: a global perspective." Policy research working paper: 8360 |
# Global Inequality
## Theoretical Perspectives on Global Stratification
As with any social issue, global or otherwise, scholars have developed a variety of theories to study global stratification. The two most widely applied perspectives are modernization theory and dependency theory.
### Modernization Theory
According to modernization theory, low-income countries are affected by their lack of industrialization and can improve their global economic standing through (Armer and Katsillis 2010):
1. an adjustment of cultural values and attitudes to work
2. industrialization and other forms of economic growth
Critics point out the inherent ethnocentric bias of this theory. It supposes all countries have the same resources and are capable of following the same path. In addition, it assumes that the goal of all countries is to be as “developed” as possible. There is no room within this theory for the possibility that industrialization and technology are not the best goals.
There is, of course, some basis for this assumption. Data show that core nations tend to have lower maternal and child mortality rates, longer life spans, and less absolute poverty. It is also true that in the poorest countries, millions of people die from the lack of clean drinking water and sanitation facilities, which are benefits most of us take for granted. At the same time, the issue is more complex than the numbers might suggest. Cultural equality, history, community, and local traditions are all at risk as modernization pushes into peripheral countries. The challenge, then, is to allow the benefits of modernization while maintaining a cultural sensitivity to what already exists.
### Dependency Theory
Dependency theory was created in part as a response to the Western-centric mindset of modernization theory. It states that global inequality is primarily caused by core nations (or high-income nations) exploiting semi-peripheral and peripheral nations (or middle-income and low-income nations), which creates a cycle of dependence (Hendricks 2010). As long as peripheral nations are dependent on core nations for economic stimulus and access to a larger piece of the global economy, they will never achieve stable and consistent economic growth. Further, the theory states that since core nations, as well as the World Bank, choose which countries to make loans to, and for what they will loan funds, they are creating highly segmented labor markets that are built to benefit the dominant market countries.
At first glance, it seems this theory ignores the formerly low-income nations that are now considered middle-income nations and are on their way to becoming high-income nations and major players in the global economy, such as China. But some dependency theorists would state that it is in the best interests of core nations to ensure the long-term usefulness of their peripheral and semi-peripheral partners. Following that theory, sociologists have found that entities are more likely to outsource a significant portion of a company’s work if they are the dominant player in the equation; in other words, companies want to see their partner countries healthy enough to provide work, but not so healthy as to establish a threat (Caniels and Roeleveld 2009).
### Summary
Modernization theory and dependency theory are two of the most common lenses sociologists use when looking at the issues of global inequality. Modernization theory posits that countries go through evolutionary stages and that industrialization and improved technology are the keys to forward movement. Dependency theory, on the other hand, sees modernization theory as Eurocentric and patronizing. With this theory, global inequality is the result of core nations creating a cycle of dependence by exploiting resources and labor in peripheral and semi-peripheral countries.
### Section Quiz
### Short Answer
### Further Research
For more information about economic modernization, check out the Hudson Institute.
Learn more about economic dependency at the University of Texas Inequality Project.
### References
Armer, J. Michael, and John Katsillis. 2010. “Modernization Theory.” Encyclopedia of Sociology, edited by E. F. Borgatta. Retrieved January 5, 2012 (http://edu.learnsoc.org/Chapters/3%20theories%20of%20sociology/11%20modernization%20theory.htm).
Caniels, Marjolein, C.J. Roeleveld, and Adriaan Roeleveld. 2009. “Power and Dependence Perspectives on Outsourcing Decisions.” European Management Journal 27:402–417. Retrieved January 4, 2012 (http://ou-nl.academia.edu/MarjoleinCaniels/Papers/645947/Power_and_dependence_perspectives_on_outsourcing_decisions).
Chang, Leslie T. 2008. Factory Girls: From Village to City in Changing China. New York: Random House.
Hendricks, John. 2010. “Dependency Theory.” Encyclopedia of Sociology, edited by E.F. Borgatta. Retrieved January 5, 2012 (http://edu.learnsoc.org/Chapters/3%20theories%20of%20sociology/5%20dependency%20theory.htm). |
# Race and Ethnicity
## Introduction
Trayvon Martin was a seventeen-year-old Black teenager. On the evening of February 26, 2012, he was visiting with his father and his father’s fiancée in the Sanford, Florida multi-ethnic gated community where his father's fiancée lived. Trayvon went on foot to buy a snack from a nearby convenience store. As he was returning, George Zimmerman, a White Hispanic man and the community’s neighborhood watch program coordinator, noticed him. In light of a recent rash of break-ins, Zimmerman called the police to report a person acting suspiciously, which he had done on many other occasions. During the call, Zimmerman said in reference to suspicious people, "[expletive] punks. Those [expletive], they always get away." The 911 operator told Zimmerman not to follow the teen, as was also stated in the police neighborhood watch guidelines that had been provided to Zimmerman. But Zimmerman did follow the teen, and, soon after, they had a physical confrontation. Several people in the community heard yelling, cries for help, and saw two people on the ground. According to Zimmerman, Martin attacked him, and in the ensuing scuffle, Zimmerman shot and killed Martin (CNN Library 2021).
A public outcry followed Martin’s death. There were allegations of racial profiling—the use of race alone to determine whether to detain or investigate someone. As part of the initial investigation, Zimmerman was extensively interviewed by police, but was released under Florida's "Stand Your Ground" Law, which indicated police could not arrest him for his actions. About six weeks later, Zimmerman was arrested and charged with second-degree murder by a special prosecutor, Angela Corey, who had been appointed by Florida's governor. In the ensuing trial, he was found not guilty (CNN Library 2021).
The shooting, the public response, and the trial that followed offer a snapshot of the sociology of race. Do you think race played a role in Martin’s death? Do you think race had an influence on the initial decision not to arrest Zimmerman, or on his later acquittal? Does society fear Black men, leading to racial profiling at an institutional level?
### References
CNN Library. (February 17, 2021). "Trayvon Martin Shooting Fast Facts." CNN US. Retrieved March 18, 2021 (http://www.cnn.com/2013/06/05/us/trayvon-martin-shooting-fast-facts/)
Davis, Guy. (June 1, 2020). “George Floyd protests go international as demonstrations break out across the world.” ABC News. Retrieved March 18, 2021 (https://abcnews.go.com/International/george-floyd-protests-international-demonstrations-break-world/story?id=70991689) |
# Race and Ethnicity
## Racial, Ethnic, and Minority Groups
While many students first entering a sociology classroom are accustomed to conflating the terms “race,” “ethnicity,” and “minority group,” these three terms have distinct meanings for sociologists. The idea of race refers to superficial physical differences that a particular society considers significant, while ethnicity describes shared culture. And the term "minority groups" describe groups that are subordinate, or that lack power in society regardless of skin color or country of origin. For example, in modern U.S. history, the elderly might be considered a minority group due to a diminished status that results from popular prejudice and discrimination against them. Ten percent of nursing home staff admitted to physically abusing an elderly person in the past year, and 40 percent admitted to committing psychological abuse (World Health Organization 2011). In this chapter we focus on racial and ethnic minorities.
### What Is Race?
A human race is a grouping of humankind based on shared physical or social qualities that can vary from one society to another.
Historically, the concept of race has changed across cultures and eras, and has eventually become less connected with ancestral and familial ties, and more concerned with superficial physical characteristics. In the past, theorists developed categories of race based on various geographic regions, ethnicities, skin colors, and more. Their labels for racial groups have connoted regions or skin tones, for example.
German physician, zoologist, and anthropologist Johann Friedrich Blumenbach (1752-1840) introduced one of the famous groupings by studying human skulls. Blumenbach divided humans into five races (MacCord 2014):
1. Caucasian or White race: people of European, Middle Eastern, and North African origin
2. Ethiopian or Black race: people of sub-Saharan Africans origin (sometimes spelled Aethiopian)
3. Malayan or Brown race: people of Southeast Asian origin and Pacific Islanders
4. Mongolian or Yellow race: people of all East Asian and some Central Asian origin
5. American or Red race: people of North American origin or American Indians
Over time, descriptions of race like Blumenbach's have fallen into disuse, and the social construction of race is a more accepted way of understanding racial categories. Social science organizations including the American Association of Anthropologists, the American Sociological Association, and the American Psychological Association have all officially rejected explanations of race like those listed above. Research in this school of thought suggests that race is not biologically identifiable and that previous racial categories were based on pseudoscience; they were often used to justify racist practices (Omi and Winant 1994; Graves 2003). For example, some people used to think that genetics of race determined intelligence. While this idea was mostly put to rest in the later 20th Century, it resurged several times in the past 50 years, including the widely read and cited 1994 book, The Bell Curve. Researchers have since provided substantial evidence that refutes a biological-racial basis for intelligence, including the widespread closing of IQ gaps as Black people gained more access to education (Dickens 2006). This research and other confirming studies indicate that any generally lower IQ among a racial group was more about nurture than nature, to put it into the terms of the Socialization chapter.
While many of the historical considerations of race have been corrected in favor of more accurate and sensitive descriptions, some of the older terms remain. For example, it is generally unacceptable and insulting to refer to Asian people or Native American people with color-based terminology, but it is acceptable to refer to White and Black people in that way. In 2020, a number of publications announced that they would begin capitalizing the names of races, though not everyone used the same approach (Seipel 2020). This practice comes nearly a hundred years after sociologist and leader W.E.B. Du Bois drove newsrooms to capitalize "Negro," the widely used term at the time. And, finally, some members of racial groups (or ethnic groups, which are described below) "reclaim" terms previously used to insult them (Rao 2018). These examples are more evidence of the social construction of race, and our evolving relationships among people and groups.
### What Is Ethnicity?
Ethnicity is sometimes used interchangeably with race, but they are very different concepts. Ethnicity is based on shared culture—the practices, norms, values, and beliefs of a group that might include shared language, religion, and traditions, among other commonalities. Like race, the term ethnicity is difficult to describe and its meaning has changed over time. And as with race, individuals may be identified or self-identify with ethnicities in complex, even contradictory, ways. For example, ethnic groups such as Irish, Italian American, Russian, Jewish, and Serbian might all be groups whose members are predominantly included in the “White” racial category. Ethnicity, like race, continues to be an identification method that individuals and institutions use today—whether through the census, diversity initiatives, nondiscrimination laws, or simply in personal day-to-day relations.
In some cases, ethnicity is incorrectly used as a synonym for national origin, but those constructions are technically different. National origin (itself sometimes confused with nationality) has to do with the geographic and political associations with a person's birthplace or residence. But people from a nation can be of a wide range of ethnicities, often unknown to people outside of the region, which leads to misconceptions. For example, someone in the United States may, with no ill-intent, refer to all Vietnamese people as an ethnic group. But Vietnam is home to 54 formally recognized ethnic groups.
Adding to the complexity: Sometimes, either to build bridges between ethnic groups, promote civil rights, gain recognition, or other reasons, diverse but closely associated ethnic groups may develop a "pan-ethnic" group. For example, the various ethnic groups and national origins of people from Vietnam, Cambodia, Laos, and adjoining nations, who may share cultural, linguistic, or other values, may group themselves together in a collective identity. If they do so, they may not seek to erase their individual ethnicities, but finding the correct description and association can be challenging and depend on context. The large number of people who make up the Asian American community may embrace their collective identity in the context of the United States. However, that embrace may depend on people's ages, and may be expressed differently when speaking to different populations (Park 2008). For example, someone who identifies as Asian American while at home in Houston may not refer to themselves as such when they visit extended family in Japan. In a similar manner, a grouping of people from Mexico, Central America and South America—often referred to as Latinx, Latina, or Latino—may be embraced by some and rejected by others in the group (Martinez 2019).
### What Are Minority Groups?
Sociologist Louis Wirth (1945) defined a minority group as “any group of people who, because of their physical or cultural characteristics, are singled out from the others in the society in which they live for differential and unequal treatment, and who therefore regard themselves as objects of collective discrimination.” The term minority connotes discrimination, and in its sociological use, the term subordinate group can be used interchangeably with the term minority group, while the term dominant group is often substituted for the group that represents rulers or is in the majority who can access power and privilege in a given society. These definitions correlate to the concept that the dominant group is that which holds the most power in a given society, while subordinate groups are those who lack power compared to the dominant group.
Note that being a numerical minority is not a characteristic of being a minority group; sometimes larger groups can be considered minority groups due to their lack of power. It is the lack of power that is the predominant characteristic of a minority, or subordinate group. For example, consider apartheid in South Africa, in which a numerical majority (the Black inhabitants of the country) were exploited and oppressed by the White minority.
According to Charles Wagley and Marvin Harris (1958), a minority group is distinguished by five characteristics: (1) unequal treatment and less power over their lives, (2) distinguishing physical or cultural traits like skin color or language, (3) involuntary membership in the group, (4) awareness of subordination, and (5) high rate of in-group marriage. Additional examples of minority groups might include the LGBTQ community, religious practitioners whose faith is not widely practiced where they live, and people with disabilities.
Scapegoat theory, developed initially from Dollard’s (1939) Frustration-Aggression theory, suggests that the dominant group will displace its unfocused aggression onto a subordinate group. History has shown us many examples of the scapegoating of a subordinate group. An example from the last century is the way Adolf Hitler blamed the Jewish population for Germany’s social and economic problems. In the United States, recent immigrants have frequently been the scapegoat for the nation’s—or an individual’s—woes. Many states have enacted laws to disenfranchise immigrants; these laws are popular because they let the dominant group scapegoat a subordinate group.
### Multiple Identities
Prior to the twentieth century, racial intermarriage (referred to as miscegenation) was extremely rare, and in many places, illegal. While the sexual subordination of enslaved people did result in children of mixed race, these children were usually considered Black, and therefore, property. There was no concept of multiple racial identities with the possible exception of the Creole. Creole society developed in the port city of New Orleans, where a mixed-race culture grew from French and African inhabitants. Unlike in other parts of the country, “Creoles of color” had greater social, economic, and educational opportunities than most African Americans.
Increasingly during the modern era, the removal of miscegenation laws and a trend toward equal rights and legal protection against racism have steadily reduced the social stigma attached to racial exogamy (exogamy refers to marriage outside a person’s core social unit). It is now common for the children of racially mixed parents to acknowledge and celebrate their various ethnic identities. Golfer Tiger Woods, for instance, has Chinese, Thai, African American, Native American, and Dutch heritage; he jokingly refers to his ethnicity as “Cablinasian,” a term he coined to combine several of his ethnic backgrounds. While this is the trend, it is not yet evident in all aspects of our society. For example, the U.S. Census only recently added additional categories for people to identify themselves, such as non-White Hispanic. A growing number of people chose multiple races to describe themselves on the 2020 Census, indicating that individuals have multiple identities.
### Summary
Race is fundamentally a social construct. Ethnicity is a term that describes shared culture and national origin. Minority groups are defined by their lack of power.
### Section Quiz
### Short Answer
### Further Research
Explore aspects of race and ethnicity at PBS’s site, “What Is Race?”.
### References
Caver, Helen Bush, and Mary T. Williams. 2011. “Creoles.” Multicultural America, Countries and Their Cultures, December 7. Retrieved February 13, 2012 (http://www.everyculture.com/multi/Bu-Dr/Creoles.html).
Dickens, William T. and Flynn, James R. 2006. "Black Americans Reduce the Racial IQ Gap." Psychological Science. Volume 17 Number 10. (http://www.iapsych.com/iqmr/fe/LinkedDocuments/dickens2006a.pdf)
Dollard, J., et al. 1939. Frustration and Aggression. New Haven, CT: Yale University Press.
Graves, Joseph. 2003. The Emperor's New Clothes: Biological Theories of Race at the Millennium. New Brunswick, NJ: Rutgers University Press.
MacCord, Kate. 2014. "Johann Friedrich Blumenbach (1752-1840)." Embryo Project Encyclopedia. Retrieved March 18, 2021 (http://embryo.asu.edu/handle/10776/7512).
Martinez, Daniel E. and Gonzalez, Kelsey E. 2019. "Panethnicity as a reactive identity: primary panethnic identification among Latino-Hispanics in the United States." Ethnic and Racial Studies. Volume 44 2021. (https://doi.org/10.1080/01419870.2020.1752392)
Omi, Michael, and Howard Winant. 1994. Racial Formation in the United States: from the 1960s to the 1990s (2nd ed.). New York, NY: Routledge.
Park, Jerry Z. 2008. "Second-Generation Asian American Pan-Ethnic Identity: Pluralized Meanings of a Racial Label." Sociological Perspectives. Volume 51, Issue 3. DOI: 10.1525/sop.2008.51.3.541
Rao, Sameer. 2018. "Can East Asian Americans Reclaim 'Yellow' for Themselves." Color Lines. September 28 2018. (https://www.colorlines.com/articles/read-can-east-asian-americans-reclaim-yellow-themselves)
Seipel, Brooke. 2020 "Why the AP and Others Are Now Capitalizing the 'B' in Black" The Hill. June 19 2020. (https://thehill.com/homenews/media/503642-why-the-ap-and-others-are-now-capitalizing-the-b-in-black)
Wagley, Charles, and Marvin Harris. 1958. Minorities in the New World: Six Case Studies. New York: Columbia University Press.
Wirth, Louis. 1945. “The Problem of Minority Groups.” The Science of Man in the World Crisis, edited by R. Linton: 347. In Hacker, Helen Mayer. 1951. Women as a Minority Group. Retrieved December 1, 2011 (http://media.pfeiffer.edu/lridener/courses/womminor.html).
World Health Organization. 2011. “Elder Maltreatment.” Fact Sheet N-357. Retrieved December 19, 2011 (http://www.who.int/mediacentre/factsheets/fs357/en/index.html). |
# Race and Ethnicity
## Theoretical Perspectives on Race and Ethnicity
### Theoretical Perspectives on Race and Ethnicity
We can examine race and ethnicity through three major sociological perspectives: functionalism, conflict theory, and symbolic interactionism. As you read through these theories, ask yourself which one makes the most sense and why.
### Functionalism
Functionalism emphasizes that all the elements of society have functions that promote solidarity and maintain order and stability in society. Hence, we can observe people from various racial and ethnic backgrounds interacting harmoniously in a state of social balance. Problems arise when one or more racial or ethnic groups experience inequalities and discriminations. This creates tension and conflict resulting in temporary dysfunction of the social system. For example, the killing of a Black man George Floyd by a White police officer in 2020 stirred up protests demanding racial justice and changes in policing in the United States. To restore the society’s pre-disturbed state or to seek a new equilibrium, the police department and various parts of the system require changes and compensatory adjustments.
Another way to apply the functionalist perspective to race and ethnicity is to discuss the way racism can contribute positively to the functioning of society by strengthening bonds between in-group members through the ostracism of out-group members. Consider how a community might increase solidarity by refusing to allow outsiders access. On the other hand, Rose (1951) suggested that dysfunctions associated with racism include the failure to take advantage of talent in the subjugated group, and that society must divert from other purposes the time and effort needed to maintain artificially constructed racial boundaries. Consider how much money, time, and effort went toward maintaining separate and unequal educational systems prior to the civil rights movement.
In the view of functionalism, racial and ethnic inequalities must have served an important function in order to exist as long as they have. This concept, sometimes, can be problematic. How can racism and discrimination contribute positively to society? Nash (1964) focused his argument on the way racism is functional for the dominant group, for example, suggesting that racism morally justifies a racially unequal society. Consider the way slave owners justified slavery in the antebellum South, by suggesting Black people were fundamentally inferior to White and preferred slavery to freedom.
### Interactionism
For symbolic interactionists, race and ethnicity provide strong symbols as sources of identity. In fact, some interactionists propose that the symbols of race, not race itself, are what lead to racism. Famed Interactionist Herbert Blumer (1958) suggested that racial prejudice is formed through interactions between members of the dominant group: Without these interactions, individuals in the dominant group would not hold racist views. These interactions contribute to an abstract picture of the subordinate group that allows the dominant group to support its view of the subordinate group, and thus maintains the status quo. An example of this might be an individual whose beliefs about a particular group are based on images conveyed in popular media, and those are unquestionably believed because the individual has never personally met a member of that group.
Another way to apply the interactionist perspective is to look at how people define their races and the race of others. Some people who claim a White identity have a greater amount of skin pigmentation than some people who claim a Black identity; how did they come to define themselves as Black or White?
### Conflict Theory
Conflict theories are often applied to inequalities of gender, social class, education, race, and ethnicity. A conflict theory perspective of U.S. history would examine the numerous past and current struggles between the White ruling class and racial and ethnic minorities, noting specific conflicts that have arisen when the dominant group perceived a threat from the minority group. In the late nineteenth century, the rising power of Black Americans after the Civil War resulted in draconian Jim Crow laws that severely limited Black political and social power. For example, Vivien Thomas (1910–1985), the Black surgical technician who helped develop the groundbreaking surgical technique that saves the lives of “blue babies” was classified as a janitor for many years, and paid as such, despite the fact that he was conducting complicated surgical experiments. The years since the Civil War have showed a pattern of attempted disenfranchisement, with gerrymandering and voter suppression efforts aimed at predominantly minority neighborhoods.
### Intersection Theory
Feminist sociologist Patricia Hill Collins (1990) further developed intersection theory, originally articulated in 1989 by Kimberlé Crenshaw, which suggests we cannot separate the effects of race, class, gender, sexual orientation, and other attributes (Figure 11.4). When we examine race and how it can bring us both advantages and disadvantages, it is important to acknowledge that the way we experience race is shaped, for example, by our gender and class. Multiple layers of disadvantage intersect to create the way we experience race. For example, if we want to understand prejudice, we must understand that the prejudice focused on a White woman because of her gender is very different from the layered prejudice focused on an Asian woman in poverty, who is affected by stereotypes related to being poor, being a woman, and her ethnic status.
### Culture of Prejudice
Culture of prejudice refers to the theory that prejudice is embedded in our culture. We grow up surrounded by images of stereotypes and casual expressions of racism and prejudice. Consider the casually racist imagery on grocery store shelves or the stereotypes that fill popular movies and advertisements. It is easy to see how someone living in the Northeastern United States, who may know no Mexican Americans personally, might gain a stereotyped impression from such sources as Speedy Gonzalez or Taco Bell’s talking Chihuahua. Because we are all exposed to these images and thoughts, it is impossible to know to what extent they have influenced our thought processes.
### Summary
Functionalist views of race study the role dominant and subordinate groups play to create a stable social structure. Conflict theorists examine power disparities and struggles between various racial and ethnic groups. Interactionists see race and ethnicity as important sources of individual identity and social symbolism. The concept of culture of prejudice recognizes that all people are subject to stereotypes that are ingrained in their culture.
### Section Quiz
### Short Answer
### Further Research
Are you aware of your own or others' privilege? Watch this TED Talk on White privilege to explore the concept.
### References
Collins, Patricia Hill. 2008. Distinguishing Features of Black Feminist Thought. London: Routledge.
Durkheim, Émile. 1982 [1895]. . Translated by W.D. Halls. New York: Free Press.
Nash, Manning. 1964. “Race and the Ideology of Race.” Current Anthropology 3(3): 285–288.
Rose, Arnold. 1958 [1951]. The Roots of Prejudice, fifth edition. Paris, France: Unesco. Retrieved November 19 (http://unesdoc.unesco.org/images/0007/000733/073342eo.pdf). |
# Race and Ethnicity
## Prejudice, Discrimination, and Racism
It is important to learn about stereotypes before discussing the terms prejudice, discrimination, and racism that are often used interchangeably in everyday conversation. Stereotypes are oversimplified generalizations about groups of people. Stereotypes can be based on race, ethnicity, age, gender, sexual orientation—almost any characteristic. They may be positive (usually about one’s own group) but are often negative (usually toward other groups, such as when members of a dominant racial group suggest that a subordinate racial group is stupid or lazy). In either case, the stereotype is a generalization that doesn’t take individual differences into account.
Where do stereotypes come from? In fact, new stereotypes are rarely created; rather, they are recycled from subordinate groups that have assimilated into society and are reused to describe newly subordinate groups. For example, many stereotypes that are currently used to characterize new immigrants were used earlier in American history to characterize Irish and Eastern European immigrants.
### Prejudice
Prejudice refers to the beliefs, thoughts, feelings, and attitudes someone holds about a group. A prejudice is not based on personal experience; instead, it is a prejudgment, originating outside actual experience. Recall from the chapter on Crime and Deviance that the criminalization of marijuana was based on anti-immigrant sentiment; proponents used fictional, fear-instilling stories of "reefer madness" and rampant immoral and illegal activities among Spanish-speaking people to justify new laws and harsh treatment of marijuana users. Many people who supported criminalizing marijuana had never met any of the new immigrants who were rumored to use it; the ideas were based in prejudice.
While prejudice is based in beliefs outside of experience, experience can lead people to feel that their prejudice is confirmed or justified. This is a type of confirmation bias. For example, if someone is taught to believe that a certain ethnic group has negative attributes, every negative act committed someone in that group can be seen as confirming the prejudice. Even a minor social offense committed by a member of the ethnic group, like crossing the street outside the crosswalk or talking too loudly on a bus, could confirm the prejudice.
While prejudice often originates outside experience, it isn't instinctive. Prejudice—as well as the stereotypes that lead to it and the discrimination that stems from it—is most often taught and learned. The teaching arrives in many forms, from direct instruction or indoctrination, to observation and socialization. Movies, books, charismatic speakers, and even a desire to impress others can all support the development of prejudices.
### Discrimination
While prejudice refers to biased thinking, discrimination consists of actions against a group of people. Discrimination can be based on race, ethnicity, age, religion, health, and other categories. For example, discrimination based on race or ethnicity can take many forms, from unfair housing practices such as redlining to biased hiring systems. Overt discrimination has long been part of U.S. history. In the late nineteenth century, it was not uncommon for business owners to hang signs that read, "Help Wanted: No Irish Need Apply." And southern Jim Crow laws, with their "Whites Only" signs, exemplified overt discrimination that is not tolerated today.
Discrimination also manifests in different ways. The scenarios above are examples of individual discrimination, but other types exist. Institutional discrimination occurs when a societal system has developed with embedded disenfranchisement of a group, such as the U.S. military's historical nonacceptance of minority sexualities (the "don't ask, don't tell" policy reflected this norm).
While the form and severity of discrimination vary significantly, they are considered forms of oppression. Institutional discrimination can also include the promotion of a group's status, such in the case of privilege, which is the benefits people receive simply by being part of the dominant group.
Most people have some level of privilege, whether it has to do with health, ability, race, or gender. When discussing race, the focus is often on White privilege, which is the societal privilege that benefits White people, or those perceived to be White, over non-White people in some societies, including the United States.
Most White people are willing to admit that non-White people live with a set of disadvantages due to the color of their skin. But until they gain a good degree of self-awareness, few people are willing to acknowledge the benefits they themselves receive by being a part of the dominant group. Why not? Some may feel it lessens their accomplishments, others may feel a degree of guilt, and still others may feel that admitting to privilege makes them seem like a bad or mean person. But White (or other dominant) privilege is an institutional condition, not a personal one. It exists whether the person asks for it or not. In fact, a pioneering thinker on the topic, Peggy McIntosh, noted that she didn't recognize privilege because, in fact, it was not based in meanness. Instead, it was an "invisible weightless knapsack full of special provisions" that she didn't ask for, yet from which she still benefitted (McIntosh 1989). As the reference indicates, McIntosh's first major publication about White privilege was released in 1989; many people have only become familiar with the term in recent years.
Prejudice and discrimination can overlap and intersect in many ways. To illustrate, here are four examples of how prejudice and discrimination can occur. Unprejudiced nondiscriminators are open-minded, tolerant, and accepting individuals. Unprejudiced discriminators might be those who unthinkingly practice sexism in their workplace by not considering women or gender nonconforming people for certain positions that have traditionally been held by men. Prejudiced nondiscriminators are those who hold racist beliefs but don't act on them, such as a racist store owner who serves minority customers. Prejudiced discriminators include those who actively make disparaging remarks about others or who perpetuate hate crimes.
### Racism
Racism is a stronger type of prejudice and discrimination used to justify inequalities against individuals by maintaining that one racial category is somehow superior or inferior to others; it is a set of practices used by a racial dominant group to maximize advantages for itself by disadvantaging racial minority groups. Such practices have affected wealth gap, employment, housing discrimination, government surveillance, incarceration, drug arrests, immigration arrests, infant mortality and much more (Race Forward 2021).
Broadly, individuals belonging to minority groups experience both individual racism and systemic racism during their lifetime. While reading the following some of the common forms of racism, ask yourself, “Am I a part of this racism?” “How can I contribute to stop racism?”
1. Individual or Interpersonal Racism refers to prejudice and discrimination executed by individuals consciously and unconsciously that occurs between individuals. Examples include telling a racist joke and believing in the superiority of White people.
2. Systemic Racism, also called structural racism or institutional racism, is systems and structures that have procedures or processes that disadvantages racial minority groups. Systemic racism occurs in organizations as discriminatory treatments and unfair policies based on race that result in inequitable outcomes for White people over people of color. For example, a school system where students of color are distributed into underfunded schools and out of the higher-resourced schools.
3. Racial Profiling is a type of systemic racism that involves the singling out of racial minorities for differential treatment, usually harsher treatment. The disparate treatment of racial minorities by law enforcement officials is a common example of racial profiling in the United States. For example, a study on the Driver's License Privilege to All Minnesota Residents from 2008 to 2010 found that the percentage of Latinos arrested was disproportionally high (Feist 2013). Similarly, the disproportionate number of Black men arrested, charged, and convicted of crimes reflect racial profiling.
4. Historical Racism is economic inequality or social disparity caused by past racism. For example, African-Americans have had their opportunities in wealth, education and employment adversely affected due to the mistreatment of their ancestors during the slavery and post-slavery period (Wilson 2012).
5. Cultural Racism occurs when the assumption of inferiority of one or more races is built into the culture of a society. For example, the European culture is considered supposedly more mature, evolved and rational than other cultures (Blaut 1992). A study showed that White and Asian American students with high GPAs experience greater social acceptance while Black and Native American students with high GPAs are rejected by their peers (Fuller-Rowell and Doan 2010).
6. Colorism is a form of racism, in which someone believes one type of skin tone is superior or inferior to another within a racial group. For example, if an employer believes a Black employee with a darker skin tone is less capable than a Black employee with lighter skin tone, that is colorism. Studies suggest that darker skinned African Americans experience more discrimination than lighter skinned African Americans (Herring, Keith, and Horton 2004; Klonoff and Landrine 2000).
7. Color-Avoidance Racism (sometimes referred to as "colorblind racism") is an avoidance of racial language by European-Americans that the racism is no longer an issue. The U.S. cultural narrative that typically focuses on individual racism fails to recognize systemic racism. It has arisen since the post-Civil Rights era and supports racism while avoiding any reference to race (Bonilla-Silva (2015).
### How to Be an Antiracist
Almost all mainstream voices in the United States oppose racism. Despite this, racism is prevalent in several forms. For example, when a newspaper uses people's race to identify individuals accused of a crime, it may enhance stereotypes of a certain minority. Another example of racist practices is racial steering, in which real estate agents direct prospective homeowners toward or away from certain neighborhoods based on their race.
Racist attitudes and beliefs are often more insidious and harder to pin down than specific racist practices. They become more complex due to implicit bias (also referred to as unconscious bias) which is the process of associating stereotypes or attitudes towards categories of people without conscious awareness – which can result in unfair actions and decisions that are at odds with one’s conscious beliefs about fairness and equality (Osta and Vasquez 2021). For example, in schools we often see “honors” and “gifted” classes quickly filled with White students while the majority of Black and Latino students are placed in the lower track classes. As a result, our mind consciously and unconsciously starts to associate Black and Latino students with being less intelligent, less capable. Osta and Vasquez (2021) argue that placing the student of color into a lower and less rigorous track, we reproduce the inequity and the vicious cycle of structural racism and implicit bias continues.
If everyone becomes antiracist, breaking the vicious cycle of structural racism and implicit bias may not be far away. To be antiracist is a radical choice in the face of history, requiring a radical reorientation of our consciousness (Kendi 2019). Proponents of anti-racism indicate that we must work collaboratively within ourselves, our institutions, and our networks to challenge racism at local, national and global levels. The practice of anti-racism is everyone’s ongoing work that everyone should pursue at least the following (Carter and Snyder 2020):
1. Understand and own the racist ideas in which we have been socialized and the racist biases that these ideas have created within each of us.
2. Identify racist policies, practices, and procedures and replace them with antiracist policies, practices, and procedures.
Anti-racism need not be confrontational in the sense of engaging in direct arguments with people, feeling terrible about your privilege, or denying your own needs or success. In fact, many people who are a part of a minority acknowledge the need for allies from the dominant group (Melaku 2020). Understanding and owning the racist ideas, and recognizing your own privilege, is a good and brave thing.
We cannot erase racism simply by enacting laws to abolish it, because it is embedded in our complex reality that relates to educational, economic, criminal, political, and other social systems. Importantly, everyone can become antiracist by making conscious choices daily. Being racist or antiracist is not about who you are; it is about what you do (Carter and Snyder 2020).
What does it mean to you to be an “anti-racist”? How do see the recent events or protests in your community, country or somewhere else? Are they making any desired changes?
### Summary
Stereotypes are oversimplified ideas about groups of people. Prejudice refers to thoughts and feelings, while discrimination refers to actions. Racism is both prejudice and discrimination due to the belief that one race is inherently superior or inferior to other races. Antiracists fight against the systems of racism by employing antiracist policies and practices in institutions and communities.
### Section Quiz
### Short Answer
### Further Research
How far should First Amendment rights extend? Read more about the subject at the First Amendment Center.
Learn more about institutional racism at the Southern Poverty Law Center's website.
Learn more about how prejudice develops by watching the short documentary "Eye of the Storm"
### References
Blaut, James M. 1992. "The theory of cultural racism." Antipode. 24(4): 289-299.
Bonilla-Silva, Eduardo. 2015. The structure of racism in color-blind, “post-racial” America. American Behavioral Scientist. 59:1358-76.
Bouie, Jamelle. (August 19, 2014). "Why the Fires in Ferguson Won't End Soon." Slate.com. Retrieved October 9, 2014 (http://www.slate.com/articles/news_and_politics/politics/2014/08/ferguson_protests_over_michael_brown_won_t_end_soon_the_black_community.2.html).
Carter, Jordan, and Ian Snyder. (July 21, 2020). “What Does It Mean to Be an Anti-racist?” National League of Cities (NLC). Retrieved March 18, 2021 (https://www.nlc.org/article/2020/07/21/what-does-it-mean-to-be-an-anti-racist/).
Feist, Benjamin, Teresa Nelson, and Ian Bratlie. 2013. "Racial Profiling in Greater Minnesota and the Case for Expanding the Driver's License Privilege to All Minnesota Residents." Law Raza. 5(1): 3.
Fuller-Rowell, Thomas E., and Stacey N. Doan. 2010. “The social costs of academic success across ethnic groups.” Child development. 81(6): 1696-1713.
Herring, C., V. M. Keith, and H.D. Horton. 2004. Skin Deep: How Race and Complexion Matter in the “Color-Blind” Era (Ed.), Chicago, IL: University of Illinois Press.
Hudson, David L. 2009. “Students Lose Confederate-Flag Purse Case in 5th Circuit.” Retrieved December 7, 2011 (http://www.firstamendmentcenter.org/students-lose-confederate-flag-purse-case-in-5th-circuit).
Kendi, Ibram X. 2019. How to be an antiracist. One world.
Klonoff, E., and H. Landrine. 2000. “Is Skin Color a Marker for Racial Discrimination? Explaining the Skin Color-Hypertension Relationship.” Journal of Behavioral Medicine. 23: 329–338.
Landor, Antoinette M., Leslie Gordon Simons, Ronald L. Simons, Gene H. Brody, Chalandra M. Bryant, Frederick X. Gibbons, Ellen M. Granberg, and Janet N. Melby. 2013. "Exploring the impact of skin tone on family dynamics and race-related outcomes." Journal of Family Psychology. 27 (5): 817-826.
Lowery, Wesley and Darryl Fears. (August 31, 2014). "Michael Brown and Dorian Johnson, the friend who witnessed his shooting". The Washington Post. Retrieved October 9 , 2014. (http://www.washingtonpost.com/politics/michael-brown-and-dorian-johnson-the-friend-who-witnessed-his-shooting/2014/08/31/bb9b47ba-2ee2-11e4-9b98-848790384093_story.html).
McIntosh, Peggy. 1988. “White Privilege: Unpacking the Invisible Knapsack.” White Privilege and Male Privilege: A Personal Account of Coming to See Correspondences Through Work in Women’s Studies. Wellesley, MA: Wellesley College Center for Research on Women.
Melaku, Tsedele and Beeman, Angie and Smith, David G. and Johnson, Brad W. 2020. "Be A Better Ally."
Missouri Attorney General’s Office. (n.d.) "Racial Profiling Report." Retrieved October 9, 2014 (http://ago.mo.gov/VehicleStops/2013/reports/161.pdf).
Osta, Kathleen, and Hugh Vasquez. 2021. “Implicit Bias and Structural Racialization”. National Equity Project. Retrieved March 18, 2021 (https://www.nationalequityproject.org/frameworks/implicit-bias-structural-racialization).
Race Forward. 2021. “What Is Systemic Racism?” Retrieved March 18, 2021 (https://www.raceforward.org/videos/systemic-racism).
Nobles, Frances, and Julie Bosman. (August 17, 2014). "Autopsy Shows Michael Brown Was Struck at Least Six Times." The New York Times. Retrieved October 9, 2014 (http://www.nytimes.com/2014/08/18/us/michael-brown-autopsy-shows-he-was-shot-at-least-6-times.html).
Wilson, William Julius. 2012. The Truly Disadvantaged: The inner city, the underclass, and public policy. University of Chicago Press.
Wilson, William Julius. 2012. The Truly Disadvantaged: The inner city, the underclass, and public policy. University of Chicago Press.
Yerevanci. 2013. "Public Opinion of Interracial Marriage in the United States." Wikimedia Commons. Retrieved December 23, 2014 (http://commons.wikimedia.org/wiki/File:Public_opinion_of_interracial_marriage_in_the_United_States.png). |
# Race and Ethnicity
## Intergroup Relationships
Intergroup relations (relationships between different groups of people) range along a spectrum between tolerance and intolerance. The most tolerant form of intergroup relations is pluralism, in which no distinction is made between minority and majority groups, but instead there’s equal standing. At the other end of the continuum are amalgamation, expulsion, and even genocide—stark examples of intolerant intergroup relations.
### Pluralism
Pluralism is represented by the ideal of the United States as a “salad bowl”: a great mixture of different cultures where each culture retains its own identity and yet adds to the flavor of the whole. True pluralism is characterized by mutual respect on the part of all cultures, both dominant and subordinate, creating a multicultural environment of acceptance. In reality, true pluralism is a difficult goal to reach. In the United States, the mutual respect required by pluralism is often missing, and the nation’s past model of a melting pot posits a society where cultural differences aren’t embraced as much as erased.
### Assimilation
Assimilation describes the process by which a minority individual or group gives up its own identity by taking on the characteristics of the dominant culture. In the United States, which has a history of welcoming and absorbing immigrants from different lands, assimilation has been a function of immigration.
Most people in the United States have immigrant ancestors. In relatively recent history, between 1890 and 1920, the United States became home to around 24 million immigrants. In the decades since then, further waves of immigrants have come to these shores and have eventually been absorbed into U.S. culture, sometimes after facing extended periods of prejudice and discrimination. Assimilation may lead to the loss of the minority group’s cultural identity as they become absorbed into the dominant culture, but assimilation has minimal to no impact on the majority group’s cultural identity.
Some groups may keep only symbolic gestures of their original ethnicity. For instance, many Irish Americans may celebrate Saint Patrick’s Day, many Hindu Americans enjoy a Diwali festival, and many Mexican Americans may celebrate Cinco de Mayo (a May 5 acknowledgment of the Mexican victory over the French Empire at the Battle of Puebla). However, for the rest of the year, other aspects of their originating culture may be forgotten.
Assimilation is antithetical to the “salad bowl” created by pluralism; rather than maintaining their own cultural flavor, subordinate cultures give up their own traditions in order to conform to their new environment. Sociologists measure the degree to which immigrants have assimilated to a new culture with four benchmarks: socioeconomic status, spatial concentration, language assimilation, and intermarriage. When faced with racial and ethnic discrimination, it can be difficult for new immigrants to fully assimilate. Language assimilation, in particular, can be a formidable barrier, limiting employment and educational options and therefore constraining growth in socioeconomic status.
### Amalgamation
Amalgamation is the process by which a minority group and a majority group combine to form a new group. Amalgamation creates the classic “melting pot” analogy; unlike the “salad bowl,” in which each culture retains its individuality, the “melting pot” ideal sees the combination of cultures that results in a new culture entirely.
Amalgamationin the form of miscegenation is achieved through intermarriage between races. In the United States, antimiscegenation laws, which criminalized interracial marriage, flourished in the South during the Jim Crow era. It wasn’t until 1967’s Loving v. Virginia that the last antimiscegenation law was struck from the books, making these laws unconstitutional.
### Genocide
Genocide, the deliberate annihilation of a targeted (usually subordinate) group, is the most toxic intergroup relationship. Historically, we can see that genocide has included both the intent to exterminate a group and the function of exterminating of a group, intentional or not.
Possibly the most well-known case of genocide is Hitler’s attempt to exterminate the Jewish people in the first part of the twentieth century. Also known as the Holocaust, the explicit goal of Hitler’s “Final Solution” was the eradication of European Jewish people, as well as the destruction of other minority groups such as Catholics, people with disabilities, and LGBTQ people. With forced emigration, concentration camps, and mass executions in gas chambers, Hitler’s Nazi regime was responsible for the deaths of 12 million people, 6 million of whom were Jewish. Hitler’s intent was clear, and the high Jewish death toll certainly indicates that Hitler and his regime committed genocide. But how do we understand genocide that is not so overt and deliberate?
The treatment of the Native Americans by the European colonizers is an example of genocide committed against indigenous people. Some historians estimate that Native American populations dwindled from approximately 12 million people in the year 1500 to barely 237,000 by the year 1900 (Lewy 2004). European settlers coerced American Indians off their own lands, often causing thousands of deaths in forced removals, such as occurred in the Cherokee or Potawatomi Trail of Tears. Settlers also enslaved Native Americans and forced them to give up their religious and cultural practices. But the major cause of Native American death was neither slavery nor war nor forced removal: it was the introduction of European diseases and Native American lack of immunity to them. Smallpox, diphtheria, and measles flourished among indigenous American tribes who had no exposure to the diseases and no ability to fight them. Quite simply, these diseases decimated the tribes. The use of diseases as weapon was most likely unintentional in some cases and intentional in others. For example, during the Seven Years War, the British gave smallpox-infected blankets to the Native tribes in order to "reduce them," and this and similar practices likely continued throughout the centuries-long assault on the Native American people.
Genocide is not a just a historical concept; it is practiced even in the twenty- first century. For example, ethnic and geographic conflicts in the Darfur region of Sudan have led to hundreds of thousands of deaths. As part of an ongoing land conflict, the Sudanese government and their state-sponsored Janjaweed militia have led a campaign of killing, forced displacement, and systematic rape of Darfuri people. Although a treaty was signed in 2011, the peace is fragile.
### Expulsion
Expulsion refers to a subordinate group being forced, by a dominant group, to leave a certain area or country. As seen in the examples of the Trail of Tears and the Holocaust, expulsion can be a factor in genocide. However, it can also stand on its own as a destructive group interaction. Expulsion has often occurred historically with an ethnic or racial basis. In the United States, President Franklin D. Roosevelt issued Executive Order 9066 in 1942, after the Japanese government’s attack on Pearl Harbor. The Order authorized the establishment of internment camps for anyone with as little as one-eighth Japanese ancestry (i.e., one great-grandparent who was Japanese). Over 120,000 legal Japanese residents and Japanese U.S. citizens, many of them children, were held in these camps for up to four years, despite the fact that there was never any evidence of collusion or espionage. (In fact, many Japanese Americans continued to demonstrate their loyalty to the United States by serving in the U.S. military during the War.) In the 1990s, the U.S. executive branch issued a formal apology for this expulsion; reparation efforts continue today.
### Segregation
Segregation refers to the physical separation of two groups, particularly in residence, but also in workplace and social functions. It is important to distinguish between de jure segregation (segregation that is enforced by law) and de facto segregation (segregation that occurs without laws but because of other factors). A stark example of de jure segregation is the apartheid movement of South Africa, which existed from 1948 to 1994. Under apartheid, Black South Africans were stripped of their civil rights and forcibly relocated to areas that segregated them physically from their White compatriots. Only after decades of degradation, violent uprisings, and international advocacy was apartheid finally abolished.
De jure segregation occurred in the United States for many years after the Civil War. During this time, many former Confederate states passed Jim Crow laws that required segregated facilities for Black and White people. These laws were codified in 1896’s landmark Supreme Court case Plessy v. Ferguson, which stated that “separate but equal” facilities were constitutional. For the next five decades, Black people were subjected to legalized discrimination, forced to live, work, and go to school in separate—but unequal—facilities. It wasn’t until 1954 and the Brown v. Board of Education case that the Supreme Court declared that “separate educational facilities are inherently unequal,” thus ending de jure segregation in the United States.
De facto segregation, however, cannot be abolished by any court mandate. Few institutions desegregated as a result of Brown; in fact, government and even military intervention was necessary to enforce the ruling, and it took the Civil Rights Act and other laws to formalize the equality. Segregation is still alive and well in the United States, with different racial or ethnic groups often segregated by neighborhood, borough, or parish. Sociologists use segregation indices to measure racial segregation of different races in different areas. The indices employ a scale from zero to 100, where zero is the most integrated and 100 is the least. In the New York metropolitan area, for instance, the Black-White segregation index was seventy-nine for the years 2005–2009. This means that 79 percent of either Black or White people would have to move in order for each neighborhood to have the same racial balance as the whole metro region (Population Studies Center 2010).
### Summary
Intergroup relations range from a tolerant approach of pluralism to intolerance as severe as genocide. In pluralism, groups retain their own identity. In assimilation, groups conform to the identity of the dominant group. In amalgamation, groups combine to form a new group identity.
### Section Quiz
### Short Answer
### Further Research
So you think you know your own assumptions? Check and find out with the Implicit Association Test
What do you know about the treatment of Australia’s aboriginal population? Find out more by viewing the feature-length documentary .
### References
Asi, Maryam, and Daniel Beaulieu. 2013. “Arab Households in the United States: 2006–2010.” U.S. Census Bureau. Retrieved November 19, 2014 (http://www.census.gov/prod/2013pubs/acsbr10-20.pdf).
Lewy, Guenter. 2004. “Were American Indians the Victims of Genocide?” Retrieved December 6, 2011 (http://hnn.us/articles/7302.html).
Norris, Tina, Paula L. Vines, and Elizabeth M. Hoeffel. 2012. “The American Indian and Alaska Native Population: 2010.” U.S. Census Bureau. Retrieved November 19, 2014 (http://www.census.gov/prod/cen2010/briefs/c2010br-10.pdf).
Population Studies Center. 2010. “New Racial Segregation Measures for States and Large Metropolitan Areas: Analysis of the 2005–2009 American Community Survey.” Population Studies Center: Institute for Social Research. Retrieved November 29, 2011 (http://www.psc.isr.umich.edu/dis/census/segregation.html).
Tatz, Colin. 2006. "Confronting Australian Genocide." The Indigenous Experience: Global Perspectives. Edited by Roger Maaka and Chris Andersen. Toronto, Canada: Canadian Scholars Press.
U.S. Census Bureau. 2014. “State and County Quickfacts.” Retrieved November 19, 2014 (http://quickfacts.census.gov/qfd/states/00000.html). |
# Race and Ethnicity
## Race and Ethnicity in the United States
When colonists came to the New World, they found a land that did not need “discovering” since it was already inhabited. While the first wave of immigrants came from Western Europe, eventually the bulk of people entering North America were from Northern Europe, then Eastern Europe, then Latin America and Asia. And let us not forget the forced immigration of enslaved Africans. Most of these groups underwent a period of disenfranchisement in which they were relegated to the bottom of the social hierarchy before they managed (for those who could) to achieve social mobility. Because of this achievement, the U.S. is still a “dream destination” for millions of people living in other countries. Many thousands of people, including children, arrive here every year both documented and undocumented. Most Americans welcome and support new immigrants wholeheartedly. For example, the Development, Relief, and Education for Alien Minors (DREAM) Act introduced in 2001 provides a means for undocumented immigrants who arrived in the U.S. as children to gain a pathway to permanent legal status. Similarly, the Deferred Action for Childhood Arrivals (DACA) introduced in 2012 gives young undocumented immigrants a work permit and protection from deportation (Georgetown Law 2021). Today, the U.S. society is multicultural, multiracial and multiethnic that is composed of people from several national origins.
The U.S. Census Bureau collects racial data in accordance with guidelines provided by the U.S. Office of Management and Budget (OMB 2016). These data are based on self-identification; generally reflect a social definition of race recognized in this country that include racial and national origin or sociocultural groups. People may choose to report more than one race to indicate their racial mixture, such as “American Indian” and “White.” People who identify their origin as Hispanic, Latino, or Spanish may be of any race. OMB requires five minimum categories: White, Black or African American, American Indian or Alaska Native, Asian, and Native Hawaiian or Other Pacific Islander. The U.S. Census Bureau’s QuickFacts as of July 1, 2019 showed that over 328 million people representing various racial groups were living in the U.S. ().
To clarify the terminology in the table, note that the U.S. Census Bureau defines racial groups as follows:
1. White – A person having origins in any of the original peoples of Europe, the Middle East, or North Africa.
2. Black or African American – A person having origins in any of the Black racial groups of Africa.
3. American Indian or Alaska Native – A person having origins in any of the original peoples of North and South America (including Central America) and who maintains tribal affiliation or community attachment.
4. Asian – A person having origins in any of the original peoples of the Far East, Southeast Asia, or the Indian subcontinent including, for example, Cambodia, China, India, Japan, Korea, Malaysia, Pakistan, the Philippine Islands, Thailand, and Vietnam.
5. Native Hawaiian or Other Pacific Islander – A person having origins in any of the original peoples of Hawaii, Guam, Samoa, or other Pacific Islands.
Information on race is required for many Federal programs and is critical in making policy decisions, particularly for civil rights including racial justice. States use these data to meet legislative redistricting principles. Race data also are used to promote equal employment opportunities and to assess racial disparities in health and environmental risks that demonstrates the extent to which this multiculturality is embraced. The many manifestations of multiculturalism carry significant political repercussions. The sections below will describe how several groups became part of U.S. society, discuss the history of intergroup relations for each faction, and assess each group’s status today.
### Native Americans
Native Americans are Indigenous peoples, the only nonimmigrant people in the United States. According to the National Congress of American Indians, Native Americans are “All Native people of the United States and its trust territories (i.e., American Indians, Alaska Natives, Native Hawaiians, Chamorros, and American Samoans), as well as persons from Canadian First Nations and Indigenous communities in Mexico and Central and South America who are U.S. residents (NCAI 2020, p. 11).” Native Americans once numbered in the millions but by 2010 made up only 0.9 percent of U.S. populace; see above (U.S. Census 2010). Currently, about 2.9 million people identify themselves as Native American alone, while an additional 2.3 million identify themselves as Native American mixed with another ethnic group (Norris, Vines, and Hoeffel 2012).
### History of Intergroup Relations
Native American culture prior to European settlement is referred to as Pre-Columbian: that is, prior to the coming of Christopher Columbus in 1492. Mistakenly believing that he had landed in the East Indies, Columbus named the indigenous people “Indians,” a name that has persisted for centuries despite being a geographical misnomer and one used to blanket hundreds of sovereign tribal nations (NCAI 2020).
The history of intergroup relations between European colonists and Native Americans is a brutal one. As discussed in the section on genocide, the effect of European settlement of the Americans was to nearly destroy the indigenous population. And although Native Americans’ lack of immunity to European diseases caused the most deaths, overt mistreatment and massacres of Native Americans by Europeans were devastating as well.
From the first Spanish colonists to the French, English, and Dutch who followed, European settlers took what land they wanted and expanded across the continent at will. If indigenous people tried to retain their stewardship of the land, Europeans fought them off with superior weapons. Europeans’ domination of the Americas was indeed a conquest; one scholar points out that Native Americans are the only minority group in the United States whose subordination occurred purely through conquest by the dominant group (Marger 1993).
After the establishment of the United States government, discrimination against Native Americans was codified and formalized in a series of laws intended to subjugate them and keep them from gaining any power. Some of the most impactful laws are as follows:
1. The Indian Removal Act of 1830 forced the relocation of any Native tribes east of the Mississippi River to lands west of the river.
2. The Indian Appropriation Acts funded further removals and declared that no Indian tribe could be recognized as an independent nation, tribe, or power with which the U.S. government would have to make treaties. This made it even easier for the U.S. government to take land it wanted.
3. The Dawes Act of 1887 reversed the policy of isolating Native Americans on reservations, instead forcing them onto individual properties that were intermingled with White settlers, thereby reducing their capacity for power as a group.
Native American culture was further eroded by the establishment of boarding schools in the late nineteenth century. These schools, run by both Christian missionaries and the United States government, had the express purpose of “civilizing” Native American children and assimilating them into White society. The boarding schools were located off-reservation to ensure that children were separated from their families and culture. Schools forced children to cut their hair, speak English, and practice Christianity. Physical and sexual abuses were rampant for decades; only in 1987 did the Bureau of Indian Affairs issue a policy on sexual abuse in boarding schools. Some scholars argue that many of the problems that Native Americans face today result from almost a century of mistreatment at these boarding schools.
### Current Status
The eradication of Native American culture continued until the 1960s, when Native Americans were able to participate in and benefit from the civil rights movement. The Indian Civil Rights Act of 1968 guaranteed Indian tribes most of the rights of the United States Bill of Rights. New laws like the Indian Self-Determination Act of 1975 and the Education Assistance Act of the same year recognized tribal governments and gave them more power. Indian boarding schools have dwindled to only a few, and Native American cultural groups are striving to preserve and maintain old traditions to keep them from being lost forever. Today, Native Americans are citizens of three sovereigns: their tribal nations, the United States, and the state in which they reside (NCAI 2020).
However, Native Americans (some of whom wish to be called American Indians so as to avoid the “savage” connotations of the term “native”) still suffer the effects of centuries of degradation. Long-term poverty, inadequate education, cultural dislocation, and high rates of unemployment contribute to Native American populations falling to the bottom of the economic spectrum. Native Americans also suffer disproportionately with lower life expectancies than most groups in the United States.
### African Americans
As discussed in the section on race, the term African American can be a misnomer for many individuals. Many people with dark skin may have their more recent roots in Europe or the Caribbean, seeing themselves as Dominican American or Dutch American, for example. Further, actual immigrants from Africa may feel that they have more of a claim to the term African American than those who are many generations removed from ancestors who originally came to this country.
The U.S. Census Bureau (2019) estimates that at least 13.4 percent of the United States' population is Black.
### How and Why They Came
African Americans are the exemplar minority group in the United States whose ancestors did not come here by choice. A Dutch sea captain brought the first Africans to the Virginia colony of Jamestown in 1619 and sold them as indentured servants. (Indentured servants are people who are committed to work for a certain period of time, typically without formal pay). This was not an uncommon practice for either Black or White people, and indentured servants were in high demand. For the next century, Black and White indentured servants worked side by side. But the growing agricultural economy demanded greater and cheaper labor, and by 1705, Virginia passed the slave codes declaring that any foreign-born non-Christian could be enslaved, and that enslaved people were considered property.
The next 150 years saw the rise of U.S. slavery, with Black Africans being kidnapped from their own lands and shipped to the New World on the trans-Atlantic journey known as the Middle Passage. Once in the Americas, the Black population grew until U.S.-born Black people outnumbered those born in Africa. But colonial (and later, U.S.) slave codes declared that the child of an enslaved person was also an enslaved person, so the slave class was created. By 1808, the slave trade was internal in the United States, with enslaved people being bought and sold across state lines like livestock.
### History of Intergroup Relations
There is no starker illustration of the dominant-subordinate group relationship than that of slavery. In order to justify their severely discriminatory behavior, slaveholders and their supporters viewed Black people as innately inferior. Enslaved people were denied even the most basic rights of citizenship, a crucial factor for slaveholders and their supporters. Slavery poses an excellent example of conflict theory’s perspective on race relations; the dominant group needed complete control over the subordinate group in order to maintain its power. Whippings, executions, rapes, and denial of schooling and health care were widely practiced.
Slavery eventually became an issue over which the nation divided into geographically and ideologically distinct factions, leading to the Civil War. And while the abolition of slavery on moral grounds was certainly a catalyst to war, it was not the only driving force. Students of U.S. history will know that the institution of slavery was crucial to the Southern economy, whose production of crops like rice, cotton, and tobacco relied on the virtually limitless and cheap labor that slavery provided. In contrast, the North didn’t benefit economically from slavery, resulting in an economic disparity tied to racial/political issues.
A century later, the civil rights movement was characterized by boycotts, marches, sit-ins, and freedom rides: demonstrations by a subordinate group and their supporters that would no longer willingly submit to domination. The major blow to America’s formally institutionalized racism was the Civil Rights Act of 1964. This Act, which is still important today, banned discrimination based on race, color, religion, sex, or national origin.
### Current Status
Although government-sponsored, formalized discrimination against African Americans has been outlawed, true equality does not yet exist. The National Urban League’s 2020 Equality Index reports that Black people’s overall equality level with White people has been generally improving. Measuring standards of civic engagement, economics, education, and others, Black people had an equality level of 71 percent in 2010 and had an equality level of 74 percent in 2020. The Index, which has been published since 2005, notes a growing trend of increased inequality with White people, especially in the areas of unemployment, insurance coverage, and incarceration. Black people also trail White people considerably in the areas of economics, health, and education (National Urban League 2020).
To what degree do racism and prejudice contribute to this continued inequality? The answer is complex. 2008 saw the election of this country’s first African American president: Barack Obama. Despite being popularly identified as Black, we should note that President Obama is of a mixed background that is equally White, and although all presidents have been publicly mocked at times (Gerald Ford was depicted as a klutz, Bill Clinton as someone who could not control his libido), a startling percentage of the critiques of Obama were based on his race. In a number of other chapters, we discuss racial disparities in healthcare, education, incarceration, and other areas.
Although Black people have come a long way from slavery, the echoes of centuries of disempowerment are still evident.
### Asian Americans
Asian Americans represent a great diversity of cultures and backgrounds. The experience of a Japanese American whose family has been in the United States for three generations will be drastically different from a Laotian American who has only been in the United States for a few years. This section primarily discusses Chinese, Japanese, Korean, and Vietnamese immigrants and shows the differences between their experiences. The most recent estimate from the U.S. Census Bureau (2019) suggest about 5.9 percent of the population identify themselves as Asian.
### How and Why They Came
The national and ethnic diversity of Asian American immigration history is reflected in the variety of their experiences in joining U.S. society. Asian immigrants have come to the United States in waves, at different times, and for different reasons.
The first Asian immigrants to come to the United States in the mid-nineteenth century were Chinese. These immigrants were primarily men whose intention was to work for several years in order to earn incomes to support their families in China. Their main destination was the American West, where the Gold Rush was drawing people with its lure of abundant money. The construction of the Transcontinental Railroad was underway at this time, and the Central Pacific section hired thousands of migrant Chinese men to complete the laying of rails across the rugged Sierra Nevada mountain range. Chinese men also engaged in other manual labor like mining and agricultural work. The work was grueling and underpaid, but like many immigrants, they persevered.
Japanese immigration began in the 1880s, on the heels of the Chinese Exclusion Act of 1882. Many Japanese immigrants came to Hawaii to participate in the sugar industry; others came to the mainland, especially to California. Unlike the Chinese, however, the Japanese had a strong government that negotiated with the U.S. government to ensure the well-being of their immigrants. Japanese men were able to bring their wives and families to the United States, and were thus able to produce second- and third-generation Japanese Americans more quickly than their Chinese counterparts.
The most recent large-scale Asian immigration came from Korea and Vietnam and largely took place during the second half of the twentieth century. While Korean immigration has been fairly gradual, Vietnamese immigration occurred primarily post-1975, after the fall of Saigon and the establishment of restrictive communist policies in Vietnam. Whereas many Asian immigrants came to the United States to seek better economic opportunities, Vietnamese immigrants came as political refugees, seeking asylum from harsh conditions in their homeland. The Refugee Act of 1980 helped them to find a place to settle in the United States.
### History of Intergroup Relations
Chinese immigration came to an abrupt end with the Chinese Exclusion Act of 1882. This act was a result of anti-Chinese sentiment burgeoned by a depressed economy and loss of jobs. White workers blamed Chinese migrants for taking jobs, and the passage of the Act meant the number of Chinese workers decreased. Chinese men did not have the funds to return to China or to bring their families to the United States, so they remained physically and culturally segregated in the Chinatowns of large cities. Later legislation, the Immigration Act of 1924, further curtailed Chinese immigration. The Act included the race-based National Origins Act, which was aimed at keeping U.S. ethnic stock as undiluted as possible by reducing “undesirable” immigrants. It was not until after the Immigration and Nationality Act of 1965 that Chinese immigration again increased, and many Chinese families were reunited.
Although Japanese Americans have deep, long-reaching roots in the United States, their history here has not always been smooth. The California Alien Land Law of 1913 was aimed at them and other Asian immigrants, and it prohibited immigrants from owning land. An even uglier action was the Japanese internment camps of World War II, discussed earlier as an illustration of expulsion.
### Current Status
Asian Americans certainly have been subject to their share of racial prejudice, despite the seemingly positive stereotype as the model minority. The model minority stereotype is applied to a minority group that is seen as reaching significant educational, professional, and socioeconomic levels without challenging the existing establishment.
This stereotype is typically applied to Asian groups in the United States, and it can result in unrealistic expectations by putting a stigma on members of this group that do not meet the expectations. Stereotyping all Asians as smart and capable can also lead to a lack of much-needed government assistance and to educational and professional discrimination.
### White Americans
White Americans are the dominant racial group in the United States. According to the U.S. Census Bureau (2019), 76.3 percent of U.S. adults currently identify themselves as White alone. In this section, we will focus on German, Irish, Italian, and Eastern European immigrants.
### Why They Came
White ethnic Europeans formed the second and third great waves of immigration, from the early nineteenth century to the mid-twentieth century. They joined a newly minted United States that was primarily made up of White Protestants from England. While most immigrants came searching for a better life, their experiences were not all the same.
The first major influx of European immigrants came from Germany and Ireland, starting in the 1820s. Germans came both for economic opportunity and to escape political unrest and military conscription, especially after the Revolutions of 1848. Many German immigrants of this period were political refugees: liberals who wanted to escape from an oppressive government. They were well-off enough to make their way inland, and they formed heavily German enclaves in the Midwest that exist to this day.
The Irish immigrants of the same time period were not always as well off financially, especially after the Irish Potato Famine of 1845. Irish immigrants settled mainly in the cities of the East Coast, where they were employed as laborers and where they faced significant discrimination.
German and Irish immigration continued into the late 19th century and earlier 20th century, at which point the numbers for Southern and Eastern European immigrants started growing as well. Italians, mainly from the Southern part of the country, began arriving in large numbers in the 1890s. Eastern European immigrants—people from Russia, Poland, Bulgaria, and Austria-Hungary—started arriving around the same time. Many of these Eastern Europeans were peasants forced into a hardscrabble existence in their native lands; political unrest, land shortages, and crop failures drove them to seek better opportunities in the United States. The Eastern European immigration wave also included Jewish people escaping pogroms (anti-Jewish massacres) of Eastern Europe and the Pale of Settlement in what was then Poland and Russia.
### History of Intergroup Relations
In a broad sense, German immigrants were not victimized to the same degree as many of the other subordinate groups this section discusses. While they may not have been welcomed with open arms, they were able to settle in enclaves and establish roots. A notable exception to this was during the lead up to World War I and through World War II, when anti-German sentiment was virulent.
Irish immigrants, many of whom were very poor, were more of an underclass than the Germans. In Ireland, the English had oppressed the Irish for centuries, eradicating their language and culture and discriminating against their religion (Catholicism). Although the Irish had a larger population than the English, they were a subordinate group. This dynamic reached into the New World, where Anglo-Americans saw Irish immigrants as a race apart: dirty, lacking ambition, and suitable for only the most menial jobs. In fact, Irish immigrants were subject to criticism identical to that with which the dominant group characterized African Americans. By necessity, Irish immigrants formed tight communities segregated from their Anglo neighbors.
The later wave of immigrants from Southern and Eastern Europe was also subject to intense discrimination and prejudice. In particular, the dominant group—which now included second- and third-generation Germans and Irish—saw Italian immigrants as the dregs of Europe and worried about the purity of the American race (Myers 2007). Italian immigrants lived in segregated slums in Northeastern cities, and in some cases were even victims of violence and lynching similar to what African Americans endured. They undertook physical labor at lower pay than other workers, often doing the dangerous work that other laborers were reluctant to take on, such as earth moving and construction.
### Current Status
German Americans are the largest group among White ethnic Americans in the country. For many years, German Americans endeavored to maintain a strong cultural identity, but they are now culturally assimilated into the dominant culture.
There are now more Irish Americans in the United States than there are Irish in Ireland. One of the country’s largest cultural groups, Irish Americans have slowly achieved acceptance and assimilation into the dominant group.
Myers (2007) states that Italian Americans’ cultural assimilation is “almost complete, but with remnants of ethnicity.” The presence of “Little Italy” neighborhoods—originally segregated slums where Italians congregated in the nineteenth century—exist today. While tourists flock to the saints’ festivals in Little Italies, most Italian Americans have moved to the suburbs at the same rate as other White groups. Italian Americans also became more accepted after World War II, partly because of other, newer migrating groups and partly because of their significant contribution to the war effort, which saw over 500,000 Italian Americans join the military and fight against the Axis powers, which included Italy itself.
As you will see in the Religion chapter, Jewish people were also a core immigrant group to the United States. They often resided in tight-knit neighborhoods in a similar way to Italian people. Jewish identity is interesting and varied, in that many Jewish people consider themselves as members of a collective ethnic group as well as a religion, and many Jewish people feel connected by their ancestry as well as their religion. In fact, much of the data around the number of Jewish Americans is presented with caveats about different definitions and identifications of what it means to be Jewish (Lipka 2013).
As we have seen, there is no minority group that fits easily in a category or that can be described simply. While sociologists believe that individual experiences can often be understood in light of their social characteristics (such as race, class, or gender), we must balance this perspective with awareness that no two individuals’ experiences are alike. Making generalizations can lead to stereotypes and prejudice. The same is true for White ethnic Americans, who come from diverse backgrounds and have had a great variety of experiences.
### Hispanic Americans
The U.S. Census Bureau uses two ethnicities in collecting and reporting data: “Hispanic or Latino” and “Not Hispanic or Latino." Hispanic or Latino is a person of Cuban, Mexican, Puerto Rican, South or Central American, or other Spanish culture or origin regardless of race. Hispanic Americans have a wide range of backgrounds and nationalities.
The segment of the U.S. population that self-identifies as Hispanic in 2019 was recently estimated at 18.5 percent of the total (U.S. Census Bureau 2019). According to the 2010 U.S. Census, about 75 percent of the respondents who identify as Hispanic report being of Mexican, Puerto Rican, or Cuban origin. Remember that the U.S. Census allows people to report as being more than one ethnicity.
Not only are there wide differences among the different origins that make up the Hispanic American population, but there are also different names for the group itself. Hence, there have been some disagreements over whether Hispanic or Latino is the correct term for a group this diverse, and whether it would be better for people to refer to themselves as being of their origin specifically, for example, Mexican American or Dominican American. This section will compare the experiences of Mexican Americans and Cuban Americans.
### How and Why They Came
Mexican Americans form the largest Hispanic subgroup and also the oldest. Mexican migration to the United States started in the early 1900s in response to the need for inexepensive agricultural labor. Mexican migration was often circular; workers would stay for a few years and then go back to Mexico with more money than they could have made in their country of origin. The length of Mexico’s shared border with the United States has made immigration easier than for many other immigrant groups.
Cuban Americans are the second-largest Hispanic subgroup, and their history is quite different from that of Mexican Americans. The main wave of Cuban immigration to the United States started after Fidel Castro came to power in 1959 and reached its crest with the Mariel boatlift in 1980. Castro’s Cuban Revolution ushered in an era of communism that continues to this day. To avoid having their assets seized by the government, many wealthy and educated Cubans migrated north, generally to the Miami area.
### History of Intergroup Relations
For several decades, Mexican workers crossed the long border into the United States, both "documented" and "undocumented" to work in the fields that provided produce for the developing United States. Western growers needed a steady supply of labor, and the 1940s and 1950s saw the official federal Bracero Program (bracero is Spanish for strong-arm) that offered protection to Mexican guest workers. Interestingly, 1954 also saw the enactment of “Operation Wetback,” which deported thousands of illegal Mexican workers. From these examples, we can see the U.S. treatment of immigration from Mexico has been ambivalent at best.
Sociologist Douglas Massey (2006) suggests that although the average standard of living than in Mexico may be lower in the United States, it is not so low as to make permanent migration the goal of most Mexicans. However, the strengthening of the border that began with 1986’s Immigration Reform and Control Act has made one-way migration the rule for most Mexicans. Massey argues that the rise of illegal one-way immigration of Mexicans is a direct outcome of the law that was intended to reduce it.
Cuban Americans, perhaps because of their relative wealth and education level at the time of immigration, have fared better than many immigrants. Further, because they were fleeing a Communist country, they were given refugee status and offered protection and social services. The Cuban Migration Agreement of 1995 has curtailed legal immigration from Cuba, leading many Cubans to try to immigrate illegally by boat. According to a 2009 report from the Congressional Research Service, the U.S. government applied a “wet foot/dry foot” policy toward Cuban immigrants; Cubans who were intercepted while still at sea were returned to Cuba, while those who reached the shore were permitted to stay in the United States. This policy ended in 2017.
### Current Status
Mexican Americans, especially those who are here undocumented, are at the center of a national debate about immigration. Myers (2007) observes that no other minority group (except the Chinese) has immigrated to the United States in such an environment of legal dispute. He notes that in some years, three times as many Mexican immigrants may have entered the United States undocumented as those who arrived documented. It should be noted that this is due to enormous disparity of economic opportunity on two sides of an open border, not because of any inherent inclination to break laws. In his report, “Measuring Immigrant Assimilation in the United States,” Jacob Vigdor (2008) states that Mexican immigrants experience relatively low rates of economic and civic assimilation. He further suggests that “the slow rates of economic and civic assimilation set Mexicans apart from other immigrants, and may reflect the fact that the large numbers of Mexican immigrants residing in the United States undocumented have few opportunities to advance themselves along these dimensions.”
By contrast, Cuban Americans are often seen as a model minority group within the larger Hispanic group. Many Cubans had higher socioeconomic status when they arrived in this country, and their anti-Communist agenda has made them welcome refugees to this country. In south Florida, especially, Cuban Americans are active in local politics and professional life. As with Asian Americans, however, being a model minority can mask the issue of powerlessness that these minority groups face in U.S. society.
### Summary
The history of the U.S. people contains an infinite variety of experiences that sociologist understand follow patterns. From the indigenous people who first inhabited these lands to the waves of immigrants over the past 500 years, migration is an experience with many shared characteristics. Most groups have experienced various degrees of prejudice and discrimination as they have gone through the process of assimilation.
### Section Quiz
### Short Answer
### Further Research
Are people interested in reclaiming their ethnic identities? Read the article .
What is the current racial composition of the United States? Review up-to-the minute statistics at the United States Census Bureau.
### References
Abdollah, Tami and Trevor Hughes. (February 27, 2021). “Hate crimes against Asian Americans are on the rise. Here's what activists, lawmakers and police are doing to stop the violence.” USA TODAY. Retrieved March 18, 2021 (https://www.usatoday.com/story/news/nation/2021/02/27/asian-hate-crimes-attacks-fueled-covid-19-racism-threaten-asians/4566376001/).
ACLU. 2011. “Appellate Court Upholds Decision Blocking Arizona’s Extreme Racial Profiling Law.” American Civil Liberties Union. Retrieved December 8, 2011 (http://www.aclu.org/immigrants-rights/appellate-court-upholds-decision-blocking-arizona-s-extreme-racial-profiling-law-0).
American Indian Cultural Support. 2005. “Mascots: Racism in Schools by State.” Retrieved December 8, 2011 (http://www.aics.org/mascot/mascot.html (http://www.aics.org/mascot/mascot.html).
Frimpong, Kwadwo. (November 12, 2020). “Black people are still seeking racial justice – why and what to do about it.” The Brookings Institution. Retrieved March 18, 2021 (https://www.brookings.edu/blog/how-we-rise/2020/11/12/black-people-are-still-seeking-racial-justice-why-and-what-to-do-about-it/).
Georgetown Law Library. 2021. “DACA and the DREAM Act.” Retrieved March 18, 2021 (https://guides.ll.georgetown.edu/c.php?g=592919&p=4170929).
Greely, Andrew M. 1972. That Most Distressful Nation: The Taming of the American Irish. Chicago: Quadrangle Books.
Harb, Ali. (January 27, 2018). "US Census fails to add MENA category: Arabs to remain “White” in count." Middle East Eye. Retrieved March 18, 2021 (https://www.middleeasteye.net/news/us-census-fails-add-mena-category-arabs-remain-white-count).
Lewy, Guenter. 2004. "Were American Indians the Victims of Genocide?" Retrieved December 6, 2011 (http://hnn.us/articles/7302.html).
Lipka, Michael. 2016. "A Closer Look At Jewish Identity in Israel and the U.S." Pew Research Center. March 16 2016. (https://www.pewresearch.org/fact-tank/2016/03/16/a-closer-look-at-jewish-identity-in-israel-and-the-u-s/)
Marger, Martin. 2003. Race and Ethnic Relations: American and Global Perspectives. Belmont, CA: Wadsworth.
Massey, Douglas S. 2006. “Seeing Mexican Immigration Clearly.” Cato Unbound. Retrieved December 4, 2011 (http://www.cato-unbound.org/2006/08/20/douglas-s-massey/seeing-mexican-immigration-clearly/).
Myers, John P. 2007. Dominant-Minority Relations in America. Boston: Pearson.
National Congress of American Indians. 2005. “The National Congress of American Indians Resolution #TUL-05-087: Support for NCAA Ban on ‘Indian’ Mascots.” Retrieved December 8, 2011 (http://www.ncai.org/attachments/Resolution_dZoHILXNEzXOuYlebzAihFwqFzfNnTHDGJVwjaujdNvnsFtxUVd_TUL-05-087.pdf).
National Congress of American Indians (NCAI). 2020. “Tribal Nations and the United States: An Introduction.” Retrieved March 18, 2021 (https://www.ncai.org/tribalnations/introduction/Indian_Country_101_Updated_February_2019.pdf).
Office of Management and Budget. 2016. "Standards for maintaining, collecting, and presenting federal data on race and ethnicity." Federal Register. 81(190): 67398-58790. Retrieved March 18, 2021 (https://www.govinfo.gov/content/pkg/FR-2016-09-30/pdf/2016-23672.pdf).
Senate Bill 1070. 2010. State of Arizona. Retrieved December 8, 2011 (http://www.azleg.gov/legtext/49leg/2r/bills/sb1070s.pdf).
Shapiro, Emily and Whitney Lloyd. (March 12, 2021). “$27 million settlement for George Floyd's family approved by Minneapolis City Council.” ABC News. Retrieved March 18, 2021 (https://abcnews.go.com/US/27-million-settlement-george-floyds-family-approved-minneapolis/story?id=76419755).
Tatz, Colin. 2006. "Confronting Australian Genocide." Pp. 125-140 in The Indigenous Experience: Global Perspectives. Edited by Roger Maaka and Chris Andersen. Toronto, Canada: Canadian Scholars.
U.S. Census Bureau. 2010. “State and County Quickfacts.” Retrieved February 22, 2012 (http://quickfacts.census.gov/qfd/states/00000.html).
U.S. Census Bureau. (July 1, 2019). “Quick Facts.” Retrieved March 18, 2021 (https://www.census.gov/quickfacts/fact/dashboard/US).
U.S. Department of Homeland Security. 2010. “Persons Obtaining Legal Permanent Resident Status by Region and Selected Country of Last Residence: Fiscal Years 1820 to 2010.” Yearbook of Immigration Statistics. Retrieved December 6, 2011 (http://www.dhs.gov/files/statistics/publications/LPR10.shtm).
Vigdor, Jacob L. 2008. “Measuring Immigrant Assimilation in the United States.” Manhattan Institute for Policy Research Civic Report 53. Retrieved December 4, 2011 (http://www.manhattan-institute.org/html/cr_53.htm). |
# Gender, Sex, and Sexuality
## Introduction
Imagine that there's a fire in a building nearby. As you watch the flames and smoke pour out of windows, you also watch firefighters run inside. Minutes go by and more people arrive--crowds, news trucks, ambulances. Firefighters working the hoses start pointing to a top-floor window, where a lone member of their crew emerges half-pulling, half-carrying a victim of the fire. Behind them, through the window, you can see the fire in the background, flames that the firefighter must have pushed through to get to the victim. Eventually, others reach them with large ladders, and they bring the nearly unconscious victim down to the street.
Close up, you can see the heroic firefighter is covered in dirt and soot. A large gash is visible in their suit, and they're immediately given medical attention. As the EMTs pull off the firefighters' helmet, you're surprised to see features you identify as a woman's. You had just assumed the person was a man, but you were incorrect.
You wouldn't be alone. For centuries, nearly all firefighters had been men. As a child, saying fireman and firemen may have been perfectly appropriate, because all the people you met in the profession were, in fact, men. But as with many professions that were formerly almost exclusively gender-specific, firefighting has become more integrated.
What does that mean for the people in those professions? They must endure physical challenges, overcome stereotypes about any physical limitations, and likely deal with a culture built over a long time to appeal to and serve the needs of men. As they train, firefighters may be yelled at and undergo levels of punishment for not achieving the necessary standards. Does the dynamic of those interactions change when a man in a superior position is for the first time giving orders and issuing reprimands to people of another gender? Should they be able to treat women the same way they treated men? What would be equal in that situation?
Consider another profession.
What would you think about if you witnessed a young woman being pepper sprayed by a man? Is she fulfilling the role society may assume for her? Does it matter that the person spraying her is a man, and that he has a degree of control over her?
Military police and security personnel are required to be pepper sprayed at least once during their training. The logic goes: They may have to utilize this deterrent against other people, and so they should have experienced it. While there are no guarantees that the future enforcement officer will use the substances judiciously, having experienced the painful effects of pepper spray is deemed more likely to produce a level of empathy and restraint.
But is this what she signed up for? Assuming that these military personnel have undergone some level of training prior to this event—they've invested their lives and others have invested in them—could she turn back? How would her peers react? How would her family and others react?
Saving someone from a burning building takes a degree of courage and ability that is very rare, regardless of gender. Voluntary pepper spraying is an extreme situation, again regardless of gender. But gender plays a role in how we see the people involved in both situations. Gender and sexuality are among the most powerful and impactful elements of people's identities, and drive the way they see the world and the way the world sees them. People of different genders go through difficult circumstances and events based partly on their role in society—a role that they do not often define for themselves. And when people express, identify, or outwardly display signs that they do not fit in a societies, established categories, they may face exclusion and discrimination.
### References
International Olympic Committee, Medical and Scientific Department. 2012. “IOC Regulations on Female Hyperandrogenism.” Retrieved December 8, 2014 (http://www.olympic.org/Documents/Commissions_PDFfiles/Medical_commission/2012-06-22-IOC-Regulations-on-Female-Hyperandrogenism-eng.pdf).
Maugh, Thomas H., III. 2009. “Row Over South African Athlete Highlights Ambiguities of Gender.” Los Angeles Times. Retrieved December 8, 2014 (http://articles.latimes.com/2009/aug/21/science/sci-runner-side21). |
# Gender, Sex, and Sexuality
## Sex, Gender, Identity, and Expression
When filling out a document such as a job application or school registration form, you are often asked to provide your name, address, phone number, birth date, and sex or gender. But have you ever been asked to provide your sex and your gender? Like most people, you may not have realized that sex and gender are not the same. However, sociologists and most other social scientists view them as conceptually distinct. Sex refers to physical or physiological differences between males and females, including both primary sex characteristics (the reproductive system) and secondary characteristics such as height and muscularity. Gender refers to behaviors, personal traits, and social positions that society attributes to being female or male.
A person’s sex, as determined by their biology, does not always correspond with their gender. Therefore, the terms sex and gender are not interchangeable. A baby who is born with male genitalia will most likely be identified as male. As a child or adult, however, they may identify with the feminine aspects of culture. Since the term sex refers to biological or physical distinctions, characteristics of sex will not vary significantly between different human societies. Generally, persons of the female sex, regardless of culture, will eventually menstruate and develop breasts that can lactate. Characteristics of gender, on the other hand, may vary greatly between different societies. For example, in U.S. culture, it is considered feminine (or a trait of the female gender) to wear a dress or skirt. However, in many Middle Eastern, Asian, and African cultures, sarongs, robes, or gowns are considered masculine. The kilt worn by a Scottish man does not make him appear feminine in that culture.
The dichotomous or binary view of gender (the notion that someone is either male or female) is specific to certain cultures and is not universal. In some cultures gender is viewed as fluid. In the past, some anthropologists used the term berdache to refer to individuals who occasionally or permanently dressed and lived as a different gender. The practice has been noted among certain Native American tribes (Jacobs, Thomas, and Lang 1997). Samoan culture accepts what Samoans refer to as a “third gender.” Fa’afafine, which translates as “the way of the woman,” is a term used to describe individuals who are born biologically male but embody both masculine and feminine traits. Fa’afafines are considered an important part of Samoan culture. Individuals from other cultures may mislabel their sexuality because fa’afafines have a varied sexual life that may include men and women (Poasa 1992).
### Sexuality and Sexual Orientation
A person's sexuality is their capacity to experience sexual feelings and attraction. Studying sexual attitudes and practices is a particularly interesting field of sociology because sexual behavior and attitudes about sexual behavior have cultural and societal influences and impacts. As you will see in the Relationships, Marriage, and Family chapter, each society interprets sexuality and sexual activity in different ways, with different attitudes about premarital sex, the age of sexual consent, homosexuality, masturbation, and other sexual behaviors (Widmer 1998).
A person’s sexual orientation is their physical, mental, emotional, and sexual attraction to a particular sex (male and/or female). Sexual orientation is typically divided into several categories: heterosexuality, the attraction to individuals of the other sex; homosexuality, the attraction to individuals of the same sex; bisexuality, the attraction to individuals of either sex; asexuality, a lack of sexual attraction or desire for sexual contact; pansexuality, an attraction to people regardless of sex, gender, gender identity, or gender expression; omnisexuality, an attraction to people of all sexes, genders, gender identities, and gender expressions that considers the person's gender, and queer, an umbrella term used to describe sexual orientation, gender identity or gender expression. Other categories may not refer to a sexual attraction, but rather a romantic one. For example, an aromantic person does not experience romantic attraction; this is different from asexuality, which refers to a lack of sexual attraction. And some sexual orientations do not refer to gender in their description, though those who identify as having that orientation may feel attraction to a certain gender. For example, demisexual refers to someone who feels a sexual attraction to someone only after they form an emotional bond; the term itself doesn't distinguish among gender identities, but the person may feel attraction based on gender (PFLAG 2021). It is important to acknowledge and understand that many of these orientations exist on on a spectrum, and there may be no specific term to describe how an individual feels. Some terms have been developed to address this—such as graysexual or grayromantic—but their usage is a personal choice (Asexual Visibility and Education Network 2021).
People who are attracted to others of a different gender are typically referred to as "straight," and people attracted to others of the same gender are typically referred to as "gay" for men and "lesbian" for women. As discussed, above, however, there are many more sexual and romantic orientations, so the term "gay," for example, should not be used to describe all of them. Proper terminology includes the acronyms LGBT and LGBTQ, which stands for “Lesbian, Gay, Bisexual, Transgender” (and “Queer” or “Questioning” when the Q is added). In other cases, people and organizations may add "I" to represent Intersex people (described below), and "A" for Asexual or Aromantic people (or sometimes for "Allies"), as well as one "P" to describe Pansexual people and sometimes another "P" to describe Polysexual people. Finally, some people and organizations add a plus sign (+) to represent other possible identities or orientations. Sexuality and gender terminology are constantly changing, and may mean different things to different people; they are not universal, and each individual defines them for themselves (UC Davis LGBTQIA Resource Center 2020). Finally, a person who does not fully understand all of these terms can still be supportive of people who have those orientations or others; in fact, advocacy and support organizations indicate it is much better to admit you don't know something than to make assumptions or apply an incorrect label to someone (GLAAD 2021).
While the descriptions above are evidence of a vast degree of diversity, the United States and many other countries are heteronormative societies, meaning many people assume heterosexual orientation is biologically determined and is the default or normal type of orientation. While awareness and acceptance of different sexual orientations and identities seems to be increasing, the influence of a heteronormative society can lead LGBTQ people to be treated like "others," even by people who do not deliberately seek to cause them harm. This can lead to significant distress (Boyer 2020). Causes of these heteronormative behaviors and expectations are tied to implicit biases; they can be especially harmful for children and young adults (Tompkins 2017).
There is not a wealth of research describing exactly when people become aware of their sexual orientation. According to current scientific understanding, individuals are usually aware of their sexual orientation between middle childhood and early adolescence (American Psychological Association 2008). They do not have to participate in sexual activity to be aware of these emotional, romantic, and physical attractions; people can be celibate and still recognize their sexual orientation, and may have very different experiences of discovering and accepting their sexual orientation. Some studies have shown that a percentage of people may start to have feelings related to attraction or orientation at ages nine or ten, even if these feelings are not sexual (Calzo 2018). At the point of puberty, some may be able to announce their sexual orientation, while others may be unready or unwilling to make their sexual orientation or identity known since it goes against society’s historical norms (APA 2008). And finally, some people recognize their true sexual orientation later in life—in their 30s, 40s, and beyond.
There is no scientific consensus regarding the exact reasons why an individual holds a specific sexual orientation. Research has been conducted to study the possible genetic, hormonal, developmental, social, and cultural influences on sexual orientation, but there has been no evidence that links sexual orientation to one factor (APA 2008). Alfred Kinsey was among the first to conceptualize sexuality as a continuum rather than a strict dichotomy of gay or straight. He created a six-point rating scale that ranges from exclusively heterosexual to exclusively homosexual. See the figure below. In his 1948 work Sexual Behavior in the Human Male, Kinsey writes, “Males do not represent two discrete populations, heterosexual and homosexual. The world is not to be divided into sheep and goats … The living world is a continuum in each and every one of its aspects” (Kinsey 1948). Many of Kinsey's specific research findings have been criticized or discredited, but his influence on future research is widely accepted.
Later scholarship by Eve Kosofsky Sedgwick expanded on Kinsey’s notions. She coined the term “homosocial” to oppose “homosexual,” describing nonsexual same-sex relations. Sedgwick recognized that in U.S. culture, males are subject to a clear divide between the two sides of this continuum, whereas females enjoy more fluidity. This can be illustrated by the way women in the United States can express homosocial feelings (nonsexual regard for people of the same sex) through hugging, handholding, and physical closeness. In contrast, U.S. males refrain from these expressions since they violate the heteronormative expectation that male sexual attraction should be exclusively for females. Research suggests that it is easier for women violate these norms than men, because men are subject to more social disapproval for being physically close to other men (Sedgwick 1985).
Because of the deeply personal nature of sexual orientation, as well as the societal biases against certain orientations, many people may question their sexual orientation before fully accepting it themselves. In a similar way, parents may question their children's sexual orientation based on certain behaviors. Simply viewing the many web pages and discussion forums dedicated to people expressing their questions makes it very clear that sexual orientation is not always clear. Feelings of guilt, responsibility, rejection, and simple uncertainty can make the process and growth very challenging. For example, a woman married to a man who recognizes that she is asexual, or a man married to a woman who recognizes that he is attracted to men, may both have extreme difficulty coming to terms with their sexuality, as well as disclosing it to others. At younger ages, similarly challenging barriers and difficulties exist. For example, adolescence can be a difficult and uncertain time overall, and feelings of different or changing orientation or nonconformity can only add to the challenges (Mills-Koonce 2018).
### Gender Roles
As we grow, we learn how to behave from those around us. In this socialization process, children are introduced to certain roles that are typically linked to their biological sex. The term gender role refers to society’s concept of how men and women are expected to look and how they should behave. These roles are based on norms, or standards, created by society. In U.S. culture, masculine roles are usually associated with strength, aggression, and dominance, while feminine roles are usually associated with passivity, nurturing, and subordination. Role learning starts with socialization at birth. Even today, our society is quick to outfit male infants in blue and girls in pink, even applying these color-coded gender labels while a baby is in the womb.
One way children learn gender roles is through play. Parents typically supply boys with trucks, toy guns, and superhero paraphernalia, which are active toys that promote motor skills, aggression, and solitary play. Daughters are often given dolls and dress-up apparel that foster nurturing, social proximity, and role play. Studies have shown that children will most likely choose to play with “gender appropriate” toys (or same-gender toys) even when cross-gender toys are available because parents give children positive feedback (in the form of praise, involvement, and physical closeness) for gender normative behavior (Caldera, Huston, and O’Brien 1998). As discussed in the Socialization chapter, some parents and experts become concerned about young people becoming too attached to these stereotypical gender roles.
The drive to adhere to masculine and feminine gender roles continues later in life, in a tendency sometimes referred to as "occupational sorting" (Gerdeman 2019). Men tend to outnumber women in professions such as law enforcement, the military, and politics. Women tend to outnumber men in care-related occupations such as childcare, healthcare (even though the term “doctor” still conjures the image of a man), and social work. These occupational roles are examples of typical U.S. male and female behavior, derived from our culture’s traditions. Adherence to these roles demonstrates fulfillment of social expectations but not necessarily personal preference (Diamond 2002); sometimes, people work in a profession because of societal pressure and/or the opportunities afforded to them based on their gender.
Historically, women have had difficulty shedding the expectation that they cannot be a "good mother" and a "good worker" at the same time, which results in fewer opportunities and lower levels of pay (Ogden 2019). Generally, men do not share this difficulty: Since the assumed role of a men as a fathers does not seem to conflict with their perceived work role, men who are fathers (or who are expected to become fathers) do not face the same barriers to employment or promotion (González 2019). This is sometimes referred to as the "motherhood penalty" versus the "fatherhood premium," and is prevalent in many higher income countries (Bygren 2017). These concepts and their financial and societal implications will be revisited later in the chapter.
### Gender Identity
U.S. society allows for some level of flexibility when it comes to acting out gender roles. To a certain extent, men can assume some feminine roles and women can assume some masculine roles without interfering with their gender identity. Gender identity is a person’s deeply held internal perception of one's gender.
Transgender people's sex assigned at birth and their gender identity are not necessarily the same. A transgender woman is a person who was assigned male at birth but who identifies and/or lives as a woman; a transgender man was assigned female at birth but lives as a man. While determining the size of the transgender population is difficult, it is estimated that 1.4 million adults (Herman 2016) and 2 percent of high school students in the U.S. identify as transgender (Johns 2019). The term "transgender" does not indicate sexual orientation or a particular gender expression, and we should avoid making assumptions about people's sexual orientation based on knowledge about their gender identity (GLAAD 2021).
Some transgender individuals may undertake a process of transition, in which they move from living in a way that is more aligned with the sex assigned at birth to living in a way that is aligned with their gender identity. Transitioning may take the form of social, legal or medical aspects of someone's life, but not everyone undertakes any or all types of transition. Social transition may involve the person's presentation, name, pronouns, and relationships. Legal transition can include changing their gender on government or other official documents, changing their legal name, and so on. Some people may undergo a physical or medical transition, in which they change their outward, physical, or sexual characteristics in order for their physical being to better align with their gender identity (UCSF Transgender Care 2019). Not all transgender individuals choose to alter their bodies: many will maintain their original anatomy but may present themselves to society as another gender. This is typically done by adopting the dress, hairstyle, mannerisms, or other characteristic typically assigned to another gender. It is important to note that people who cross-dress, or wear clothing that is traditionally assigned to a gender different from their biological sex, are not necessarily transgender. Cross-dressing is typically a form of self-expression or personal style, and it does not indicate a person's gender identity or that they are transgender (TSER 2021).
There is no single, conclusive explanation for why people are transgender. Transgender expressions and experiences are so diverse that it is difficult to identify their origin. Some hypotheses suggest biological factors such as genetics or prenatal hormone levels as well as social and cultural factors such as childhood and adulthood experiences. Most experts believe that all of these factors contribute to a person’s gender identity (APA 2008).
Intersex is a general term used to describe people whose sex traits, reproductive anatomy, hormones, or chromosomes are different from the usual two ways human bodies develop. Some intersex traits are recognized at birth, while others are not recognizable until puberty or later in life (interACT 2021). While some intersex people have physically recognizable features that are described by specific medical terms, intersex people and newborns are healthy. Most in the medical and intersex community reject unnecessary surgeries intended to make a baby conform to a specific gender assignment; medical ethicists indicate that any surgery to alter intersex characteristics or traits—if desired—should be delayed until an individual can decide for themselves (Behrens 2021). If a physical trait or medical condition prohibits a baby from urinating or performing another bodily function (which is very rare), then a medical procedure such as surgery will be needed; in other cases, hormonal issues related to intersex characteristics may require medical intervention. Intersex and transgender are not interchangeable terms; many transgender people have no intersex traits, and many intersex people do not consider themselves transgender. Some intersex people believe that intersex people should be included within the LGBTQ community, while others do not (Koyama n.d.).
Those who identify with the sex they were assigned at birth are often referred to as cisgender, utilizing the Latin prefix "cis," which means "on the same side." (The prefix "trans" means "across.") Because they are in the majority and do not have a potential component to transition, many cisgender people do not self-identify as such. As with transgender people, the term or usage of cisgender does not indicate a person's sexual orientation, gender, or gender expression (TSER 2021). And as many societies are heteronormative, they are also cisnormative, which is the assumption or expectation that everyone is cisgender, and that anything other than cisgender is not normal.
The language of sexuality, sexual orientation, gender identity, and gender expression is continually changing and evolving. In order to get an overview of some of the most commonly used terms, explore the Trans Student Educational Resources Online Glossary: http://openstax.org/r/tsero
When individuals do not feel comfortable identifying with the gender associated with their biological sex, then they may experience gender dysphoria. Gender dysphoria is a diagnostic category in the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5) that describes individuals who do not identify as the gender that most people would assume they are. This dysphoria must persist for at least six months and result in significant distress or dysfunction to meet DSM-5 diagnostic criteria. In order for children to be assigned this diagnostic category, they must verbalize their desire to become the other gender. It is important to note that not all transgender people experience gender dysphoria, and that its diagnostic categorization is not universally accepted. For example, in 2019, the World Health Organization reclassified “gender identity disorder” as “gender incongruence,” and categorized it under sexual health rather than a mental disorder. However, health and mental health professionals indicate that the presence of the diagnostic category does assist in supporting those who need treatment or help.
People become aware that they may be transgender at different ages. Even if someone does not have a full (or even partial) understanding of gender terminology and its implications, they can still develop an awareness that their gender assigned at birth does not align with their gender identity. Society, particularly in the United States, has been reluctant to accept transgender identities at any age, but we have particular difficulty accepting those identities in children. Many people feel that children are too young to understand their feelings, and that they may "grow out of it." And it is true that some children who verbalize their identification or desire to live as another gender may ultimately decide to live in alignment with their assigned gender. But if a child consistently describes themselves as a gender (or as both genders) and/or expresses themselves as that gender over a long period of time, their feelings cannot be attributed to going through a "phase" (Mayo Clinic 2021).
Some children, like many transgender people, may feel pressure to conform to social norms, which may lead them to suppress or hide their identity. Experts find evidence of gender dysphoria—the long-term distress associated with gender identification—in children as young as seven (Zaliznyak 2020). Again, most children have a limited understanding of the social and societal impacts of being transgender, but they can feel strongly that they are not aligned with their assigned sex. And considering that many transgender people do not come out or begin to transition until much later in life—well into their twenties—they may live for a long time under that distress.
### Discrimination Against LGBTQ people
Recall from the chapter on Crime and Deviance that the FBI's hate crime data indicates that crimes against LGBTQ people have been increasing, and that those crimes account for nearly one in five hate crimes committed in the United States (FBI 2020). While the disbanding of anti-LGBTQ laws in the United States has reduced government or law enforcement oppression or abuse, it has not eliminated it. In other countries, however, LGBTQ people can face even more danger. Reports from the United Nations, Human Rights Watch, and the International Lesbian, Gay, Trans, and Intersex Association (ILGA) indicate that many countries impose penalties for same-sex relationships, gender noncomformity, and other acts deemed opposed to the cultural or religious observances of the nation. As of 2020, six United Nations members imposed the death penalty for consensual same-sex acts, and another 61 countries penalized same sex acts, through jail time, corporal punishment (such as lashing), or other measures. These countries include prominent United States allies such as the United Arab Emirates and Saudi Arabia (both of which can legally impose the death penalty for same-sex acts). Some nearby nations criminalize same-sex relations: Barbados can impose lifetime imprisonment for same-sex acts, and Jamaica, St. Kitts and Nevis, and Saint Lucia have lesser penalties, though Saint Lucia's government indicates it does not enforce those laws (ILGA 2020). Even when the government criminal code does not formalize anti-LGBTQ penalties, local ordinances or government agents may have wide discretion. For example, many people fleeing Central American countries do so as a result of anti-LGBTQ violence, sometimes at the hands of police (Human Rights Watch 2020).
Such severe treatment at the hands of the government is no longer the case in the United States. But until the 1960s and 1970s, every state in the country criminalized same-sex acts, which allowed the military to dishonorably discharge gay veterans (stripping them of all benefits) and law enforcement agencies to investigate and detain people suspected of same-sex acts. Police regularly raided bars and clubs simply for allowing gay and lesbian people to dance together. Public decency laws allowed police to arrest people if they did not wear clothing aligning with the typical dress for their biological sex. Criminalization of same-sex acts began to unravel at the state level in the 1960's and 1970s, and was fully invalidated in a 2003 Supreme Court decision.
Hate crimes and anti-LGBTQ legislation are overt types of discrimination, but LGBTQ people are also treated differently from straight and cisgender people in schools, housing, and in healthcare. This can have effects on mental health, employment and financial opportunities, and relationships. For example, more than half of LGBTQ adults and 70 percent of those who are transgender or gender nonconforming report experiencing discrimination from a health care professional; this leads to delays or reluctance in seeking care or preventative visits, which has negative health outcomes (American Heart Association 2020). Similarly, elderly LGBTQ people are far less likely to come out to healthcare professionals than are straight or cisgender people, which may also lead to healthcare issues at an age that is typically highly reliant on medical care (Foglia 2014).
Much of this discrimination is based on stereotypes and misinformation. Some is based on heterosexism, which Herek (1990) suggests is both an ideology and a set of institutional practices that privilege straight people and heterosexuality over other sexual orientations. Much like racism and sexism, heterosexism is a systematic disadvantage embedded in our social institutions, offering power to those who conform to heterosexual orientation while simultaneously disadvantaging those who do not. Homophobia, an extreme or irrational aversion to gay, lesbian, bisexual, or all LGBTQ people, which often manifests as prejudice and bias. Transphobia is a fear, hatred, or dislike of transgender people, and/or prejudice and discrimination against them by individuals or institutions.
### Fighting discrimination and being an ally
Major policies to prevent discrimination based on sexual orientation have not come into effect until recent years. In 2011, President Obama overturned “don’t ask, don’t tell,” a controversial policy that required gay and lesbian people in the US military to keep their sexuality undisclosed. In 2015, the Supreme Court ruled in the case of Obgerfell vs. Hodges that the right to civil marriage was guaranteed to same-sex couples. And, as discussed above, in the landmark 2020 Supreme Court decision added sexual orientation and gender identity as categories protected from employment discrimination by the Civil Rights Act. At the same time, laws passed in several states permit some level of discrimination against same-sex couples and other LGBTQ people based on a person's individual religious beliefs or prejudices.
Supporting LGTBQ people requires effort to better understand them without making assumptions. Understand people by listening, respecting them, and by remembering that every person—LGBTQ or otherwise— is different. Being gay, lesbian, bisexual, transgender, queer, intersex, or asexual is not a choice, but the way a person expresses or reveals that reality is their choice. Your experience or knowledge of other LGBTQ people (even your own experience if you are LGBTQ) cannot dictate how another person feels or acts. Finally, as discussed in the Race and Ethnicity chapter, intersectionality means that people are defined by more than their gender identity and sexual orientation. People from different age groups, races, abilities, and experiences within the LGTBQ community have different perspectives and needs.
While each individual has their own perspective, respecting their feelings and protecting their equality and wellbeing does have some common elements. These include referring to a person as they would like to be referred to, including the avoidance of abbreviations or slang terms unless you are sure they accept them. For example, many people and organizations (including those referenced in this chapter) use the abbreviation "trans" to represent transgender people, but a non-transgender person should not use that abbreviation unless they know the person or subject is comfortable with it. Respect also includes people's right to privacy: One person should never out a person to someone else or assume that someone is publicly out. LGBTQ allies can support everyone's rights to be equal and empowered members of society, including within organizations, institutions, and even individual classrooms.
Supporting others may require a change in mindset and practice. For example, if a transgender person wants to be referred to by a different name, or use different pronouns, it might take some getting used to, especially if you have spent years referring to the person by another name or by other pronouns. However, making the change is worthwhile and not overly onerous.
You can learn more about being an ally through campus, government, and organizational resources like the Human Rights Campaign's guide https://www.hrc.org/resources/being-an-lgbtq-ally
Language is an important part of culture, and it has been evolving to better include and describe people who are not gender-binary. In many languages, including English, pronouns are gendered. That is, pronouns are intended to identify the gender of the individual being referenced. English has traditionally been binary, providing only “he/him/his,” for male subjects and “she/her/hers,” for female subjects.
This binary system excludes those who identify as neither male nor female. The word “they,” which was used for hundreds of years as a singular pronoun, is more inclusive. As a result, in fact, Merriam Webster selected this use of “they” as Word of the Year for 2019. “They” and other pronouns are now used to reference those who do not identify as male or female on the spectrum of gender identities.
Gender inclusive language has impacts beyond personal references. In biology, anatomy, and healthcare, for example, people commonly refer to organs or processes with gender associations. However, more accurate and inclusive language avoids such associations. For example, women do not produce eggs; ovaries produce eggs. Men are not more likely to be color-blind; those with XY chromosomes are more likely to be color blind (Gender Inclusive Biology 2019).
Beyond the language of gender, the language of society and culture itself can be either a barrier or an opening to inclusivity. Societal norms are important sociological concepts, and behaviors outside of those norms can lead to exclusion. By disassociating gender identity, gender expression, and sexual orientation from the concept of norms, we can begin to eliminate the implicit and explicit biases regarding those realities. In everyday terms, this can take the form of avoiding references to what is normal or not normal in regard to sexuality or gender (Canadian Public Health Association 2019).
### Summary
The terms “sex” and “gender” refer to two different identifiers. Sex denotes biological characteristics differentiating males and females, while gender denotes social and cultural characteristics of masculine and feminine behavior. Sex and gender are not always synchronous. Individuals who strongly identify with the opposing gender are considered transgender.
### Section Quiz
### Short Answer
### Further Research
To learn about what organizations are doing to improve diversity and social justice education for young people, review Learning For Justice's educational materials.
For more information on gender identity and advocacy for transgender individuals see the Global Action for Trans Equality web site.
Visit The Trevor Project website for more information on suicide prevention and crisis intervention for LGBTQ (lesbian, gay, bisexual, transgender, queer, and questioning) young people.
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# Gender, Sex, and Sexuality
## Gender and Gender Inequality
### Gender and Socialization
The phrase “boys will be boys” is often used to justify behavior such as pushing, shoving, or other forms of aggression from young boys. The phrase implies that such behavior is unchangeable and something that is part of a boy’s nature. Aggressive behavior, when it does not inflict significant harm, is often accepted from boys and men because it is congruent with the cultural script for masculinity. The “script” written by society is in some ways similar to a script written by a playwright. Just as a playwright expects actors to adhere to a prescribed script, society expects women and men to behave according to the expectations of their respective gender roles. Scripts are generally learned through a process known as socialization, which teaches people to behave according to social norms.
### Socialization
Children learn at a young age that there are distinct expectations for boys and girls. Cross-cultural studies reveal that children are aware of gender roles by age two or three. At four or five, most children are firmly entrenched in culturally appropriate gender roles (Kane 1996). Children acquire these roles through socialization, a process in which people learn to behave in a particular way as dictated by societal values, beliefs, and attitudes. For example, society often views riding a motorcycle as a masculine activity and, therefore, considers it to be part of the male gender role. Attitudes such as this are typically based on stereotypes, oversimplified notions about members of a group. Gender stereotyping involves overgeneralizing about the attitudes, traits, or behavior patterns of women or men. For example, women may be thought of as too timid or weak to ride a motorcycle.
Gender stereotypes form the basis of sexism. Sexism refers to prejudiced beliefs that value one sex over another. It varies in its level of severity. In parts of the world where women are strongly undervalued, young girls may not be given the same access to nutrition, healthcare, and education as boys. Further, they will grow up believing they deserve to be treated differently from boys (UNICEF 2011; Thorne 1993). While it is illegal in the United States when practiced as discrimination, unequal treatment of women continues to pervade social life. It should be noted that discrimination based on sex occurs at both the micro- and macro-levels. Many sociologists focus on discrimination that is built into the social structure; this type of discrimination is known as institutional discrimination (Pincus 2008).
Gender socialization occurs through four major agents of socialization: family, education, peer groups, and mass media. Each agent reinforces gender roles by creating and maintaining normative expectations for gender-specific behavior. Exposure also occurs through secondary agents such as religion and the workplace. Repeated exposure to these agents over time leads men and women into a false sense that they are acting naturally rather than following a socially constructed role.
Family is the first agent of socialization. There is considerable evidence that parents socialize sons and daughters differently. Generally speaking, girls are given more latitude to step outside of their prescribed gender role (Coltrane and Adams 2004; Kimmel 2000; Raffaelli and Ontai 2004). However, differential socialization typically results in greater privileges afforded to sons. For instance, boys are allowed more autonomy and independence at an earlier age than daughters. They may be given fewer restrictions on appropriate clothing, dating habits, or curfew. Sons are also often free from performing domestic duties such as cleaning or cooking and other household tasks that are considered feminine. Daughters are limited by their expectation to be passive and nurturing, generally obedient, and to assume many of the domestic responsibilities.
Even when parents set gender equality as a goal, there may be underlying indications of inequality. For example, boys may be asked to take out the garbage or perform other tasks that require strength or toughness, while girls may be asked to fold laundry or perform duties that require neatness and care. It has been found that fathers are firmer in their expectations for gender conformity than are mothers, and their expectations are stronger for sons than they are for daughters (Kimmel 2000). This is true in many types of activities, including preference for toys, play styles, discipline, chores, and personal achievements. As a result, boys tend to be particularly attuned to their father’s disapproval when engaging in an activity that might be considered feminine, like dancing or singing (Coltraine and Adams 2008). Parental socialization and normative expectations also vary along lines of social class, race, and ethnicity. African American families, for instance, are more likely than Caucasians to model an egalitarian role structure for their children (Staples and Boulin Johnson 2004).
The reinforcement of gender roles and stereotypes continues once a child reaches school age. Until very recently, schools were rather explicit in their efforts to stratify boys and girls. The first step toward stratification was segregation. Girls were encouraged to take home economics or humanities courses and boys to take math and science.
Studies suggest that gender socialization still occurs in schools today, perhaps in less obvious forms (Lips 2004). Teachers may not even realize they are acting in ways that reproduce gender differentiated behavior patterns. Yet any time they ask students to arrange their seats or line up according to gender, teachers may be asserting that boys and girls should be treated differently (Thorne 1993).
Even in levels as low as kindergarten, schools subtly convey messages to girls indicating that they are less intelligent or less important than boys. For example, in a study of teacher responses to male and female students, data indicated that teachers praised male students far more than female students. Teachers interrupted girls more often and gave boys more opportunities to expand on their ideas (Sadker and Sadker 1994). Further, in social as well as academic situations, teachers have traditionally treated boys and girls in opposite ways, reinforcing a sense of competition rather than collaboration (Thorne 1993). Boys are also permitted a greater degree of freedom to break rules or commit minor acts of deviance, whereas girls are expected to follow rules carefully and adopt an obedient role (Ready 2001).
Mimicking the actions of significant others is the first step in the development of a separate sense of self (Mead 1934). Like adults, children become agents who actively facilitate and apply normative gender expectations to those around them. When children do not conform to the appropriate gender role, they may face negative sanctions such as being criticized or marginalized by their peers. Though many of these sanctions are informal, they can be quite severe. For example, a girl who wishes to take karate class instead of dance lessons may be called a “tomboy” and face difficulty gaining acceptance from both male and female peer groups (Ready 2001). Boys, especially, are subject to intense ridicule for gender nonconformity (Coltrane and Adams 2004; Kimmel 2000).
Mass media serves as another significant agent of gender socialization. In television and movies, women tend to have less significant roles and are often portrayed as wives or mothers. When women are given a lead role, it often falls into one of two extremes: a wholesome, saint-like figure or a malevolent, hypersexual figure (Etaugh and Bridges 2003). This same inequality is pervasive in children’s movies (Smith 2008). Research indicates that in the ten top-grossing G-rated movies released between 1991 and 2013, nine out of ten characters were male (Smith 2008).
Television commercials and other forms of advertising also reinforce inequality and gender-based stereotypes. Women are almost exclusively present in ads promoting cooking, cleaning, or childcare-related products (Davis 1993). Think about the last time you saw a man star in a dishwasher or laundry detergent commercial. In general, women are underrepresented in roles that involve leadership, intelligence, or a balanced psyche. Of particular concern is the depiction of women in ways that are dehumanizing, especially in music videos. Even in mainstream advertising, however, themes intermingling violence and sexuality are quite common (Kilbourne 2000).
### Social Stratification and Inequality
Stratification refers to a system in which groups of people experience unequal access to basic, yet highly valuable, social resources. There is a long history of gender stratification in the United States. When looking to the past, it would appear that society has made great strides in terms of abolishing some of the most blatant forms of gender inequality (see timeline below) but underlying effects of male dominance still permeate many aspects of society.
1. Before 1809—Women could not execute a will
2. Before 1840—Women were not allowed to own or control property
3. Before 1920—Women were not permitted to vote
4. Before 1963—Employers could legally pay a woman less than a man for the same work
5. Before 1973—Women did not have the right to a safe and legal abortion (Imbornoni 2009)
### The Pay Gap
Despite making up nearly half (49.8 percent) of payroll employment, men vastly outnumber women in authoritative, powerful, and, therefore, high-earning jobs (U.S. Census Bureau 2010). Even when a woman’s employment status is equal to a man’s, she will generally make only 81 cents for every dollar made by her male counterpart (Payscale 2020). Women in the paid labor force also still do the majority of the unpaid work at home. On an average day, 84 percent of women (compared to 67 percent of men) spend time doing household management activities (U.S. Census Bureau 2011). This double duty keeps working women in a subordinate role in the family structure (Hochschild and Machung 1989).
Gender stratification through the division of labor is not exclusive to the United States. According to George Murdock’s classic work, Outline of World Cultures (1954), all societies classify work by gender. When a pattern appears in all societies, it is called a cultural universal. While the phenomenon of assigning work by gender is universal, its specifics are not. The same task is not assigned to either men or women worldwide. But the way each task’s associated gender is valued is notable. In Murdock’s examination of the division of labor among 324 societies around the world, he found that in nearly all cases the jobs assigned to men were given greater prestige (Murdock and White 1968). Even if the job types were very similar and the differences slight, men’s work was still considered more vital.
Part of the gender pay gap can be attributed to unique barriers faced by women regarding work experience and promotion opportunities. A mother of young children is more likely to drop out of the labor force for several years or work on a reduced schedule than is the father. As a result, women in their 30s and 40s are likely, on average, to have less job experience than men. This effect becomes more evident when considering the pay rates of two groups of women: those who did not leave the workforce and those who did: In the United States, childless women with the same education and experience levels as men are typically paid with closer (but not exact) parity to men. However, women with families and children are paid less: Mothers are recommended a 7.9 percent lower starting salary than non-mothers, which is 8.6 percent lower than men (Correll 2007).
This evidence points to levels of discrimination that go beyond behaviors by individual companies or organizations. As discussed earlier in the gender roles section, many of these gaps are rooted in America’s social patterns of discrimination, which involve the roles that different genders play in child-rearing, rather than individual discrimination by employers in hiring and salary decisions. On the other hand, legal and ethical practices demand that organizations do their part to promote more equity among all genders.
### The Glass Ceiling
The idea that women are unable to reach the executive suite is known as the glass ceiling. It is an invisible barrier that women encounter when trying to win jobs in the highest level of business. At the beginning of 2021, for example, a record 41 of the world’s largest 500 companies were run by women. While a vast improvement over the number twenty years earlier – where only two of the companies were run by women – these 41 chief executives still only represent eight percent of those large companies (Newcomb 2020).
Why do women have a more difficult time reaching the top of a company? One idea is that there is still a stereotype in the United States that women aren’t aggressive enough to handle the boardroom or that they tend to seek jobs and work with other women (Reiners 2019). Other issues stem from the gender biases based on gender roles and motherhood discussed above.
Another idea is that women lack mentors, executives who take an interest and get them into the right meetings and introduce them to the right people to succeed (Murrell & Blake-Beard 2017).
### Women in Politics
One of the most important places for women to help other women is in politics. Historically in the United States, like many other institutions, political representation has been mostly made up of White men. By not having women in government, their issues are being decided by people who don’t share their perspective. The number of women elected to serve in Congress has increased over the years, but does not yet accurately reflect the general population. For example, in 2018, the population of the United States was 49 percent male and 51 percent female, but the population of Congress was 78.8 percent male and 21.2 percent female (Manning 2018). Over the years, the number of women in the federal government has increased, but until it accurately reflects the population, there will be inequalities in our laws.
### Movements for Change: Feminism
One of the underlying issues that continues to plague women in the United States is misogyny. This is the hatred of or, aversion to, or prejudice against women. Over the years misogyny has evolved as an ideology that men are superior to women in all aspects of life. There have been multiple movements to try and fight this prejudice.
In 1963, writer and feminist Betty Friedan published The Feminine Mystique in which she contested the post-World War II belief that it was women’s sole destiny to marry and bear children. Friedan’s book began to raise the consciousness of many women who agreed that homemaking in the suburbs sapped them of their individualism and left them unsatisfied. In 1966, the National Organization for Women (NOW) formed and proceeded to set an agenda for the feminist movement. Framed by a statement of purpose written by Friedan, the agenda began by proclaiming NOW’s goal to make possible women’s participation in all aspects of American life and to gain for them all the rights enjoyed by men.
Feminists engaged in protests and actions designed to bring awareness and change. For example, the New York Radical Women demonstrated at the 1968 Miss America Pageant in Atlantic City to bring attention to the contest’s—and society’s—exploitation of women. The protestors tossed instruments of women’s oppression, including high-heeled shoes, curlers, girdles, and bras, into a “freedom trash can.” News accounts incorrectly described the protest as a “bra burning,” which at the time was a way to demean and trivialize the issue of women’s rights (Gay 2018).
Other protests gave women a more significant voice in a male-dominated social, political, and entertainment climate. For decades, Ladies Home Journal had been a highly influential women’s magazine, managed and edited almost entirely by men. Men even wrote the advice columns and beauty articles. In 1970, protesters held a sit-in at the magazine’s offices, demanding that the company hire a woman editor-in-chief, add women and non-White writers at fair pay, and expand the publication’s focus.
Feminists were concerned with far more than protests, however. In the 1970s, they opened battered women’s shelters and successfully fought for protection from employment discrimination for pregnant women, reform of rape laws (such as the abolition of laws requiring a witness to corroborate a woman’s report of rape), criminalization of domestic violence, and funding for schools that sought to counter sexist stereotypes of women. In 1973, the U.S. Supreme Court in Roe v. Wade invalidated a number of state laws under which abortions obtained during the first three months of pregnancy were illegal. This made a nontherapeutic abortion a legal medical procedure nationwide.
Gloria Steinem had pushed through gender barriers to take on serious journalism subjects, and had emerged as a prominent advocate for women’s rights. Through her work, Steinem met Dorothy Pittman-Hughes, who had founded New York City’s first shelter for domestic violence victims as well as the city’s Agency for Child Development. Together they founded Ms. Magazine, which avoided articles on homemaking and fashion in favor of pieces on women’s rights and empowerment. Ms. showcased powerful and accomplished women such as Shirley Chisholm and Sissy Farenthold, and was among the first publications to bring domestic violence, sexual harassment, and body image issues to the national conversation (Pogrebrin 2011).
Many advances in women’s rights were the result of women’s greater engagement in politics. For example, Patsy Mink, the first Asian American woman elected to Congress, was the co-author of the Education Amendments Act of 1972, Title IX of which prohibits sex discrimination in education. Mink had been interested in fighting discrimination in education since her youth, when she opposed racial segregation in campus housing while a student at the University of Nebraska. She went to law school after being denied admission to medical school because of her gender. Like Mink, many other women sought and won political office, many with the help of the National Women’s Political Caucus (NWPC). In 1971, the NWPC was formed by Bella Abzug, Gloria Steinem, Shirley Chisholm, and other leading feminists to encourage women’s participation in political parties, elect women to office, and raise money for their campaign.
Shirley Chisholm personally took up the mantle of women’s involvement in politics. Born of immigrant parents, she earned degrees from Brooklyn College and Columbia University, and began a career in early childhood education and advocacy. In the 1950’s she joined various political action groups, worked on election campaigns, and pushed for housing and economic reforms. After leaving one organization over its refusal to involve women in the decision-making process, she sought to increase gender and racial diversity within political and activist organizations throughout New York City. In 1968, she became the first Black woman elected to Congress. Refusing to take the quiet role expected of new Representatives, she immediately began sponsoring bills and initiatives. She spoke out against the Vietnam War, and fought for programs such as Head Start and the national school lunch program, which was eventually signed into law after Chisholm led an effort to override a presidential veto. Chisholm would eventually undertake a groundbreaking presidential run in 1972, and is viewed as paving the way for other women, and especially women of color, achieving political and social prominence (Emmrich 2019).
### Theoretical Perspectives on Gender
Sociological theories help sociologists to develop questions and interpret data. For example, a sociologist studying why middle-school girls are more likely than their male counterparts to fall behind grade-level expectations in math and science might use a feminist perspective to frame her research. Another scholar might proceed from the conflict perspective to investigate why women are underrepresented in political office, and an interactionist might examine how the symbols of femininity interact with symbols of political authority to affect how women in Congress are treated by their male counterparts in meetings.
### Structural Functionalism
Structural functionalism has provided one of the most important perspectives of sociological research in the twentieth century and has been a major influence on research in the social sciences, including gender studies. Viewing the family as the most integral component of society, assumptions about gender roles within marriage assume a prominent place in this perspective.
Functionalists argue that gender roles were established well before the pre-industrial era when men typically took care of responsibilities outside of the home, such as hunting, and women typically took care of the domestic responsibilities in or around the home. These roles were considered functional because women were often limited by the physical restraints of pregnancy and nursing and unable to leave the home for long periods of time. Once established, these roles were passed on to subsequent generations since they served as an effective means of keeping the family system functioning properly.
When changes occurred in the social and economic climate of the United States during World War II, changes in the family structure also occurred. Many women had to assume the role of breadwinner (or modern hunter-gatherer) alongside their domestic role in order to stabilize a rapidly changing society. When the men returned from war and wanted to reclaim their jobs, society fell back into a state of imbalance, as many women did not want to forfeit their wage-earning positions (Hawke 2007).
### Conflict Theory
According to conflict theory, society is a struggle for dominance among social groups (like women versus men) that compete for scarce resources. When sociologists examine gender from this perspective, we can view men as the dominant group and women as the subordinate group. According to conflict theory, social problems are created when dominant groups exploit or oppress subordinate groups. Consider the Women’s Suffrage Movement or the debate over women’s “right to choose” their reproductive futures. It is difficult for women to rise above men, as dominant group members create the rules for success and opportunity in society (Farrington and Chertok 1993).
Friedrich Engels, a German sociologist, studied family structure and gender roles. Engels suggested that the same owner-worker relationship seen in the labor force is also seen in the household, with women assuming the role of the proletariat. This is due to women’s dependence on men for the attainment of wages, which is even worse for women who are entirely dependent upon their spouses for economic support. Contemporary conflict theorists suggest that when women become wage earners, they can gain power in the family structure and create more democratic arrangements in the home, although they may still carry the majority of the domestic burden, as noted earlier (Rismanand and Johnson-Sumerford 1998).
### Feminist Theory
Feminist theory is a type of conflict theory that examines inequalities in gender-related issues. It uses the conflict approach to examine the maintenance of gender roles and inequalities. Radical feminism, in particular, considers the role of the family in perpetuating male dominance. In patriarchal societies, men’s contributions are seen as more valuable than those of women. Patriarchal perspectives and arrangements are widespread and taken for granted. As a result, women’s viewpoints tend to be silenced or marginalized to the point of being discredited or considered invalid.
Sanday’s study of the Indonesian Minangkabau (2004) revealed that in societies some consider to be matriarchies (where women comprise the dominant group), women and men tend to work cooperatively rather than competitively regardless of whether a job is considered feminine by U.S. standards. The men, however, do not experience the sense of bifurcated consciousness under this social structure that modern U.S. females encounter (Sanday 2004).
### Symbolic Interactionism
Symbolic interactionism aims to understand human behavior by analyzing the critical role of symbols in human interaction. This is certainly relevant to the discussion of masculinity and femininity. Imagine that you walk into a bank hoping to get a small loan for school, a home, or a small business venture. If you meet with a male loan officer, you may state your case logically by listing all the hard numbers that make you a qualified applicant as a means of appealing to the analytical characteristics associated with masculinity. If you meet with a female loan officer, you may make an emotional appeal by stating your good intentions as a means of appealing to the caring characteristics associated with femininity.
Because the meanings attached to symbols are socially created and not natural, and fluid, not static, we act and react to symbols based on the current assigned meaning. The word gay, for example, once meant “cheerful,” but by the 1960s it carried the primary meaning of “homosexual.” In transition, it was even known to mean “careless” or “bright and showing” (Oxford American Dictionary 2010). Furthermore, the word gay (as it refers to a person), carried a somewhat negative and unfavorable meaning fifty years ago, but it has since gained more neutral and even positive connotations. When people perform tasks or possess characteristics based on the gender role assigned to them, they are said to be doing gender. This notion is based on the work of West and Zimmerman (1987). Whether we are expressing our masculinity or femininity, West and Zimmerman argue, we are always "doing gender." Thus, gender is something we do or perform, not something we are.
In other words, both gender and sexuality are socially constructed. The social construction of sexuality refers to the way in which socially created definitions about the cultural appropriateness of sex-linked behavior shape the way people see and experience sexuality. This is in marked contrast to theories of sex, gender, and sexuality that link male and female behavior to biological determinism, or the belief that men and women behave differently due to differences in their biology.
### Summary
Children become aware of gender roles in their earliest years, and they come to understand and perform these roles through socialization, which occurs through four major agents: family, education, peer groups, and mass media. Socialization into narrowly prescribed gender roles results in the stratification of men and women. The impacts of discrimination and inequality have deep implications for economics, social mobility, and political power. The feminist movement undertook protests, improvement programs, and political focus in order to improve equality and the lives of women. Each sociological perspective offers a valuable view for understanding how and why gender inequality occurs in our society.
### Section Quiz
### Short Answer
### Further Research
Learn more about Women’s Rights movements in the United States.
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# Gender, Sex, and Sexuality
## Sexuality
### Sexual Attitudes and Practices
In the area of sexuality, sociologists focus their attention on sexual attitudes and practices, not on physiology or anatomy. As mentioned earlier, sexuality is viewed as a person’s capacity for sexual feelings. Studying sexual attitudes and practices is a particularly interesting field of sociology because sexual behavior is a cultural universal. Throughout time and place, the vast majority of human beings have participated in sexual relationships (Broude 2003). Each society, however, interprets sexuality and sexual activity in different ways. At the same time, sociologists have learned that certain norms are shared among most societies. The incest taboo is present in every society, though which relative is deemed unacceptable for sex varies widely from culture to culture. For example, sometimes the relatives of the father are considered acceptable sexual partners for a woman while the relatives of the mother are not. Likewise, societies generally have norms that reinforce their accepted social system of sexuality.
What is considered “normal” in terms of sexual behavior is based on the mores and values of the society. Societies that value monogamy, for example, would likely oppose extramarital sex. Individuals are socialized to sexual attitudes by their family, education system, peers, media, and religion. Historically, religion has been the greatest influence on sexual behavior in most societies, but in more recent years, peers and the media have emerged as two of the strongest influences, particularly among U.S. teens (Potard, Courtois, and Rusch 2008). Let us take a closer look at sexual attitudes in the United States and around the world.
### Sexuality around the World
Cross-national research on sexual attitudes in industrialized nations reveals that normative standards differ across the world. For example, several studies have shown that Scandinavian students are more tolerant of premarital sex than are U.S. students (Grose 2007). A study of 37 countries reported that non-Western societies—like China, Iran, and India—valued chastity highly in a potential mate, while Western European countries—such as France, the Netherlands, and Sweden—placed little value on prior sexual experiences (Buss 1989).
Even among Western cultures, attitudes can differ. For example, according to a 33,590-person survey across 24 countries, 89 percent of Swedes responded that there is nothing wrong with premarital sex, while only 42 percent of Irish responded this way. From the same study, 93 percent of Filipinos responded that sex before age 16 is always wrong or almost always wrong, while only 75 percent of Russians responded this way (Widmer, Treas, and Newcomb 1998). Sexual attitudes can also vary within a country. For instance, 45 percent of Spaniards responded that homosexuality is always wrong, while 42 percent responded that it is never wrong; only 13 percent responded somewhere in the middle (Widmer, Treas, and Newcomb 1998).
Of industrialized nations, several European nations are is thought to be the most liberal when it comes to attitudes about sex, including sexual practices and sexual openness. Sweden, for example, has very few regulations on sexual images in the media, and sex education, which starts around age six, is a compulsory part of Swedish school curricula. Switzerland, Belgium, Iceland, Denmark, and The Netherlands have similar policies. Their more open approach to sex has helped countries avoid some of the major social problems associated with sex. For example, rates of teen pregnancy and sexually transmitted disease are among the world’s lowest in Switzerland and the Netherlands – lower than other European countries and far lower than the United States (Grose 2007 and Dutch News 2017). It would appear that these approaches are models for the benefits of sexual freedom and frankness. However, implementing their ideals and policies regarding sexuality in other, more politically conservative, nations would likely be met with resistance.
### Sexuality in the United States
The United States prides itself on being the land of the “free,” but it is rather restrictive when it comes to its citizens’ general attitudes about sex compared to other industrialized nations. In an international survey, 25 percent of U.S. respondents stated that premarital sex is always wrong, while the average among the 24 countries surveyed was 17 percent, with less than ten percent of respondents from France, Germany, and Spain saying premarital sex was unacceptable (Chamie 2018). Similar discrepancies were found in questions about the condemnation of sex before the age of 16, extramarital sex, and homosexuality, with total disapproval of these acts being 12, 13, and 11 percent higher, respectively, in the United States, than the study’s average (Widmer, Treas, and Newcomb 1998). U.S. culture is particularly restrictive in its attitudes about sex when it comes to women and sexuality.
It is widely believed that men are more sexual than are women. In fact, there was a popular notion that men think about sex every seven seconds. Research, however, suggests that men think about sex an average of 19 times per day, which is closer to once an hour, compared to 10 times per day for women (Fisher, Moore, and Pittenger 2011).
Belief that men have—or have the right to—more sexual urges than women creates a double standard. Ira Reiss, a pioneer researcher in the field of sexual studies, defined the double standard as prohibiting premarital sexual intercourse for women but allowing it for men (Reiss 1960). This standard has evolved into allowing women to engage in premarital sex only within committed love relationships, but allowing men to engage in sexual relationships with as many partners as they wish without condition (Milhausen and Herold 1999). Due to this double standard, a woman is likely to have fewer sexual partners in her life time than a man. According to a Centers for Disease Control and Prevention (CDC) survey, the average thirty-five-year-old woman has had three opposite-sex sexual partners while the average thirty-five-year-old man has had twice as many (Centers for Disease Control 2011).
The future of a society’s sexual attitudes may be somewhat predicted by the values and beliefs that a country’s youth expresses about sex and sexuality. Data from the most recent National Survey of Family Growth reveals that 70 percent of boys and 78 percent of girls ages fifteen to nineteen said they “agree” or “strongly agree” that “it’s okay for an unmarried female to have a child" (National Survey of Family Growth 2013). In a separate survey, 65 percent of teens stated that they “strongly agreed” or “somewhat agreed” that although waiting until marriage for sex is a nice idea, it’s not realistic (NBC News 2005). This does not mean that today’s youth have given up traditional sexual values such as monogamy. Nearly all college men (98.9 percent) and women (99.2 percent) who participated in a 2002 study on sexual attitudes stated they wished to settle down with one mutually exclusive sexual partner at some point in their lives, ideally within the next five years (Pedersen et al. 2002).
### Sex Education
One of the biggest controversies regarding sexual attitudes is sexual education in U.S. classrooms. Unlike many other countries, sex education is not required in all public school curricula in the United States. The heart of the controversy is not about whether sex education should be taught in school (studies have shown that only seven percent of U.S. adults oppose sex education in schools); it is about the type of sex education that should be taught.
Much of the debate is over the issue of abstinence as compared to a comprehensive sex education program. Abstinence-only programs focus on avoiding sex until marriage and/or delaying it as long as possible. So they do not focus on other types of prevention of unwanted pregnancies and sexually transmitted infections. As a result, according to the Sexuality and Information Council of the United States, only 38 percent of high schools and 14 percent of middle schools across the country teach all 19 topics identified as critical for sex education by the Centers for Disease Control and Prevention (Janfaza 2020).
Research suggests that while government officials may still be debating about the content of sexual education in public schools, the majority of U.S. adults are not. Two-thirds (67 percent) of Americans say education about safer sexual practices is more effective than abstinence-only education in terms of reducing unintended pregnancies. A slightly higher percentage—69 percent—say that emphasizing safer sexual practices and contraception in sexuality education is a better way to reduce the spread of STIs than is emphasizing abstinence (Davis 2018).
Even with these clear majorities in favor of comprehensive education, the Federal government offers roughly $85 million per year to communities that will drive abstinence-only sex education (Columbia Public Health 2017 a). The results, as stated earlier, are relatively clear: the United States has nearly four times the rate of teenage pregnancy than a country like Germany, which has a comprehensive sex education program.
In a similar educational issue not necessarily related to sexuality, researchers and public health advocates find that young girls feel underprepared for puberty. Ages of first menstruation (menarche) and breast development are continually declining in the United States, but education about these changes typically doesn't begin until middle school, which is generally too late. Young people indicate concerns about misinformation and discomfort during the informal conversations about the topics with friends, sisters, or mothers (Columbia Public Health 2017 b)
### Sociological Perspectives on Sex and Sexuality
Sociologists representing all three major theoretical perspectives study the role sexuality plays in social life today. Scholars recognize that sexuality continues to be an important and defining social location and that the manner in which sexuality is constructed has a significant effect on perceptions, interactions, and outcomes.
### Structural Functionalism
When it comes to sexuality, functionalists stress the importance of regulating sexual behavior to ensure marital cohesion and family stability. Since functionalists identify the family unit as the most integral component in society, they maintain a strict focus on it at all times and argue in favor of social arrangements that promote and ensure family preservation.
Functionalists such as Talcott Parsons (1955) have long argued that the regulation of sexual activity is an important function of the family. Social norms surrounding family life have, traditionally, encouraged sexual activity within the family unit (marriage) and have discouraged activity outside of it (premarital and extramarital sex). From a functionalist point of view, the purpose of encouraging sexual activity in the confines of marriage is to intensify the bond between spouses and to ensure that procreation occurs within a stable, legally recognized relationship. This structure gives offspring the best possible chance for appropriate socialization and the provision of basic resources.
In this context, the functionalist perspective does not take into account the increasing legal acceptance of same-sex marriage, or the rise in LGBTQ couples who choose to bear and raise children through a variety of available resources.
### Conflict Theory
From a conflict theory perspective, sexuality is another area in which power differentials are present and where dominant groups actively work to promote their worldview as well as their economic interests.
For conflict theorists, there were two key dimensions to the debate over marriage equality—one ideological and the other economic. Dominant groups wish for their worldview—which embraces traditional marriage and the nuclear family—to win out over what they see as the intrusion of a secular, individually driven worldview. On the other hand, many LGBTQ activists argue that legal marriage is a fundamental right that cannot be denied based on sexual orientation and that, historically, there already exists a precedent for changes to marriage laws: the 1960s legalization of formerly forbidden interracial marriages is one example.
From an economic perspective, activists in favor of same-sex marriage point out that legal marriage brings with it certain entitlements, many of which are financial in nature, like Social Security benefits and medical insurance (Solmonese 2008). Denial of these benefits to same-sex couples is wrong, they argue. Conflict theory suggests that as long as people struggle over these social and financial resources, there will be some degree of conflict.
### Symbolic Interactionism
Interactionists focus on the meanings associated with sexuality and with sexual orientation. Since femininity is devalued in U.S. society, those who adopt such traits are subject to ridicule; this is especially true for boys or men. Just as masculinity is the symbolic norm, so too has heterosexuality come to signify normalcy. Prior to 1973, the American Psychological Association (APA) defined homosexuality as an abnormal or deviant disorder. Interactionist labeling theory recognizes the impact this has made. Before 1973, the APA was powerful in shaping social attitudes toward homosexuality by defining it as pathological. Today, the APA cites no association between sexual orientation and psychopathology and sees homosexuality as a normal aspect of human sexuality (APA 2008).
Recall Cooley’s “looking-glass self,” which suggests that self develops as a result of our interpretation and evaluation of the responses of others (Cooley 1902). Constant exposure to derogatory labels, jokes, and pervasive homophobia would lead to a negative self-image, or worse, self-hate. The CDC reports that homosexual youths (as referred to in the study) who experience high levels of social rejection are six times more likely to have high levels of depression and eight times more likely to have attempted suicide (CDC 2011).
### Queer Theory
Queer Theory is an interdisciplinary approach to sexuality studies that identifies Western society’s rigid splitting of gender into specific roles and questions the manner in which we have been taught to think about sexual orientation. According to Jagose (1996), Queer [Theory] focuses on mismatches between anatomical sex, gender identity, and sexual orientation, not just division into male/female or homosexual/hetereosexual. By calling their discipline “queer,” scholars reject the effects of labeling; instead, they embraced the word “queer” and reclaimed it for their own purposes. The perspective highlights the need for a more flexible and fluid conceptualization of sexuality—one that allows for change, negotiation, and freedom. This mirrors other oppressive schemas in our culture, especially those surrounding gender and race (Black versus White, man versus woman).
Queer theorist Eve Kosofsky Sedgwick argued against U.S. society’s monolithic definition of sexuality and its reduction to a single factor: the sex of someone’s desired partner. Sedgwick identified dozens of other ways in which people’s sexualities were different, such as:
1. Even identical genital acts mean very different things to different people.
2. Sexuality makes up a large share of the self-perceived identity of some people, a small share of others’.
3. Some people spend a lot of time thinking about sex, others little.
4. Some people like to have a lot of sex, others little or none.
5. Many people have their richest mental/emotional involvement with sexual acts that they don’t do, or don’t even want to do.
6. Some people like spontaneous sexual scenes, others like highly scripted ones, others like spontaneous-sounding ones that are nonetheless totally predictable.
7. Some people experience their sexuality as deeply embedded in a matrix of gender meanings and gender differentials. Others do not (Sedgwick 1990).
Thus, theorists utilizing queer theory strive to question the ways society perceives and experiences sex, gender, and sexuality, opening the door to new scholarly understanding.
Throughout this chapter we have examined the complexities of gender, sex, and sexuality. Differentiating between sex, gender, and sexual orientation is an important first step to a deeper understanding and critical analysis of these issues. Understanding the sociology of sex, gender, and sexuality will help to build awareness of the inequalities experienced by people outside the dominant groups.
### Summary
When studying sex and sexuality, sociologists focus their attention on sexual attitudes and practices, not on physiology or anatomy. Norms regarding gender and sexuality vary across cultures. In general, the United States tends to be fairly conservative in its sexual attitudes. As a result, programs such as sex education are often limited or selective in what topics they cover.
### Section Quiz
### Short Answer
### Further Research
To learn about different approaches to sex education, visit Advocates for Youth.
### References
American Psychological Association (APA). 2008. “Answers to Your Questions: For a Better Understanding of Sexual Orientation and Homosexuality.” Washington, DC. Retrieved January 10, 2012 (http://www.apa.org/topics/sexuality/orientation.aspx).
Broude, Gwen J. 2003. “Sexual Attitudes and Practices.” Pp. 177–184 in Encyclopedia of Sex and Gender: Men and Women in the World's Cultures Volume 1. New York, NY: Springer.
Buss, David M. 1989. “Sex Differences in Human Mate Preferences: Evolutionary Hypothesis Tested in 37 Cultures.” Behavioral and Brain Sciences 12(1):1–49.
Centers for Disease Control and Prevention. 2011. “Lesbian, Gay, Bisexual, and Transgender Health.” January 25. Retrieved February 13, 2012 (http://www.cdc.gov/lgbthealth/youth.htm).
Chamie, Joseph. 2018. “Premarital Sex Increasing Worldwide.” Inter Press Service. April 5 2018. (http://www.ipsnews.net/2018/04/premarital-sex-increasing-worldwide/)
Columbia Public Health. 2017. a. “Abstinence-Only Education Is a Failure.” Columbia University Mailman School of Health. August 22 2017. (https://www.publichealth.columbia.edu/public-health-now/news/abstinence-only-education-failure)
Columbia Public Health. 2017. b. “Study Finds Girls Unprepared for Puberty.” Columbia University Mailman School of Health. January 5 2017. (https://www.publichealth.columbia.edu/public-health-now/news/study-finds-girls-feel-unprepared-puberty)
Cooley, Charles Horton. 1902. Human Nature and the Social Order. New York: Scribner.
Davis, Carolyn J. and Cox, Daniel and Griffin, Rob and Jones, Robert P. 2018. “Young People Set To Impact Debate on Public Health.” PRRI. April 17 2018. (https://www.prri.org/research/young-people-set-to-impact-the-debate-on-womens-health-issues/)
Dutch News. 2017. “The Netherlands has the lowest rate of teenage mothers in the EU.” Dutch News. December 11 2017. (https://www.dutchnews.nl/news/2017/12/the-netherlands-has-lowest-rate-of-teenage-mothers-in-the-eu/)
Fisher, T.D., Z.T. Moore, and M. Pittenger. 2011. “Sex on the Brain?: An Examination of Frequency of Sexual Cognitions as a Function of Gender, Erotophilia, and Social Desirability.” The Journal of Sex Research 49(1):69–77.
Grose, Thomas K. 2007. “Straight Facts About the Birds and Bees.” US News and World Report, March 18. Retrieved February 13, 2012 (http://www.usnews.com/usnews/news/articles/070318/26sex.htm).
Hall, Donald. 2003. Queer Theories. London: Palgrave MacMillan.
Jagose, Annamarie. 1996. Queer Theory: An Introduction. New York: New York University Press.
Janfanza, Rachel. 2020. “The Nuanced Push for American Sex Education.” Harvard Political Review. January 24 2020. (https://harvardpolitics.com/american-sex-education/)
Milhausen, Robin, and Edward Herold. 1999. “Does the Sexuality Double Standard Still Exist? Perceptions of University Women.” Journal of Sex Research 36(4):361–368.
National Public Radio (NPR). 2004. NPR/Kaiser/Kennedy School Poll: Sex Education in America. Retrieved February 13, 2012 (http://www.npr.org/templates/story/story.php?storyId=1622610).
National Survey of Family Growth. 2013. "Key Statistics From the National Survey for Family Growth." Centers for Disease Control and Prevention. Retrieved October 13, 2014 (http://www.cdc.gov/nchs/nsfg/key_statistics/a.htm").
National Survey of Sexual Health and Behavior. 2010. “Findings from the National Survey of Sexual Health and Behavior, Centre for Sexual Health Promotion, Indiana University.” Journal of Sexual Medicine 7(s5):243–373.
NBC News/People. 2005. National Survey of Young Teens’ Sexual Attitudes and Behaviors. January 27.
Parsons, Talcott, Robert F. Bales, James Olds, Morris Zelditsch, and Philip E. Slater. 1955. Family, Socialization, and Interaction Process. New York: Free Press.
Pedersen, W.C., L.C. Miller, A. Putcha-Bhagavatula, and Y. Yang. 2002. “Evolved Sex Differences in the Number of Partners Desired? The Long and the Short of It.” Psychological Science 13(2):157–161.
Potard, C., R. Courtoisand, and E. Rusch. 2008. “The Influence of Peers on Risky Sexual Behavior During Adolescence.” European Journal of Contraception & Reproductive Health Care 13(3):264–270.
Sedgwick, Eve Kosofsky. 1990. Epistemology of the Closet. Berkeley, CA: University of California Press.
Solmonese, Joe. 2008. “Gay Marriage Makes Financial Sense.” BusinessWeek. Retrieved February 22, 2012 (http://www.businessweek.com/debateroom/archives/2008/04/_pro_preempting.html).
Transgender Law & Policy Institute. 2007. Retrieved February 13, 2012 (www.transgenderlaw.org).
Turner, William B. 2000. A Genealogy of Queer Theory. Philadelphia, PA: Temple University Press. |
# Aging and the Elderly
## Introduction
9-year old twins Osiris and Joli loved making meals with Bibi, their grandmother. Osiris loved the cooking; Joli loved stealing the ingredients. The kids didn't get very involved with the chicken, but perked up with the fufu and almost took over the dough balls. Bibi yelled at Joli to stop eating raw batter, but she didn't mean it.
Bibi loved having them around. She sang mash-ups of 90s songs and big band music, mixing in funny mentions of their day-to-day lives. As she prepped the cassava, she'd throw the discarded pieces in a waste bowl like she was playing basketball. Bibi told them a story about how one of her schoolteachers was was so young that all the students thought she was one of them. “So when she told us her last name, I thought it was her first name and called her by it. So she sent me outside for punishment!”
The kids burst into peals of laughter. Bibi joined in as she moved a pan.
Suddenly the stove erupted in flame. The oil in the pan had spilled over. Bibi grabbed a glass of water on the table. Joli screamed at her to stop, but Bibi had already thrown the water onto the oil. The flames flared and splattered across the stove and onto the counter. A paper towel caught fire. Everyone was screaming. Osiris and Joli's mother, Gloria, was in the room a moment later. Pushing Bibi away, she turned off the stove and threw a towel on some of the flames. She took a fire extinguisher from the cabinet and, after a few seconds of fiddling with the pin and hose, emptied it onto the fire.
“Mom!” Gloria yelled. “Why would you put water on an oil fire? You know that's the last thing to do!”
Bibi, in the corner, seemed to hold on to the wall to remain standing. She shook her head and looked at the children. “It's a fire. You put water on it.”
“No you don't. You taught me never to do that. You told me to use salt...anything but water. You could have burned down the house!”
Bibi was crying. She looked at the children and sank toward the floor. “I don't remember that. I'm so sorry. It's a fire, I thought. Put water on it.” Gloria sent the children out of the room and sat her mother down.
Aside from the scare from the fire, why might Bibi be crying? What difficulties do older people face in undertaking day-to-day activities? What difficulties do their family members face? In this chapter, we will explore the identities and issues of older people in our societies, and consider our attitudes and obligations toward them.
### References
Boston University School of Medicine. 2014. “New England Centenarian Study Overview.” Retrieved November 2, 2014 (http://www.bumc.bu.edu/centenarian/overview/).
Diebel, Matthew. 2014. “Yes, Six People Born in the 19th Century Are Still With Us.” USA Today. Retrieved November 2, 2014 (http://www.usatoday.com/story/news/world/2014/09/05/six-people-still-alive-who-were-born-in-the-19th-century/15122367/).
Gerontology Research Group. 2014. “Current Validated Living Supercentenarians.” Retrieved November 2, 2014 (http://www.grg.org/Adams/E.HTM).
United States Census Bureau. 2011. “Census Bureau Releases Comprehensive Analysis of Fast-Growing 90-and0Older Population.” Newsroom Archive, November 17. Retrieved November 1, 2014 (https://www.census.gov/newsroom/releases/archives/aging_population/cb11-194.html).
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# Aging and the Elderly
## Who Are the Elderly? Aging in Society
Think of U.S. movies and television shows you have watched recently. Did any of them feature older actors and actresses? What roles did they play? How were these older actors portrayed? Were they cast as main characters in a love story? Did they seem fully capable, safe, productive, and happy? Or were they a challenge to those around them? Were they grouchy or overly set in their ways?
Many media portrayals of the elderly reflect negative cultural attitudes toward aging. In the United States, society tends to glorify youth and associate it with beauty and sexuality. In comedies, the elderly are often associated with grumpiness or hostility. Rarely do the roles of older people convey the fullness of life experienced by seniors—as employees, lovers, or the myriad roles they have in real life. What values does this reflect?
One hindrance to society’s fuller understanding of aging is that people rarely understand the process of aging until they reach old age themselves. This lack of understanding is in stark contrast to our perspective on childhood, something we've all experienced. And as is often the case with a lack of knowledge or understanding, it leads to myths, assumptions, and stereotypes about elderly people and the aging process. While stereotypes associated with race and gender may lead to more critical thought and sensitivity, many people accept age stereotypes without question (Levy 2002). Consider this: At your school or workplace, you have likely had the opportunity (or may be required) to attend workshops on racial equity, cultural sensitivity, sexual harassment, and so on. But even though the elderly are all around us (and increasing in number every day), very few institutions conduct similar workshops or forums about the elderly. Each culture has a certain set of expectations and assumptions about aging, all of which are part of our socialization.
While the landmarks of maturing into adulthood are a source of pride, often celebrated at major milestones like First Communion, Bar Mitzvah, or Quinceañera, signs of natural aging can be cause for shame or embarrassment. Some people avoid acknowledging their aging by rejecting help when they need it , which can lead to physical injury or problems obtaining needed items or information. For example, when vaccinations for the COVID-19 virus became available, U.S. seniors who didn't have help from family and friends lagged significantly in receiving vaccines; this occurred despite of the fact that seniors were known to be the highest risk group and were the most susceptible to illness and death if they were infected (Graham 2021). Those elderly people who were resistant to reach out for help may have waited too long, and their neighbors or other community members may not have known they needed the help. Why would they take this risk? Researchers aim to uncover the motivations and challenges that may result in these circumstances and behavior.
Gerontology is a field of science that seeks to understand the process of aging and the challenges encountered as seniors grow older. Gerontologists investigate age, aging, and the aged. Gerontologists study what it is like to be an older adult in a society and the ways that aging affects members of a society. As a multidisciplinary field, gerontology includes the work of medical and biological scientists, social scientists, and even financial and economic scholars.
Social gerontology refers to a specialized field of gerontology that examines the social (and sociological) aspects of aging. Researchers focus on developing a broad understanding of the experiences of people at specific ages, such as mental and physical wellbeing, plus age-specific concerns such as the process of dying. Social gerontologists work as social researchers, counselors, community organizers, and service providers for older adults. Because of their specialization, social gerontologists are in a strong position to advocate for older adults.
Scholars in these disciplines have learned that “aging” reflects not only the physiological process of growing older but also our attitudes and beliefs about the aging process. You’ve likely seen online calculators that promise to determine your “real age” as opposed to your chronological age. These ads target the notion that people may “feel” a different age than their actual years. Some sixty-year-olds feel frail and elderly, while some eighty-year-olds feel sprightly.
Equally revealing is that as people grow older they define “old age” in terms of greater years than their current age (Logan 1992). Many people want to postpone old age and regard it as a phase that will never arrive. For example, many older Americans keep working well past what people consider retirement age, due to financial pressures or in order to remain, in their eyes, useful. Some older adults even succumb to stereotyping their own age group (Rothbaum 1983).
In the United States, the experience of being elderly has changed greatly over the past century. In the late 1800s and early 1900s, many U.S. households were home to multigenerational families, and the experiences and wisdom of elders was respected. They offered wisdom and support to their children and often helped raise their grandchildren (Sweetser 1984).
Multigenerational U.S. families began to decline after World War II, and their numbers reached a low point around 1980, but they are consistently on the rise. A 2010 Pew Research Center analysis of census data found that 49 million people in the United States lived in a family household with at least two adult generations—or a grandparent and at least one other generation a record at the time. By 2016, that number had grown to 64 million people living in multigenerational households, roughly 20 percent of the population (Cohn 2018).
Attitudes toward the elderly have also been affected by large societal changes that have happened over the past 100 years. Researchers believe industrialization and modernization have contributed greatly to lowering the power, influence, and prestige the elderly once held. On the other hand, the sheer numbers of elderly people in certain societies can have other effects, such as older people's influence on policies and politics based on their voting influence.
The elderly have both benefited and suffered from these rapid social changes. In modern societies, a strong economy created new levels of prosperity for many people. Healthcare has become more widely accessible, and medicine has advanced, which allows the elderly to live longer. However, older people are not as essential to the economic survival of their families and communities as they were in the past.
### Studying Aging Populations
Since its creation in 1790, the U.S. Census Bureau has been tracking age in the population. Age is an important factor to analyze with accompanying demographic figures, such as income and health. The population chart below shows projected age distribution patterns for the next several decades.
Statisticians use data to calculate the median age of a population, that is, the number that marks the halfway point in a group’s age range. In the United States, the median age is about forty (U.S. Census Bureau 2010). That means that about half of the people in the United States are under forty and about half are over forty. This median age has been increasing, which indicates the population as a whole is growing older.
A cohort is a group of people who share a statistical or demographic trait. People belonging to the same age cohort were born in the same time frame. Understanding a population’s age composition can point to certain social and cultural factors and help governments and societies plan for future social and economic challenges.
Sociological studies on aging might help explain the difference between Native American age cohorts and the general population. While Native American societies have a strong tradition of revering their elders, they also have a lower life expectancy because of lack of access to healthcare and high levels of mercury in fish, which is a traditional part of their diet.
### Phases of Aging: The Young-Old, Middle-Old, and Old-Old
In the United States, all people over eighteen years old are considered adults, but there is a large difference between a person who is twenty-one years old and a person who is forty-five years old. More specific breakdowns, such as “young adult” and “middle-aged adult,” are helpful. In the same way, groupings are helpful in understanding the elderly. The elderly are often lumped together to include everyone over the age of sixty-five. But a sixty-five-year-old’s experience of life is much different from a ninety-year-old’s.
The United States’ older adult population can be divided into three life-stage subgroups: the young-old (approximately sixty-five to seventy-four years old), the middle-old (ages seventy-five to eighty-four years old), and the old-old (over age eighty-five). Today’s young-old age group is generally happier, healthier, and financially better off than the young-old of previous generations. In the United States, people are better able to prepare for aging because resources are more widely available.
Also, many people are making proactive quality-of-life decisions about their old age while they are still young. In the past, family members made care decisions when an elderly person reached a health crisis, often leaving the elderly person with little choice about what would happen. The elderly are now able to choose housing, for example, that allows them some independence while still providing care when it is needed. Living wills, retirement planning, and medical power of attorney are other concerns that are increasingly handled in advance.
### The Graying of the United States
What does it mean to be elderly? Some define it as an issue of physical health, while others simply define it by chronological age. The U.S. government, for example, typically classifies people aged sixty-five years old as elderly, at which point citizens are eligible for federal benefits such as Social Security and Medicare. The World Health Organization has no standard, other than noting that sixty-five years old is the commonly accepted definition in most core nations, but it suggests a cut-off somewhere between fifty and fifty-five years old for semi-peripheral nations, such as those in Africa (World Health Organization 2012). AARP (formerly the American Association of Retired Persons) cites fifty as the eligible age of membership. It is interesting to note AARP’s name change; by taking the word “retired” out of its name, the organization can broaden its base to any older people in the United States, not just retirees. This is especially important now that many people are working to age seventy and beyond.
There is an element of social construction, both local and global, in the way individuals and nations define who is elderly; that is, the shared meaning of the concept of elderly is created through interactions among people in society. As the table demonstrates, different generations have varying perspectives on aging. Researchers asked questions about the ages at which people reach certain milestones or new categories in life. Members of the Baby Boom generation indicate that a person is officially "old" when they turn 73 years old. Millennials, a much younger group, felt that people became old when they turned 59. The same survey asked questions about the end of youth and the prime of life (Emling 2017). Interestingly, Boomers and GenXers both felt that youth "ended" by age 31 and that the prime of life didn't start until many years later. Millennials felt that people reached the prime of life at age 36, before youth ended at age 40. It's worth noting that at the time of the survey, the Millennials were all 36 and younger.
Demographically, the U.S. population has undergone a massive shift both in the overall population of elderly people and their share of the total population. Both are significant and impactful on major policy decisions and day-to-day life. In 1900, the population of U.S people over sixty-five years old was 3 million, representing about 4 percent of the total population. That number increased to 33 million in 1994, and was roughly 12 percent of the total population (Hobbs 1994). By 2016 that number had grown to 49 million, about 15 percent of the total population (U.S. Census Bureau 2018). This is a greater than tenfold increase in the elderly population, compared to a mere tripling of both the total population and of the population under sixty-five years old (Hobbs 1994). This increase has been called “the graying of America,” a term that describes the phenomenon of a larger and larger percentage of the population getting older and older. There are several reasons why the United States is graying so rapidly. One of these is life expectancy: the average number of years a person born today may expect to live. When we review Census Bureau statistics grouping the elderly by age, it is clear that in the United States, at least, we are living longer. In 2010, there were about 80,000 centenarians in the United States alone. They make up one of the fastest-growing segments of the population (Boston University School of Medicine 2014).
It is interesting to note that not all people in the United States age equally. Most glaring is the difference between men and women; as shows, women have longer life expectancies than men. In 2010, there were ninety sixty-five-year-old men per one hundred sixty-five-year-old women. However, there were only eighty seventy-five-year-old men per one hundred seventy-five-year-old women, and only sixty eighty-five-year-old men per one hundred eighty-five-year-old women. Nevertheless, as the graph shows, the sex ratio actually increased over time, indicating that men are closing the gap between their life spans and those of women (U.S. Census Bureau 2010).
### Baby Boomers
Of particular interest to gerontologists today is the population of Baby Boomers, the cohort born between 1946 and 1964 and now reaching their 60s and 70s. Coming of age in the 1960s and early 1970s, the baby boom generation was the first group of children and teenagers with their own spending power and therefore their own marketing power (Macunovich 2000). As this group has aged, it has redefined what it means to be young, middle-aged, and now old. People in the Boomer generation do not want to grow old the way their grandparents did; the result is a wide range of products designed to ward off the effects—or the signs—of aging. Previous generations of people over sixty-five were “old.” Baby Boomers are in “later life” or “the third age” (Gilleard and Higgs 2007).
The baby boom generation is the cohort driving much of the dramatic increase in the over-sixty-five population. shows a comparison of the U.S. population by age and gender between 2000 and 2010. The biggest bulge in the pyramid (representing the largest population group) moves up the pyramid over the course of the decade; in 2000, the largest population group was age thirty-five to fifty-five. In 2010, that group was age forty-five to sixty-five, meaning the oldest baby Boomers were just reaching the age at which the U.S. Census considers them elderly. By 2030, all Baby Boomers will be age 65 and older, and represent the largest group of elderly people.
This aging of the Baby Boom cohort has serious implications for our society. Healthcare is one of the areas most impacted by this trend. According to the U.S. Department of Health and Human Services, healthcare spending is projected to grow by 5.5 percent each year from now until 2027. The portion of government spending on Medicare (a program in which the government covers some costs of healthcare for the elderly) is expected to increase from 3 percent of gross domestic product (GDP) in 2009 to 8 percent of GDP in 2030, and to 15 percent in 2080 (CMS 2018).
Certainly, as Boomers age, they will put increasing burdens on the entire U.S. healthcare system. The American Geriatrics Society notes that from 2013-2025, there will be a 45 percent increase in demand for physicians who specialize in geriatrics. As a result, over 33,000 specialists will be needed to fill the healthcare needs in 2025. And in 2020, there were only 6,320 such specialists in the United States (AGS 2021).
Unlike the elderly of previous generations, Boomers do not expect that turning sixty-five means their active lives are over. They are not willing to abandon work or leisure activities, but they may need more medical support to keep living vigorous lives. This desire of a large group of over-sixty-five-year-olds wanting to continue with a high activity level is driving innovation in the medical industry (Shaw n.d.).
The economic impact of aging Boomers is also an area of concern for many observers. Although the baby boom generation earned more than previous generations and enjoyed a higher standard of living, they did not adequately prepare for retirement. According to most retirement and investment experts, in order to maintain their accustomed lifestyle, people need to save ten times their annual income before retiring. (Note: That's income, not salary.) So if a person has an income of $60,000 per year, they should have saved $600,000. If they made $100,000 per year, they should have saved $1 million. But most Baby Boomers have only saved an estimated $144,000, and only 40 percent have saved more than $250,000 (Gravier 2021). The causes of these shortfalls are varied, and include everything from lavish spending to economic recession to companies folding and reducing pension payments. Higher education costs increased significantly while many Baby Boomers were sending their children to college. No matter what the cause, many retirees report a great deal of stress about running out of money.
Just as some observers are concerned about the possibility of Medicare being overburdened, Social Security is considered to be at risk. Social Security is a government-run retirement program funded primarily through payroll taxes. With enough people paying into the program, there should be enough money for retirees to take out. But with the aging Boomer cohort starting to receive Social Security benefits and fewer workers paying into the Social Security trust fund, economists warn that the system will collapse by the year 2037. A similar warning came in the 1980s; in response to recommendations from the Greenspan Commission, the retirement age (the age at which people could start receiving Social Security benefits) was raised from sixty-two to sixty-seven and the payroll tax was increased. A similar hike in retirement age, perhaps to seventy, is a possible solution to the current threat to Social Security.
### Aging around the World
The United States is certainly not alone regarding its aging population; in fact, it doesn’t even have the fastest-growing group of elderly people. In 2019, the world had 703 million people aged 65 years or over. By 2050, that number is projected to double to 1.5 billion. One in six people in the world will be 65 or over (United Nations 2020).
This percentage is expected to increase and will have a huge impact on the dependency ratio: the number of citizens not in the labor force (young, disabled, or elderly) to citizens in the labor force (Bartram and Roe 2005). One country that will soon face a serious aging crisis is China, which is on the cusp of an “aging boom”— a period when its elderly population will dramatically increase. The number of people above age sixty in China today is about 178 million, which amounts to 13.3 percent of its total population (Xuequan 2011). By 2050, nearly a third of the Chinese population will be age sixty or older, which will put a significant burden on the labor force and impact China’s economic growth (Bannister, Bloom, and Rosenberg 2010). On a more global scale, the dependency ratio is projected to more than double in Eastern and South-Eastern Asia, Latin America and the Caribbean, Northern Africa and Western Asia, and Central and Southern Asia.
As healthcare improves and life expectancy increases across the world, elder care will be an emerging issue. Wienclaw (2009) suggests that with fewer working-age citizens available to provide home care and long-term assisted care to the elderly, the costs of elder care will increase.
Worldwide, the expectation governing the amount and type of elder care varies from culture to culture. For example, in Asia the responsibility for elder care lies firmly on the family (Yap, Thang, and Traphagan 2005). This is different from the approach in most Western countries, where the elderly are considered independent and are expected to tend to their own care. It is not uncommon for family members to intervene only if the elderly relative requires assistance, often due to poor health. Even then, caring for the elderly is considered voluntary. In the United States, decisions to care for an elderly relative are often conditionally based on the promise of future returns, such as inheritance or, in some cases, the amount of support the elderly provided to the caregiver in the past (Hashimoto 1996).
These differences are based on cultural attitudes toward aging. In China, several studies have noted the attitude of filial piety (deference and respect to one’s parents and ancestors in all things) as defining all other virtues (Hsu 1971; Hamilton 1990). Cultural attitudes in Japan prior to approximately 1986 supported the idea that the elderly deserve assistance (Ogawa and Retherford 1993). However, seismic shifts in major social institutions (like family and economy) have created an increased demand for community and government care. For example, the increase in women working outside the home has made it more difficult to provide in-home care to aging parents, which leads to an increase in the need for government-supported institutions (Raikhola and Kuroki 2009).
In the United States, by contrast, many people view caring for the elderly as a burden. Even when there is a family member able and willing to provide for an elderly family member, 60 percent of family caregivers are employed outside the home and are unable to provide the needed support. At the same time, however, many middle-class families are unable to bear the financial burden of “outsourcing” professional healthcare, resulting in gaps in care (Bookman and Kimbrel 2011). It is important to note that even within the United States not all demographic groups treat aging the same way. While most people in the United States are reluctant to place their elderly members into out-of-home assisted care, demographically speaking, the groups least likely to do so are Latinos, African Americans, and Asians (Bookman and Kimbrel 2011).
Globally, the United States and other core nations are fairly well equipped to handle the demands of an exponentially increasing elderly population. However, peripheral and semi-peripheral nations face similar increases without comparable resources. Poverty among elders is a concern, especially among elderly women. The feminization of the aging poor, evident in peripheral nations, is directly due to the number of elderly women in those countries who are single, illiterate, and not a part of the labor force (Mujahid 2006).
In 2002, the Second World Assembly on Aging was held in Madrid, Spain, resulting in the Madrid Plan, an internationally coordinated effort to create comprehensive social policies to address the needs of the worldwide aging population. The plan identifies three themes to guide international policy on aging: 1) publicly acknowledging the global challenges caused by, and the global opportunities created by, a rising global population; 2) empowering the elderly; and 3) linking international policies on aging to international policies on development (Zelenev 2008).
The Madrid Plan has not yet been successful in achieving all its aims. However, it has increased awareness of the various issues associated with a global aging population, as well as raising the international consciousness to the way that the factors influencing the vulnerability of the elderly (social exclusion, prejudice and discrimination, and a lack of socio-legal protection) overlap with other developmental issues (basic human rights, empowerment, and participation), leading to an increase in legal protections (Zelenev 2008).
### Summary
The social study of aging uses population data and cohorts to predict social concerns related to aging populations. In the United States, the population is increasingly older (called “the graying of the United States”), especially due to the baby Boomer segment. Global studies on aging reveal a difference in life expectancy between core and peripheral nations as well as a discrepancy in nations’ preparedness for the challenges of increasing elderly populations.
### Section Quiz
### Short Answer
### Further Research
Gregory Bator founded the television show Graceful Aging and then developed a web site offering short video clips from the show. The purpose of Graceful Aging is to both inform and entertain, with clips on topics such as sleep, driving, health, safety, and legal issues. Bator, a lawyer, works on counseling seniors about their legal needs. Log onto for a visual understanding of aging.
### References
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Bookman, Ann, and Delia Kimbrel. 2011. “Families and Elder Care in the Twenty-First Century.” The Future of Children 21:117–140.
Bostrom, Josh. 2005. “Aging Baby Boomers Will Drive Health-Care Innovation.” Infoworld. Retrieved January 31, 2012 (http://www.infoworld.com/t/business/aging-baby-Boomers-will-drive-health-care-innovation-054).
Cohn, D'Vera and Passel, Jeffrey S. 2018. “A Record 64 Million Americans Live in Multigenerational Households.” Pew Research Center. (https://www.pewresearch.org/fact-tank/2018/04/05/a-record-64-million-americans-live-in-multigenerational-households/)
Congressional Budget Office. 2008. “Long-Term Outlook for Medicare, Medicaid and Total Health Care Spending.” Retrieved January 31, 2012 (http://www.cbo.gov/ftpdocs/102xx/doc10297/Chapter2.5.1.shtml).
Emling, Shelley. 2017. (“The Age At Which You Are Officially Old.”) AARP. (https://www.aarp.org/home-family/friends-family/info-2017/what-age-are-you-old-fd.html)
Farrel, Diana, David Court, Eric Beinhocker, John Forsyth, Ezra Greenberg, Suruchi Shukla, Jonathan Ablett, and Geoffrey Greene. 2008. Talkin' 'Bout My Generation: The Economic Impact of Aging US Baby Boomers. McKinsey Global Institute. Retrieved February 12, 2012 (http://www.mckinsey.com/Insights/MGI/Research/Americas/Talkin_bout_my_generation).
Gerontological Society of America. 2008. “Baby Boomer Health Care Crisis Looms.” Science Daily, April 17. Retrieved January 31, 2012 (http://www.sciencedaily.com/releases/2008/04/080417111300.htm).
Gilleard, Chris, and Paul Higgs. 2007. “The Third Age and the Baby Boomers: Two Approaches to the Social Structuring of Later Life.” International Journal of Ageing and Later Life 2(2):13–30.
Graham, Judith. 2021. “Older Adults Without Family or Friends Lag in Race to Get Vaccines.” KHN. (https://khn.org/news/article/older-adults-without-family-or-friends-lag-in-race-to-get-vaccines/)
Hamilton, Gary. 1990. “Patriarchy, Patrimonialism, and Filial Piety: A Comparison of China and Western Europe.” British Journal of Sociology 41:77–104.
Hashimoto, Akiko. 1996. The Gift of Generations: Japanese and American Perspectives on Aging and the Social Contract. New York: Cambridge University Press.
Hobbs, Frank. 1994. “The Elderly Population.” Population Profile of the United States. Retrieved January 28, 2012 (http://www.census.gov/population/www/pop-profile/elderpop.html).
Hsu, Francis. 1971. “Filial Piety in Japan and China: Borrowing, Variation and Significance.” Journal of Comparative Family Studies 2:67–74.
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# Aging and the Elderly
## The Process of Aging
As human beings grow older, they go through different phases or stages of life. It is helpful to understand aging in the context of these phases. A life course is the period from birth to death, including a sequence of predictable life events such as physical maturation. Each phase comes with different responsibilities and expectations, which of course vary by individual and culture. Children love to play and learn, looking forward to becoming preteens. As preteens begin to test their independence, they are eager to become teenagers. Teenagers anticipate the promises and challenges of adulthood. Adults become focused on creating families, building careers, and experiencing the world as independent people. Finally, many adults look forward to old age as a wonderful time to enjoy life without as much pressure from work and family life. In old age, grandparenthood can provide many of the joys of parenthood without all the hard work that parenthood entails. And as work responsibilities abate, old age may be a time to explore hobbies and activities that there was no time for earlier in life. But for other people, old age is not a phase that they look forward to. Some people fear old age and do anything to “avoid” it by seeking medical and cosmetic fixes for the natural effects of age. These differing views on the life course are the result of the cultural values and norms into which people are socialized, but in most cultures, age is a master status influencing self-concept, as well as social roles and interactions.
Through the phases of the life course, dependence and independence levels change. At birth, newborns are dependent on caregivers for everything. As babies become toddlers and toddlers become adolescents and then teenagers, they assert their independence more and more. Gradually, children come to be considered adults, responsible for their own lives, although the point at which this occurs is widely varied among individuals, families, and cultures.
As Riley (1978) notes, aging is a lifelong process and entails maturation and change on physical, psychological, and social levels. Age, much like race, class, and gender, is a hierarchy in which some categories are more highly valued than others. For example, while many children look forward to gaining independence, Packer and Chasteen (2006) suggest that even in children, age prejudice leads to a negative view of aging. This, in turn, can lead to a widespread segregation between the old and the young at the institutional, societal, and cultural levels (Hagestad and Uhlenberg 2006).
### Biological Changes
Each person experiences age-related changes based on many factors. Biological factors, such as molecular and cellular changes, are called primary aging, while aging that occurs due to controllable factors, such as lack of physical exercise and poor diet, is called secondary aging (Whitbourne and Whitbourne 2010).
Most people begin to see signs of aging after fifty years old, when they notice the physical markers of age. Skin becomes thinner, drier, and less elastic. Wrinkles form. Hair begins to thin and gray. Men prone to balding start losing hair. The difficulty or relative ease with which people adapt to these changes is dependent in part on the meaning given to aging by their particular culture. A culture that values youthfulness and beauty above all else leads to a negative perception of growing old. Conversely, a culture that reveres the elderly for their life experience and wisdom contributes to a more positive perception of what it means to grow old.
The effects of aging can feel daunting, and sometimes the fear of physical changes (like declining energy, food sensitivity, and loss of hearing and vision) is more challenging to deal with than the changes themselves. The way people perceive physical aging is largely dependent on how they were socialized. If people can accept the changes in their bodies as a natural process of aging, the changes will not seem as frightening.
According to the federal Administration on Aging (2011), in 2009 fewer people over sixty-five years old assessed their health as “excellent” or “very good” (41.6 percent) compared to those aged eighteen to sixty-four (64.4 percent). Evaluating data from the National Center for Health Statistics and the U.S. Bureau of Labor Statistics, the Administration on Aging found that from 2006 to 2008, the most frequently reported health issues for those over sixty-five years old included arthritis (50 percent), hypertension (38 percent), heart disease (32 percent), and cancer (22 percent). About 27 percent of people age sixty and older are considered obese by current medical standards. Parker and Thorslund (2006) found that while the trend is toward steady improvement in most disability measures, there is a concomitant increase in functional impairments (disability) and chronic diseases. At the same time, medical advances have reduced some of the disabling effects of those diseases (Crimmins 2004).
Some impacts of aging are gender-specific. Some of the disadvantages aging women face arise from long-standing social gender roles. For example, Social Security favors men over women, inasmuch as women do not earn Social Security benefits for the unpaid labor they perform (usually at home) as an extension of their gender roles. In the healthcare field, elderly female patients are more likely than elderly men to see their healthcare concerns trivialized (Sharp 1995) and are more likely to have their health issues labeled psychosomatic (Munch 2004). Another female-specific aspect of aging is that mass-media outlets often depict elderly females in terms of negative stereotypes and as less successful than older men (Bazzini and Mclntosh I997).
For men, the process of aging—and society’s response to and support of the experience—may be quite different. The gradual decrease in male sexual performance that occurs as a result of primary aging is medicalized and constructed as needing treatment (Marshall and Katz 2002) so that a man may maintain a sense of youthful masculinity. On the other hand, aging men have fewer opportunities to assert their masculine identities in the company of other men (for example, through sports participation) (Drummond 1998). And some social scientists have observed that the aging male body is depicted in the Western world as genderless (Spector-Mersel 2006).
### Social and Psychological Changes
Male or female, growing older means confronting the psychological issues that come with entering the last phase of life. Young people moving into adulthood take on new roles and responsibilities as their lives expand, but an opposite arc can be observed in old age. What are the hallmarks of social and psychological change?
Retirement—the withdrawal from paid work at a certain age—is a relatively recent idea. Up until the late nineteenth century, people worked about sixty hours a week until they were physically incapable of continuing. Following the American Civil War, veterans receiving pensions were able to withdraw from the workforce, and the number of working older men began declining. A second large decline in the number of working men began in the post-World War II era, probably due to the availability of Social Security, and a third large decline in the 1960s and 1970s was probably due to the social support offered by Medicare and the increase in Social Security benefits (Munnell 2011).
In the twenty-first century, most people hope that at some point they will be able to stop working and enjoy the fruits of their labor. But do we look forward to this time or fear it? When people retire from familiar work routines, some easily seek new hobbies, interests, and forms of recreation. Many find new groups and explore new activities, but others may find it more difficult to adapt to new routines and loss of social roles, losing their sense of self-worth in the process.
Each phase of life has challenges that come with the potential for fear. Erik H. Erikson (1902–1994), in his view of socialization, broke the typical lifespan into eight phases. Each phase presents a particular challenge that must be overcome. In the final stage, old age, the challenge is to embrace integrity over despair. Some people are unable to successfully overcome the challenge. They may have to confront regrets, such as being disappointed in their children’s lives or perhaps their own. They may have to accept that they will never reach certain career goals. Or they must come to terms with what their career success has cost them, such as time with their family or declining personal health. Others, however, are able to achieve a strong sense of integrity and are able to embrace the new phase in life. When that happens, there is tremendous potential for creativity. They can learn new skills, practice new activities, and peacefully prepare for the end of life.
For some, overcoming despair might entail remarriage after the death of a spouse. A study conducted by Kate Davidson (2002) reviewed demographic data that asserted men were more likely to remarry after the death of a spouse and suggested that widows (the surviving female spouse of a deceased male partner) and widowers (the surviving male spouse of a deceased female partner) experience their postmarital lives differently. Many surviving women enjoyed a new sense of freedom, since they were living alone for the first time. On the other hand, for surviving men, there was a greater sense of having lost something, because they were now deprived of a constant source of care as well as the focus of their emotional life.
### Aging and Sexuality
Although it is sometimes difficult to have an open, public national dialogue about aging and sexuality, the reality is that our sexual selves do not disappear after age sixty-five. People continue to enjoy sex—and not always safe sex—well into their later years. In fact, some research suggests that as many as one in five new cases of AIDS occurs in adults over sixty-five years old (Hillman 2011).
In some ways, old age may be a time to enjoy sex more, not less. For women, the elder years can bring a sense of relief as the fear of an unwanted pregnancy is removed and the children are grown and taking care of themselves. However, while we have expanded the number of psycho-pharmaceuticals to address sexual dysfunction in men, it was not until recently that the medical field acknowledged the existence of female sexual dysfunctions (Bryant 2004). Additional treatments have been developed or applied to address sexual desire or dysfunction, which sometimes leads members of both sexes to believe that problems are easily resolved. But emotional and social factors play an important role, and medications on their own cannot resolve all issues (Nonacs 2018).
Aging and sexuality also concerns relationships between people of different ages, referred to as age-gap relationships by researchers. These types of relationships are certainly not confined to the elderly, but people often make assumptions about elderly people in romantic relationships with younger people (and vice versa). Research into age-gap relationships indicates that social pressure can have impacts on relationship commitment or lead to break ups. The life stages of the people can also have impacts, especially if one of them is elderly and the other is not (Karantzas 2018). A relationship between a 30-year-old and a 45-year-old most likely involves fewer discussions about serious health issues and retirement decisions than one between a 55-year-old and a 70-year-old. Both have 15-year age gaps, but the circumstances are quite different.
### Death and Dying
For most of human history, the standard of living was significantly lower than it is now. Humans struggled to survive with few amenities and very limited medical technology. The risk of death due to disease or accident was high in any life stage, and life expectancy was low. As people began to live longer, death became associated with old age.
For many teenagers and young adults, losing a grandparent or another older relative can be the first loss of a loved one they experience. It may be their first encounter with grief, a psychological, emotional, and social response to the feelings of loss that accompanies death or a similar event.
People tend to perceive death, their own and that of others, based on the values of their culture. While some may look upon death as the natural conclusion to a long, fruitful life, others may find the prospect of dying frightening to contemplate. People tend to have strong resistance to the idea of their own death, and strong emotional reactions of loss to the death of loved ones. Viewing death as a loss, as opposed to a natural or tranquil transition, is often considered normal in the United States.
What may be surprising is how few studies were conducted on death and dying prior to the 1960s. Death and dying were fields that had received little attention until a psychologist named Elisabeth Kübler-Ross began observing people who were in the process of dying. As Kübler-Ross witnessed people’s transition toward death, she found some common threads in their experiences. She observed that the process had five distinct stages: denial, anger, bargaining, depression, and acceptance. She published her findings in a 1969 book called On Death and Dying. The book remains a classic on the topic today.
Kübler-Ross found that a person’s first reaction to the prospect of dying is denial: this is characterized by the person's not wanting to believe he or she is dying, with common thoughts such as “I feel fine” or “This is not really happening to me.” The second stage is anger, when loss of life is seen as unfair and unjust. A person then resorts to the third stage, bargaining: trying to negotiate with a higher power to postpone the inevitable by reforming or changing the way he or she lives. The fourth stage, psychological depression, allows for resignation as the situation begins to seem hopeless. In the final stage, a person adjusts to the idea of death and reaches acceptance. At this point, the person can face death honestly, by regarding it as a natural and inevitable part of life and can make the most of their remaining time.
The work of Kübler-Ross was eye-opening when it was introduced. It broke new ground and opened the doors for sociologists, social workers, health practitioners, and therapists to study death and help those who were facing death. Kübler-Ross’s work is generally considered a major contribution to thanatology: the systematic study of death and dying.
Of special interests to thanatologists is the concept of “dying with dignity.” Modern medicine includes advanced medical technology that may prolong life without a parallel improvement to the quality of life one may have. In some cases, people may not want to continue living when they are in constant pain and no longer enjoying life. Should patients have the right to choose to die with dignity? Dr. Jack Kevorkian was a staunch advocate for physician-assisted suicide: the voluntary or physician-assisted use of lethal medication provided by a medical doctor to end one’s life. This right to have a doctor help a patient die with dignity is controversial. In the United States, Oregon was the first state to pass a law allowing physician-assisted suicides. In 1997, Oregon instituted the Death with Dignity Act, which required the presence of two physicians for a legal assisted suicide. This law was successfully challenged by U.S. Attorney General John Ashcroft in 2001, but the appeals process ultimately upheld the Oregon law. As of 2019, seven states and the District of Columbia have passed similar laws allowing physician assisted suicide.
The controversy surrounding death with dignity laws is emblematic of the way our society tries to separate itself from death. Health institutions have built facilities to comfortably house those who are terminally ill. This is seen as a compassionate act, helping relieve the surviving family members of the burden of caring for the dying relative. But studies almost universally show that people prefer to die in their own homes (Lloyd, White, and Sutton 2011). Is it our social responsibility to care for elderly relatives up until their death? How do we balance the responsibility for caring for an elderly relative with our other responsibilities and obligations? As our society grows older, and as new medical technology can prolong life even further, the answers to these questions will develop and change.
The changing concept of hospice is an indicator of our society’s changing view of death. Hospice is a type of healthcare that treats terminally ill people when “cure-oriented treatments” are no longer an option (Hospice Foundation of America 2012b). Hospice doctors, nurses, and therapists receive special training in the care of the dying. The focus is not on getting better or curing the illness, but on passing out of this life in comfort and peace. Hospice centers exist as a place where people can go to die in comfort, and increasingly, hospice services encourage at-home care so that someone has the comfort of dying in a familiar environment, surrounded by family (Hospice Foundation of America 2012a). While many of us would probably prefer to avoid thinking of the end of our lives, it may be possible to take comfort in the idea that when we do approach death in a hospice setting, it is in a familiar, relatively controlled place.
### Summary
Old age affects every aspect of human life: biological, social, and psychological. Although medical technology has lengthened life expectancies, it cannot eradicate aging and death. Cultural attitudes shape the way our society views old age and dying, but these attitudes shift and evolve over time.
### Section Quiz
### Short Answer
### Further Research
Read the article “A Study of Sexuality and Health among Older Adults in the United States”.
### References
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Crimmins, Eileen. 2004. “Trends in the Health of the Elderly.” Annual Review of Public Health 25:79–98.
Davidson, Kate. 2002. “Gender Differences in New Partnership Choices and Constraints for Older Widows and Widowers.” Ageing International 27: 43–60.
Drummond, Murray. 1998. “Sports, Aging Men, and Constructions of Masculinity.” Generations 32:32–35.
Erikson, Erik H. 1963 [1950]. Childhood and Society. New York: Norton.
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Grant, Jaime M. 2009. “Outing Age 2010: Public Policy Issues Affecting Lesbian, Gay, Bisexual and Transgender (LGBT) Elders.” National Gay and Lesbian Task Force Policy Institute. Washington, DC. Retrieved January 29, 2012 (http://www.thetaskforce.org/downloads/reports/reports/outingage_final.pdf).
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# Aging and the Elderly
## Challenges Facing the Elderly
Aging comes with many challenges. The loss of independence is one potential part of the process, as are diminished physical ability and age discrimination. The term senescence refers to the aging process, including biological, emotional, intellectual, social, and spiritual changes. This section discusses some of the challenges we encounter during this process.
As already observed, many older adults remain highly self-sufficient. Others require more care. Because the elderly typically no longer hold jobs, finances can be a challenge. And due to cultural misconceptions, older people can be targets of ridicule and stereotypes. The elderly face many challenges in later life, but they do not have to enter old age without dignity.
### Poverty
For many people in the United States, growing older once meant living with less income. In 1960, almost 35 percent of the elderly existed on poverty-level incomes. A generation ago, the nation’s oldest populations had the highest risk of living in poverty.
At the start of the twenty-first century, the older population was putting an end to that trend. Among people over sixty-five years old, the poverty rate fell from 30 percent in 1967 to 9.7 percent in 2008, well below the national average of 13.2 percent (U.S. Census Bureau 2009). However, given the subsequent recession, which severely reduced the retirement savings of many while taxing public support systems, how are the elderly affected? According to the Kaiser Commission on Medicaid and the Uninsured, the national poverty rate among the elderly had risen to 14 percent by 2010 (Urban Institute and Kaiser Commission 2010).
Before the recession hit, what had changed to cause a reduction in poverty among the elderly? What social patterns contributed to the shift? For several decades, a greater number of women joined the workforce. More married couples earned double incomes during their working years and saved more money for their retirement. Private employers and governments began offering better retirement programs. By 1990, senior citizens reported earning 36 percent more income on average than they did in 1980; that was five times the rate of increase for people under age thirty-five (U.S. Census Bureau 2009).
In addition, many people were gaining access to better healthcare. New trends encouraged people to live more healthful lifestyles by placing an emphasis on exercise and nutrition. There was also greater access to information about the health risks of behaviors such as cigarette smoking, alcohol consumption, and drug use. Because they were healthier, many older people continue to work past the typical retirement age and provide more opportunity to save for retirement. Will these patterns return once the recession ends? Sociologists will be watching to see. In the meantime, they are realizing the immediate impact of the recession on elderly poverty.
During the recession, older people lost some of the financial advantages that they’d gained in the 1980s and 1990s. From October 2007 to October 2009 the values of retirement accounts for people over age fifty lost 18 percent of their value. The sharp decline in the stock market also forced many to delay their retirement (Administration on Aging 2009).
### Ageism
Driving to the grocery store, Peter, twenty-three years old, got stuck behind a car on a four-lane main artery through his city’s business district. The speed limit was thirty-five miles per hour, and while most drivers sped along at forty to forty-five mph, the driver in front of him was going the minimum speed. Peter tapped on his horn. He tailgated the driver. Finally, Peter had a chance to pass the car. He glanced over. Sure enough, Peter thought, a gray-haired old man guilty of “DWE,” driving while elderly.
At the grocery store, Peter waited in the checkout line behind an older woman. She paid for her groceries, lifted her bags of food into her cart, and toddled toward the exit. Peter, guessing her to be about eighty years old, was reminded of his grandmother. He paid for his groceries and caught up with her.
“Can I help you with your cart?” he asked.
“No, thank you. I can get it myself,” she said and marched off toward her car.
Peter’s responses to both older people, the driver and the shopper, were prejudiced. In both cases, he made unfair assumptions. He assumed the driver drove cautiously simply because the man was a senior citizen, and he assumed the shopper needed help carrying her groceries just because she was an older woman.
Responses like Peter’s toward older people are fairly common. He didn’t intend to treat people differently based on personal or cultural biases, but he did. Ageism is discrimination (when someone acts on a prejudice) based on age. Dr. Robert Butler coined the term in 1968, noting that ageism exists in all cultures (Brownell). Ageist attitudes and biases based on stereotypes reduce elderly people to inferior or limited positions.
Ageism can vary in severity. Peter’s attitudes are probably seen as fairly mild, but relating to the elderly in ways that are patronizing can be offensive. When ageism is reflected in the workplace, in healthcare, and in assisted-living facilities, the effects of discrimination can be more severe. Ageism can make older people fear losing a job, feel dismissed by a doctor, or feel a lack of power and control in their daily living situations.
In early societies, the elderly were respected and revered. Many preindustrial societies observed gerontocracy, a type of social structure wherein the power is held by a society’s oldest members. In some countries today, the elderly still have influence and power and their vast knowledge is respected. Reverence for the elderly is still a part of some cultures, but it has changed in many places because of social factors.
In many modern nations, however, industrialization contributed to the diminished social standing of the elderly. Today wealth, power, and prestige are also held by those in younger age brackets. The average age of corporate executives was fifty-nine years old in 1980. In 2008, the average age had lowered to fifty-four years old (Stuart 2008). Some older members of the workforce felt threatened by this trend and grew concerned that younger employees in higher level positions would push them out of the job market. Rapid advancements in technology and media have required new skill sets that older members of the workforce are less likely to have.
Changes happened not only in the workplace but also at home. In agrarian societies, a married couple cared for their aging parents. The oldest members of the family contributed to the household by doing chores, cooking, and helping with child care. As economies shifted from agrarian to industrial, younger generations moved to cities to work in factories. The elderly began to be seen as an expensive burden. They did not have the strength and stamina to work outside the home. What began during industrialization, a trend toward older people living apart from their grown children, has become commonplace. As you saw in the opening, children of older people can also feel guilt, sadness, and sometimes anger at both taking care of aging parents and with accepting that their parents are losing their abilities. Living apart, especially if an older person is moved to a nursing home or other facility, can often exacerbate these issues.
### Mistreatment and Abuse
Mistreatment and abuse of the elderly is a major social problem. As expected, with the biology of aging, the elderly sometimes become physically frail. This frailty renders them dependent on others for care—sometimes for small needs like household tasks, and sometimes for assistance with basic functions like eating and toileting. Unlike a child, who also is dependent on another for care, an elder is an adult with a lifetime of experience, knowledge, and opinions—a more fully developed person. This makes the care-providing situation more complex.
Elder abuse occurs when a caretaker intentionally deprives an older person of care or harms the person in his or her charge. Caregivers may be family members, relatives, friends, health professionals, or employees of senior housing or nursing care. The elderly may be subject to many different types of abuse.
In a 2009 study on the topic led by Dr. Ron Acierno, the team of researchers identified five major categories of elder abuse: 1) physical abuse, such as hitting or shaking, 2) sexual abuse, including rape and coerced nudity, 3) psychological or emotional abuse, such as verbal harassment or humiliation, 4) neglect or failure to provide adequate care, and 5) financial abuse or exploitation (Acierno 2010).
The National Center on Elder Abuse (NCEA), a division of the U.S. Administration on Aging, also identifies abandonment and self-neglect as types of abuse. shows some of the signs and symptoms that the NCEA encourages people to notice.
How prevalent is elder abuse? Two recent U.S. studies found that roughly one in ten elderly people surveyed had suffered at least one form of elder abuse. Some social researchers believe elder abuse is underreported and that the number may be higher. The risk of abuse also increases in people with health issues such as dementia (Kohn and Verhoek-Oftedahl 2011). Older women were found to be victims of verbal abuse more often than their male counterparts.
In Acierno’s study, which included a sample of 5,777 respondents aged sixty and older, 5.2 percent of respondents reported financial abuse, 5.1 percent said they’d been neglected, and 4.6 endured emotional abuse (Acierno 2010). The prevalence of physical and sexual abuse was lower at 1.6 and 0.6 percent, respectively (Acierno 2010).
Other studies have focused on the caregivers to the elderly in an attempt to discover the causes of elder abuse. Researchers identified factors that increased the likelihood of caregivers perpetrating abuse against those in their care. Those factors include inexperience, having other demands such as jobs (for those who weren’t professionally employed as caregivers), caring for children, living full-time with the dependent elder, and experiencing high stress, isolation, and lack of support (Kohn and Verhoek-Oftedahl 2011).
A history of depression in the caregiver was also found to increase the likelihood of elder abuse. Neglect was more likely when care was provided by paid caregivers. Many of the caregivers who physically abused elders were themselves abused—in many cases, when they were children. Family members with some sort of dependency on the elder in their care were more likely to physically abuse that elder. For example, an adult child caring for an elderly parent while at the same time depending on some form of income from that parent, is considered more likely to perpetrate physical abuse (Kohn and Verhoek-Oftedahl 2011).
A survey in Florida found that 60.1 percent of caregivers reported verbal aggression as a style of conflict resolution. Paid caregivers in nursing homes were at a high risk of becoming abusive if they had low job satisfaction, treated the elderly like children, or felt burnt out (Kohn and Verhoek-Oftedahl 2011). Caregivers who tended to be verbally abusive were found to have had less training, lower education, and higher likelihood of depression or other psychiatric disorders. Based on the results of these studies, many housing facilities for seniors have increased their screening procedures for caregiver applicants.
### Summary
As people enter old age, they face challenges. Ageism, which involves stereotyping and discrimination against the elderly, leads to misconceptions about their abilities. Although elderly poverty has been improving for decades, many older people may be detrimentally affected by the 2008 recession. Some elderly people grow physically frail and, therefore, dependent on caregivers, which increases their risk of elder abuse.
### Section Quiz
### Short Answer
### Further Research
Veterans who served in the U.S. Armed Forces during various conflicts represent cohorts. Veterans share certain aspects of life in common. To find information on veteran populations and how they are aging, study the information on the web site of the U.S. Department of Veterans Affairs.
Learn more about the Honor Flight Network, the organization offering trips to national war memorials in Washington, DC, at no cost to the veterans.
### References
Acierno, R., Melba A. Hernandez, Ananda B. Amstadter, Heidi S. Resnick, Kenneth Steve, Wendy Muzzy, and Dean G. Kilpatrick. 2010. “Prevalence and Correlates of Emotional, Physical, Sexual, Financial Abuse and Potential Neglect in the United States.” American Journal of Public Health 100:292–7.
Administration on Aging. 2009. “Data Sources on the Impact of the 2008 Financial Crisis on the Economic Well-being of Older Americans Aging Forum Report Issue #1.” Retrieved February 13, 2012 (http://www.agingstats.gov/Main_Site/docs/DSOA_Aging_Brief.pdf).
Brownell, Patricia. 2010. “Social Issues and Social Policy Response to Abuse and Neglect of Older Adults.” Pp. 1–16 in Aging, Ageism and Abuse: Moving from Awareness to Action, edited by G. Gutman and C. Spencer. Amsterdam, the Netherlands: Elsevier.
Glantz, Aaron. 2010. “Suicide Rates Soar among WWII Vets, Records Show.” The Bay Citizen, November 11. Retrieved February 27, 2012 (http://www.baycitizen.org/veterans/story/suicide-rates-soar-among-wwii-vets/comments/#comments).
Honor Flight Network. 2011. Retrieved September 22, 2011 (http://www.honorflight.org/).
Kohn, Robert, and Wendy Verhoek-Oftedahl. 2011. “Caregiving and Elder Abuse.” Medicine & Health Rhode Island 94(2):47–49.
National Center for Veterans Analysis and Statistics. 2011. “VA Benefits and Health Care Utilization.” November 9. Retrieved February 13, 2012 (http://www.va.gov/Vetdata/docs/Quickfacts/4x6_fall_11_sharepoint_Final.pdf).
National Center of Elder Abuse. 2011. “Major Types of Elder Abuse.” Retrieved January 21, 2012 (http://ncea.aoa.gov/FAQ/Type_Abuse/).
Stuart, Spencer. 2008. “Leading CEOs: A Statistical Snapshot of S&P 500 Leaders.” Retrieved February 13, 2012 (http://content.spencerstuart.com/sswebsite/pdf/lib/2005_CEO_Study_JS.pdf).
Urban Institute and Kaiser Commission. 2010. “Poverty Rate by Age.” Retrieved January 21, 2012 (http://www.statehealthfacts.org/comparebar.jsp?ind=10&cat=1").
U.S. Census Bureau. 2009. “Webinar on 2008 Income, Poverty, and Health Insurance Estimates from the Current Population Survey.” Retrieved February 13, 2012 (http://www.census.gov/newsroom/releases/archives/news_conferences/2009-09-10_remarks_johnson.html).
U.S. Department of Veteran Affairs. 2010. “Veteran Population Projections FY 2000 to FY2036.” December. Retrieved February 13, 2012 (http://www.va.gov/vetdata/docs/quickfacts/Population-slideshow.pdf). |
# Aging and the Elderly
## Theoretical Perspectives on Aging
What roles do individual senior citizens play in your life? How do you relate to and interact with older people? What role do they play in neighborhoods and communities, in cities and in states? Sociologists are interested in exploring the answers to questions such as these through three different perspectives: functionalism, symbolic interactionism, and conflict theory.
### Functionalism
Functionalists analyze how the parts of society work together. Functionalists gauge how society’s parts are working together to keep society running smoothly. How does this perspective address aging? The elderly, as a group, are one of society’s vital parts.
Functionalists find that people with better resources who stay active in other roles adjust better to old age (Crosnoe and Elder 2002). Three social theories within the functional perspective were developed to explain how older people might deal with later-life experiences.
The earliest gerontological theory in the functionalist perspective is disengagement theory, which suggests that withdrawing from society and social relationships is a natural part of growing old. There are several main points to the theory. First, because everyone expects to die one day, and because we experience physical and mental decline as we approach death, it is natural to withdraw from individuals and society. Second, as the elderly withdraw, they receive less reinforcement to conform to social norms. Therefore, this withdrawal allows a greater freedom from the pressure to conform. Finally, social withdrawal is gendered, meaning it is experienced differently by men and women. Because men focus on work and women focus on marriage and family, when they withdraw they will be unhappy and directionless until they adopt a role to replace their accustomed role that is compatible with the disengaged state (Cummings and Henry 1961).
The suggestion that old age was a distinct state in the life course, characterized by a distinct change in roles and activities, was groundbreaking when it was first introduced. However, the theory is no longer accepted in its classic form. Criticisms typically focus on the application of the idea that seniors universally naturally withdraw from society as they age, and that it does not allow for a wide variation in the way people experience aging (Hothschild 1975).
The social withdrawal that Cummings and Henry recognized (1961), and its notion that elderly people need to find replacement roles for those they’ve lost, is addressed anew in activity theory. According to this theory, activity levels and social involvement are key to this process, and key to happiness (Havinghurst 1961; Neugarten 1964; Havinghurst, Neugarten, and Tobin 1968). According to this theory, the more active and involved an elderly person is, the happier he or she will be. Critics of this theory point out that access to social opportunities and activity are not equally available to all. Moreover, not everyone finds fulfillment in the presence of others or participation in activities. Reformulations of this theory suggest that participation in informal activities, such as hobbies, are what most affect later life satisfaction (Lemon, Bengtson, and Petersen 1972).
According to continuity theory, the elderly make specific choices to maintain consistency in internal (personality structure, beliefs) and external structures (relationships), remaining active and involved throughout their elder years. This is an attempt to maintain social equilibrium and stability by making future decisions on the basis of already developed social roles (Atchley 1971; Atchley 1989). One criticism of this theory is its emphasis on so-called “normal” aging, which marginalizes those with chronic diseases such as Alzheimer’s.
### Conflict Perspective
Theorists working the conflict perspective view society as inherently unstable, an institution that privileges the powerful wealthy few while marginalizing everyone else. According to the guiding principle of conflict theory, social groups compete with other groups for power and scarce resources. Applied to society’s aging population, the principle means that the elderly struggle with other groups—for example, younger society members—to retain a certain share of resources. At some point, this competition may become conflict.
For example, some people complain that the elderly get more than their fair share of society’s resources. In hard economic times, there is great concern about the huge costs of Social Security and Medicare. One of every four tax dollars, or about 28 percent, is spent on these two programs. In 1950, the federal government paid $781 million in Social Security payments. Now, the payments are 870 times higher. In 2008, the government paid $296 billion (Statistical Abstract 2011). The medical bills of the nation’s elderly population are rising dramatically. While there is more care available to certain segments of the senior community, it must be noted that the financial resources available to the aging can vary tremendously by race, social class, and gender.
There are three classic theories of aging within the conflict perspective. Modernization theory (Cowgill and Holmes 1972) suggests that the primary cause of the elderly losing power and influence in society are the parallel forces of industrialization and modernization. As societies modernize, the status of elders decreases, and they are increasingly likely to experience social exclusion. Before industrialization, strong social norms bound the younger generation to care for the older. Now, as societies industrialize, the nuclear family replaces the extended family. Societies become increasingly individualistic, and norms regarding the care of older people change. In an individualistic industrial society, caring for an elderly relative is seen as a voluntary obligation that may be ignored without fear of social censure.
The central reasoning of modernization theory is that as long as the extended family is the standard family, as in preindustrial economies, elders will have a place in society and a clearly defined role. As societies modernize, the elderly, unable to work outside of the home, have less to offer economically and are seen as a burden. This model may be applied to both the developed and the developing world, and it suggests that as people age they will be abandoned and lose much of their familial support since they become a nonproductive economic burden.
Another theory in the conflict perspective is age stratification theory (Riley, Johnson, and Foner 1972). Though it may seem obvious now, with our awareness of ageism, age stratification theorists were the first to suggest that members of society might be stratified by age, just as they are stratified by race, class, and gender. Because age serves as a basis of social control, different age groups will have varying access to social resources such as political and economic power. Within societies, behavioral age norms, including norms about roles and appropriate behavior, dictate what members of age cohorts may reasonably do. For example, it might be considered deviant for an elderly woman to wear a bikini because it violates norms denying the sexuality of older females. These norms are specific to each age strata, developing from culturally based ideas about how people should “act their age.”
Thanks to amendments to the Age Discrimination in Employment Act (ADEA), which drew attention to some of the ways in which our society is stratified based on age, U.S. workers no longer must retire upon reaching a specified age. As first passed in 1967, the ADEA provided protection against a broad range of age discrimination and specifically addressed termination of employment due to age, age specific layoffs, advertised positions specifying age limits or preferences, and denial of healthcare benefits to those over sixty-five years old (U.S. EEOC 2012).
Age stratification theory has been criticized for its broadness and its inattention to other sources of stratification and how these might intersect with age. For example, one might argue that an older white male occupies a more powerful role, and is far less limited in his choices, compared to an older white female based on his historical access to political and economic power.
Finally, exchange theory (Dowd 1975), a rational choice approach, suggests we experience an increased dependence as we age and must increasingly submit to the will of others because we have fewer ways of compelling others to submit to us. Indeed, inasmuch as relationships are based on mutual exchanges, as the elderly become less able to exchange resources, they will see their social circles diminish. In this model, the only means to avoid being discarded is to engage in resource management, like maintaining a large inheritance or participating in social exchange systems via child care. In fact, the theory may depend too much on the assumption that individuals are calculating. It is often criticized for affording too much emphasis to material exchange and devaluing nonmaterial assets such as love and friendship.
### Symbolic Interactionism
Generally, theories within the symbolic interactionist perspective focus on how society is created through the day-to-day interaction of individuals, as well as the way people perceive themselves and others based on cultural symbols. This microanalytic perspective assumes that if people develop a sense of identity through their social interactions, their sense of self is dependent on those interactions. A woman whose main interactions with society make her feel old and unattractive may lose her sense of self. But a woman whose interactions make her feel valued and important will have a stronger sense of self and a happier life.
Symbolic interactionists stress that the changes associated with old age, in and of themselves, have no inherent meaning. Nothing in the nature of aging creates any particular, defined set of attitudes. Rather, attitudes toward the elderly are rooted in society.
One microanalytical theory is Rose’s (1962) subculture of aging theory, which focuses on the shared community created by the elderly when they are excluded (due to age), voluntarily or involuntarily, from participating in other groups. This theory suggests that elders will disengage from society and develop new patterns of interaction with peers who share common backgrounds and interests. For example, a group consciousness may develop within such groups as AARP around issues specific to the elderly like the Medicare “doughnut hole,” focused on creating social and political pressure to fix those issues. Whether brought together by social or political interests, or even geographic regions, elders may find a strong sense of community with their new group.
Another theory within the symbolic interaction perspective is selective optimization with compensation theory. Baltes and Baltes (1990) based their theory on the idea that successful personal development throughout the life course and subsequent mastery of the challenges associated with everyday life are based on the components of selection, optimization, and compensation. Though this happens at all stages in the life course, in the field of gerontology, researchers focus attention on balancing the losses associated with aging with the gains stemming from the same. Here, aging is a process and not an outcome, and the goals (compensation) are specific to the individual.
According to this theory, our energy diminishes as we age, and we select (selection) personal goals to get the most (optimize) for the effort we put into activities, in this way making up for (compensation) the loss of a wider range of goals and activities. In this theory, the physical decline postulated by disengagement theory may result in more dependence, but that is not necessarily negative, as it allows aging individuals to save their energy for the most meaningful activities. For example, a professor who values teaching sociology may participate in a phased retirement, never entirely giving up teaching, but acknowledging personal physical limitations that allow teaching only one or two classes per year.
Swedish sociologist Lars Tornstam developed a symbolic interactionist theory called gerotranscendence: the idea that as people age, they transcend the limited views of life they held in earlier times. Tornstam believes that throughout the aging process, the elderly become less self-centered and feel more peaceful and connected to the natural world. Wisdom comes to the elderly, Tornstam’s theory states, and as the elderly tolerate ambiguities and seeming contradictions, they let go of conflict and develop softer views of right and wrong (Tornstam 2005).
Tornstam does not claim that everyone will achieve wisdom in aging. Some elderly people might still grow bitter and isolated, feel ignored and left out, or become grumpy and judgmental. Symbolic interactionists believe that, just as in other phases of life, individuals must struggle to overcome their own failings and turn them into strengths.
### Summary
The three major sociological perspectives inform the theories of aging. Theories in the functionalist perspective focus on the role of elders in terms of the functioning of society as a whole. Theories in the conflict perspective concentrate on how elders, as a group, are at odds with other groups in society. And theories in the symbolic interactionist perspective focus on how elders’ identities are created through their interactions.
### Section Quiz
### Short Answer
### Further Research
New Dynamics of Aging is a web site produced by an interdisciplinary team at the University of Sheffield. It is supposedly the largest research program on aging in the United Kingdom to date. In studying the experiences of aging and factors that shape aging, including behaviors, biology, health, culture, history, economics, and technology, researchers are promoting healthy aging and helping dispel stereotypes. Learn more by logging onto it's website here.
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Reese, Hope. 2019. “What Should We Do About Our Aging Prison Population?” JSTOR Daily. (https://daily.jstor.org/what-should-we-do-about-our-aging-prison-population/)
Riley, Matilda While, Marilyn Johnson, and Anne Foner. 1972. Aging and Society. Volume III, A Sociology of Age Stratification. New York: Russell Sage Foundation.
Rose, Arnold. 1960. “The Subculture of the Aging: A Topic for Sociological Research.” The Gerontologist 2:123–127.
Tornstam Lars. 2005. Gerotranscendence: A Developmental Theory of Positive Aging. New York: Springer Publishing Company.
U.S. Census Bureau. 2011. Statistical Abstract 2011: Table 147. Retrieved February 13, 2012 (http://www.census.gov/compendia/statab/cats/health_nutrition/medicare_medicaid.html).
U.S. Equal Employment Opportunity Commission. 2012. “The Age Discrimination in Employment Act 1967 (ADEA).” Retrieved January 30, 2012 (http://www.eeoc.gov/laws/statutes/adea.cfm).
Warren, Jenifer. 2002. “The Graying of the Prisons.” Los Angeles Times, June 9. Retrieved February 2, 2012 (http://articles.latimes.com/2002/jun/09/local/me-cons9). |
# Relationships, Marriage, and Family
## Introduction
Elena and Cam met through friends when they were in their early twenties. Elena had been out of college for two years and worked in the city procurement office; she took graduate classes in operations management, but she’d need a few more years to finish her Master’s. Cam had received extensive computing training while in the Navy, and was a database architect at an insurance company.
In their first few years of dating, the idea of marriage came up mostly through other people. Friends’ weddings seemed like monthly events, and “who’s next?” small talk was unavoidable. Elena’s grandmother and aunts added to the chorus; they talked about their home country, where women were married with a couple of children by the time they reached Elena’s age. (Elena often pointed out that they were wrong, and the average age of marriage had been climbing for decades.) These pressures were pretty minor at first. They came in the form of jokes, wedding dress texts, and the occasional insult about Cam’s salary. But every once in a while someone would sit Elena down for a serious talk, or corner Cam while he was at a family gathering.
Most of Elena’s family predicted that things would change when she earned her graduate degree and could “focus on her family.” Things did change; Elena became compliance officer for the office of city services, resulting in almost a ten percent increase in her salary. Cam became a supervisor three months later. They moved out of their apartment, which was in Cam’s mother’s garage, and into their own place downtown. They were happy. They were committed to each other. They didn’t get married.
Five years later, Elena and Cam were still living downtown, but they’d traded their rental for a condo. Aside from work, they co-founded a nonprofit where Elena taught financial literacy and Cam ran computing boot camps for recent immigrants and refugees. Maybe it was the hundreds of children they met through the organization, or maybe it was seeing their friends’ kids, or maybe it was being in her thirties, but Elena realized she wanted to be a mother. They started the adoption process, and eighteen months later welcomed a young girl who had been born in another country.
When did Elena and Cam become a family? Was it when they moved in together? When they adopted the child? Does their not being married matter?
### References
Gardner, Amanda. 2013. “More U.S. Couples Living Together Instead of Marrying, CDC Finds.” HealthDay.com. Retrieved December 29, 2014 (http://consumer.healthday.com/public-health-information-30/centers-for-disease-control-news-120/more-u-s-couples-living-together-instead-of-marrying-cdc-finds-675096.html).
Rettner, Rachel. 2013. “More Couples Living Together Outside of Marriage.” MyHealthNewsDaily/Purch. Retrieved December 29, 2014 (http://www.livescience.com/28420-cohabiting-marriage-cdc-report.html).
U.S. Census Bureau. 2008. “50 Million Children Lived with Married Parents in 2007.” July 28. Retrieved January 16, 2012 (http://www.census.gov/newsroom/releases/archives/marital_status_living_arrangements/cb08-115.html)
Useem, Andrea. 2007. “What to Expect When You’re Expecting a Co-Wife.” Slate, July 24. Retrieved January 16, 2012 (http://www.slate.com/articles/life/faithbased/2007/07/what_to_expect_when_youre_expecting_a_cowife.html). |
# Relationships, Marriage, and Family
## What Is Marriage? What Is a Family?
Marriage and family are key structures in many societies. Many of us learn from a young age that finding and joining the right person is a key to happiness and security. We’re told that children need two parents. Many of the tax laws, medical laws, retirement benefit laws, and banking and loan processes seem to favor or assume marriage. Should those assumptions be changed? Is marriage still the foundation of the family and our society?
In 1960, 66 percent of households in America were headed by a married couple. That meant that most children grew up in such households, as did their friends and extended families. Marriage could certainly be seen as the foundation of the culture. By 2010, that number of households headed by married couples had dropped to 45 percent (Luscombe 2014). The approximately 20 percent drop is more than just a statistic; it has significant practical effects. It means that nearly every child in most parts of America is either in or is close to a family that is not headed by a married couple. It means that teachers and counselors and even people who meet children in a restaurant can’t assume they live with two married parents. Some view this decline as a problem with outcomes related to values, crime, financial strength, and mental health. Sociologists may study that viewpoint to determine if it is actually true.
What is marriage? Not even sociologists are able to agree on a single meaning. For our purposes, we’ll define marriage as a legally recognized social contract between two people, traditionally based on a sexual relationship and implying a permanence of the union. In practicing cultural relativism, we should also consider variations, such as whether a legal union is required, whether more than two people can be involved, or whether the marriage is a religious one or a civil one.
Sociologists are interested in the relationship between the institution of marriage and the institution of family because, historically, marriages are what create a family, and families are the most basic social unit upon which society is built. Both marriage and family create status roles that are sanctioned by society.
The question of what constitutes a family may be an even more difficult one to answer; it’s a prime area of debate in family sociology, as well as in politics and religion. Social conservatives tend to define the family in terms of structure with each family member filling a certain role (like father, mother, or child). Sociologists, on the other hand, tend to define family more in terms of the manner in which members relate to one another than on a strict configuration of status roles. Here, we’ll define family as a socially recognized group (usually joined by blood, marriage, cohabitation, or adoption) that forms an emotional connection and serves as an economic unit of society. Sociologists identify different types of families based on how one enters into them. A family of orientation refers to the family into which a person is born. A family of procreation describes one that is formed through marriage. These distinctions have cultural significance related to issues of lineage.
Drawing on two sociological paradigms, the sociological understanding of what constitutes a family can be explained by symbolic interactionism as well as functionalism. These two theories indicate that families are groups in which participants view themselves as family members and act accordingly. In other words, families are groups in which people come together to form a strong primary group connection and maintain emotional ties to one another over a long period of time. Such families may include groups of close friends or teammates. In addition, the functionalist perspective views families as groups that perform vital roles for society—both internally (for the family itself) and externally (for society as a whole). Families provide for one another’s physical, emotional, and social well-being. Parents care for and socialize children. Later in life, adult children often care for elderly parents. While interactionism helps us understand the subjective experience of belonging to a “family,” functionalism illuminates the many purposes of families and their roles in the maintenance of a balanced society (Parsons and Bales 1956). We will go into more detail about how these theories apply to family in the following pages.
### Challenges Families Face
People in the United States as a whole are somewhat divided when it comes to determining what does and what does not constitute a family. In a 2010 survey conducted by professors at the University of Indiana, nearly all participants (99.8 percent) agreed that a husband, wife, and children constitute a family. Ninety-two percent stated that a husband and a wife without children still constitute a family. The numbers drop for less traditional structures: unmarried couples with children (83 percent), unmarried couples without children (39.6 percent), gay male couples with children (64 percent), and gay male couples without children (33 percent) (Powell et al. 2010). This survey revealed that children tend to be the key indicator in establishing “family” status: the percentage of individuals who agreed that unmarried couples and gay couples constitute a family nearly doubled when children were added.
The study also revealed that 60 percent of U.S. respondents agreed that if you consider yourself a family, you are a family (a concept that reinforces an interactionist perspective) (Powell 2010). The government, however, is not so flexible in its definition of “family.” The U.S. Census Bureau defines a family as “a group of two people or more (one of whom is the householder) related by birth, marriage, or adoption and residing together” (U.S. Census Bureau 2010). While this structured definition can be used as a means to consistently track family-related patterns over several years, it excludes individuals such as cohabitating unmarried couples. Legality aside, sociologists would argue that the general concept of family is more diverse and less structured than in years past. Society has given more leeway to the design of a family making room for what works for its members (Jayson 2010).
Family is, indeed, a subjective concept, but it is a fairly objective fact that family (whatever one’s concept of it may be) is very important to people in the United States. In a 2010 survey by Pew Research Center in Washington, DC, 76 percent of adults surveyed stated that family is “the most important” element of their life—just one percent said it was “not important” (Pew Research Center 2010). It is also very important to society. President Ronald Reagan notably stated, “The family has always been the cornerstone of American society. Our families nurture, preserve, and pass on to each succeeding generation the values we share and cherish, values that are the foundation of our freedoms” (Lee 2009). While the design of the family may have changed in recent years, the fundamentals of emotional closeness and support are still present. Most responders to the Pew survey stated that their family today is at least as close (45 percent) or closer (40 percent) than the family with which they grew up (Pew Research Center 2010).
As you may have seen in the chapter on Aging and the Elderly, different generations have varying living situations and views on aging. The same goes for living situations with family. The Pew Research Center analyzed living situation of 40-year-olds from different generations. At that age, Millennials indicated that 45 percent of them were not living in a family of their own. In contrast, when Gen Xers and Baby Boomers were about 40 years old (around 2003 and 1987, respectively), an average of 33 percent of them lived outside of a family (Barroso 2020). The dynamic of nearly a 50-50 split between family/non-family for Millennials is very different from a two-third/one third split of Boomers and Gen X.
The data also show that women are having children later in life and that men are much less likely to live in a household with their own children. In 2019, 32 percent of Millennial men were living in a household with their children, compared to 41 percent of Gen X men in 2003 and 44 percent of Boomer men in 1987 (Barroso 2020). Again, the significant drop off in parenting roles likely has an impact on attitudes toward family.
Alongside the debate surrounding what constitutes a family is the question of what people in the United States believe constitutes a marriage. Many religious and social conservatives believe that marriage can only exist between a man and a woman, citing religious scripture and the basics of human reproduction as support. Social liberals and progressives, on the other hand, believe that marriage can exist between two consenting adults—be they a man and a woman, or a woman and a woman—and that it would be discriminatory to deny such a couple the civil, social, and economic benefits of marriage.
### Marriage Patterns
With single parenting and cohabitation (when a couple shares a residence but not a marriage) becoming more acceptable in recent years, people may be less motivated to get married. In a recent survey, 39 percent of respondents answered “yes” when asked whether marriage is becoming obsolete (Pew Research Center 2010). The institution of marriage is likely to continue, but some previous patterns of marriage will become outdated as new patterns emerge. In this context, cohabitation contributes to the phenomenon of people getting married for the first time at a later age than was typical in earlier generations (Glezer 1991). Furthermore, marriage will continue to be delayed as more people place education and career ahead of “settling down.”
### One Partner or Many?
People in the United States typically equate marriage with monogamy, when someone is married to only one person at a time. In many countries and cultures around the world, however, having one spouse is not the only form of accepted marriage, even if it is the most common. Polygamy, or being married to more than one person at a time, is accepted to varying degrees around the world, with most polygamous societies existing in northern Africa and east Asia (OECD 2019). Instances of polygamy are almost exclusively in the form of a man being married to more than one woman at the same time, rather than a woman being married to more than one man (Altman and Ginat 1996).
While the majority of societies accept polygamy, the majority of people do not practice it. Even in the regions where it is most common, only an average of 11 percent of the population lives in arrangements that include more than one spouse (Kramer 2020). In these relationships, the husbands are often older, wealthy, high-status men (Altman and Ginat 1996). The average plural marriage involves no more than three wives. Negev Bedouin men in Israel, for example, typically have two wives, although it is acceptable to have up to four (Griver 2008). As urbanization increases in these cultures, polygamy is likely to decrease as a result of greater access to mass media, technology, and education (Altman and Ginat 1996).
In the United States, polygamy is illegal. A recent Gallup poll showed that 21 percent of people believe polygamy is morally acceptable, which is a major increase since earlier versions of the same poll. But the poll also found that polygamy was among the least acceptable behaviors considered in the study; for example, polygamy was far less acceptable than consensual sex between teenagers, though it was more acceptable than a married person having an affair (Brenan 2020). The act of entering into marriage while still married to another person is referred to as bigamy and is considered a felony in most states.
### Residency and Lines of Descent
When considering one’s lineage, most people in the United States look to both their father’s and mother’s sides. Both paternal and maternal ancestors are considered part of one’s family. This pattern of tracing kinship is called bilateral descent. Note that kinship, or one’s traceable ancestry, can be based on blood or marriage or adoption. Sixty percent of societies, mostly modernized nations, follow a bilateral descent pattern. Unilateral descent (the tracing of kinship through one parent only) is practiced in the other 40 percent of the world’s societies, with high concentration in pastoral cultures (O’Neal 2006).
There are three types of unilateral descent: patrilineal, which follows the father’s line only; matrilineal, which follows the mother’s side only; and ambilineal, which follows either the father’s only or the mother’s side only, depending on the situation. In patrilineal societies, such as those in rural China and India, only males carry on the family surname. This gives males the prestige of permanent family membership while females are seen as only temporary members (Harrell 2001). U.S. society assumes some aspects of patrilineal decent. For instance, most children assume their father’s last name even if the mother retains her birth name.
In matrilineal societies, inheritance and family ties are traced to women. Matrilineal descent is common in Native American societies, notably the Crow and Cherokee tribes. In these societies, children are seen as belonging to the women and, therefore, one’s kinship is traced to one’s mother, grandmother, great grandmother, and so on (Mails 1996). In ambilineal societies, which are most common in Southeast Asian countries, parents may choose to associate their children with the kinship of either the mother or the father. This choice may be based on the desire to follow stronger or more prestigious kinship lines or on cultural customs such as men following their father’s side and women following their mother’s side (Lambert 2009).
Tracing one’s line of descent to one parent rather than the other can be relevant to the issue of residence. In many cultures, newly married couples move in with, or near to, family members. In a patrilocal residence system it is customary for the wife to live with (or near) her husband’s blood relatives (or family of orientation). Patrilocal systems can be traced back thousands of years. In a DNA analysis of 4,600-year-old bones found in Germany, scientists found indicators of patrilocal living arrangements (Haak et al 2008). Patrilocal residence is thought to be disadvantageous to women because it makes them outsiders in the home and community; it also keeps them disconnected from their own blood relatives. In China, where patrilocal and patrilineal customs are common, the written symbols for maternal grandmother (wáipá) are separately translated to mean “outsider” and “women” (Cohen 2011).
Similarly, in matrilocal residence systems, where it is customary for the husband to live with his wife’s blood relatives (or her family of orientation), the husband can feel disconnected and can be labeled as an outsider. The Minangkabau people, a matrilocal society that is indigenous to the highlands of West Sumatra in Indonesia, believe that home is the place of women and they give men little power in issues relating to the home or family (Joseph and Najmabadi 2003). Most societies that use patrilocal and patrilineal systems are patriarchal, but very few societies that use matrilocal and matrilineal systems are matriarchal, as family life is often considered an important part of the culture for women, regardless of their power relative to men.
### Stages of Family Life
As we’ve established, the concept of family has changed greatly in recent decades. Historically, it was often thought that many families evolved through a series of predictable stages. Developmental or “stage” theories used to play a prominent role in family sociology (Strong and DeVault 1992). Today, however, these models have been criticized for their linear and conventional assumptions as well as for their failure to capture the diversity of family forms. While reviewing some of these once-popular theories, it is important to identify their strengths and weaknesses.
The set of predictable steps and patterns families experience over time is referred to as the family life cycle. One of the first designs of the family life cycle was developed by Paul Glick in 1955. In Glick’s original design, he asserted that most people will grow up, establish families, rear and launch their children, experience an “empty nest” period, and come to the end of their lives. This cycle will then continue with each subsequent generation (Glick 1989). Glick’s colleague, Evelyn Duvall, elaborated on the family life cycle by developing these classic stages of family (Strong and DeVault 1992):
The family life cycle was used to explain the different processes that occur in families over time. Sociologists view each stage as having its own structure with different challenges, achievements, and accomplishments that transition the family from one stage to the next. For example, the problems and challenges that a family experiences in Stage 1 as a married couple with no children are likely much different than those experienced in Stage 5 as a married couple with teenagers. The success of a family can be measured by how well they adapt to these challenges and transition into each stage. While sociologists use the family life cycle to study the dynamics of family over time, consumer and marketing researchers have used it to determine what goods and services families need as they progress through each stage (Murphy and Staples 1979).
As early “stage” theories have been criticized for generalizing family life and not accounting for differences in gender, ethnicity, culture, and lifestyle, less rigid models of the family life cycle have been developed. One example is the family life course, which recognizes the events that occur in the lives of families but views them as parting terms of a fluid course rather than in consecutive stages (Strong and DeVault 1992). This type of model accounts for changes in family development, such as the fact that in today’s society, childbearing does not always occur with marriage. It also sheds light on other shifts in the way family life is practiced. Society’s modern understanding of family rejects rigid “stage” theories and is more accepting of new, fluid models.
### Summary
Sociologists view marriage and families as societal institutions that help create the basic unit of social structure. Both marriage and a family may be defined differently—and practiced differently—in cultures across the world. Families and marriages, like other institutions, adapt to social change.
### Section Quiz
### Short Answer
### Further Research
For more information on family development and lines of descent, visit the New England Historical Genealogical Society’s web site, American Ancestors, and find out how genealogies have been established and recorded since 1845.
### References
Altman, Irwin, and Joseph Ginat. 1996. Polygamous Families in Contemporary Society. New York: Cambridge University Press.
Barroso, Amanda and Parker, Kim and Bennett, Jesse. 2020. “As Millennials Near 40, They’re Approaching Family Life Differently Than Previous Generations.” Pew Research Center. (https://www.pewresearch.org/social-trends/2020/05/27/as-millennials-near-40-theyre-approaching-family-life-differently-than-previous-generations/)
Cohen, Philip. 2011. “Chinese: Maternal Grandmothers, Outside Women.” FamilyInequality.com, Retrieved February 13, 2012 (http://familyinequality.wordpress.com/2011/11/16/chinese-maternal-grandmothers-outside-women/).
Glezer, Helen. 1991. “Cohabitation.” Family Matters 30:24–27.
Glick, Paul. 1989. “The Family Life Cycle and Social Change.” Family Relations 38(2):123–129.
Griver, Simon. 2008. “One Wife Isn’t Enough … So They Take Two or Three.” The Jewish Chronicle Online, April 24. Retrieved February 13, 2012 (http://www.thejc.com/lifestyle/lifestyle-features/one-wife-isn’t-enough-so-they-take-two-or-three).
Haak, Wolfgang et al. 2008. “Ancient DNA Reveals Male Diffusion through the Neolithic Mediterranean Route.” Proceedings of the National Association of Sciences, November 17. Retrieved February 13, 2012 (http://www.pnas.org/content/105/47/18222).
Harrell, Stevan. 2001. “Mountain Patterns: The Survival of Nuosu Culture in China.” Journal of American Folklore 114:451.
Jayson, Sharon. 2010. “What Does a ‘Family’ Look Like Nowadays?” USA Today, November 25. Retrieved February 13, 2012 (http://www.usatoday.com/yourlife/sex-relationships/marriage/2010-11-18-pew18_ST_N.htm).
Joseph, Suad, and Afsaneh Najmabadi. 2003. “Kinship and State: Southeast Asia, East Asia, Australia and the Pacific.” Pp. 351–355 in Encyclopedia of Women and Islamic Cultures: Family, Law, and Politics. Leiden, The Netherlands: Brill Academic Publishers.
Kramer, Stephanie. 2020. “Polygamy is Rare around the world and confined to a few regions.” Pew Research Center. December 2020. (https://www.pewresearch.org/fact-tank/2020/12/07/polygamy-is-rare-around-the-world-and-mostly-confined-to-a-few-regions/)
Lambert, Bernd. 2009. “Ambilineal Descent Groups in the Northern Gilbert Islands.” American Anthropologist 68(3):641–664.
Lee, Richard. 2009. The American Patriot’s Bible: The Word of God and the Shaping of America. Nashville, TN: Thomas Nelson.
Luscombe, Belinda. 2014. “There Is No Longer Any Such Thing as a Typical Family.” Time. September 4, 2014. (https://time.com/3265733/nuclear-family-typical-society-parents-children-households-philip-cohen/)
Mails, Thomas E. 1996. The Cherokee People: The Story of the Cherokees from Earliest Origins to Contemporary Times. New York: Marlowe & Co.
Murdock, George P. 1967. Ethnographic Atlas: A Summary. Pittsburgh, PA: University of Pittsburgh Press.
Murphy, Patrick, and William Staples. 1979. “A Modernized Family Life Cycle.” Journal of Consumer Research 6(1):12–22.
Museum of Broadcast Communications. 2010. “Family on Television.” Retrieved January 16, 2012.
OECD. 2019. “Maps and Facts: Polygamy Remains Common and Mostly Legal in West Africa.” No. 77. January 2019. (http://www.oecd.org/swac/maps/77-polygamy-remains%20common-West-Africa.pdf)
O’Neal, Dennis. 2006. “Nature of Kinship.” Palomar College. Retrieved January 16, 2012 (http://anthro.palomar.edu/kinship/kinship_2.htm).
Parsons, Talcott, and Robert Bales. 1955. Family Socialization and Interaction Process. London: Routledge.
Pew Research Center. 2010. “The Decline of Marriage and Rise of New Families.” November 18. Retrieved February 13, 2012 (http://pewresearch.org/pubs/1802/decline-marriage-rise-new-families).
Powell, Brian, Catherine Bolzendahl, Claudia Geist, and Lala Carr Steelman. 2010. Counted Out: Same-Sex Relations and Americans’ Definitions of Family. New York: Russell Sage Foundation.
Respers France, Lisa. 2010. “The Evolution of the TV Family.” CNN, September 1. Retrieved February 13, 2012 (http://www.cnn.com/2010/SHOWBIZ/TV/09/01/families.on.tv/index.html).
Ruoff, Jeffrey. 2002. An American Family: A Televised Life. Minneapolis: University of Minnesota Press.
Strong, B., and C. DeVault. 1992. The Marriage and Family Experience. 5th ed. St. Paul, MN: West Publishing Company.
U.S. Census Bureau. 2010. “Current Population Survey (CPS).” Retrieved January 16, 2012 (http://www.census.gov/population/www/cps/cpsdef.html).
Useem, Andrea. 2007. “What to Expect When You’re Expecting a Co-Wife.” Slate, July 24. Retrieved January 16, 2012 (http://www.slate.com/articles/life/faithbased/2007/07/what_to_expect_when_youre_expecting_a_cowife.html). |
# Relationships, Marriage, and Family
## Variations in Family Life
The combination of husband, wife, and children that 99.8 percent of people in the United States believe constitutes a family is not representative of 99.8 percent of U.S. families. According to 2010 census data, only 66 percent of children under seventeen years old live in a household with two married parents. This is a decrease from 77 percent in 1980 (U.S. Census 2011). This two-parent family structure is known as a nuclear family, referring to married parents and children as the nucleus, or core, of the group. Recent years have seen a rise in variations of the nuclear family with the parents not being married. Three percent of children live with two cohabiting parents (U.S. Census 2011).
### Single Parents, Blended Families, and Foster Families
Single-parent households are on the rise. In 2017, 32 percent of children lived with a single parent only, up from 25 percent in 2008. Of that 32 percent, 21 percent live with their mother. Four percent live with their father, which is a percentage that is growing in share; in 1968, for example, only one percent of children lived with a solo father, and three percent lived with a solo father in 2008 (Livingston 2018).
About 16 percent of children are living in blended families, those with step parents and/or step-siblings. This number has remained relatively stable since the 1980s when the Census Bureau began reliably measuring it. Four percent of children live in families with couples who are not married. (That number is partially composed of parents in same-sex relationships who were previously prohibited from getting married.)
In some cases, parents can no longer care for their children. In 2018, three million children lived with a guardian who was neither their biological nor adoptive parent. The causes range from parental mental health issues, drug use, or incarceration, as well as physical or sexual abuse of the children by the parent, or abandonment by the parent. The wide array of causes leads to a similarly wide array of arrangements and types of people and organizations involved. About half of these children live with grandparents, and about 20 percent live with other relatives (ChildStats 2019). Sometimes a grandparent or other relative temporarily assumes care of children, perhaps informally, while other times the arrangement is longer term and the state or city child welfare or similar department is involved.
25 percent of children who do not live with an adoptive or biological parent live with nonrelatives, including foster parents, temporary guardians, or people in other types of relationships with the child or the child's parents. Non-relative foster parents are state-certified adults, who care for children under the guidance and supervision of a relevant agency. Foster parents comply with guideline and are provided with financial support for the children they care for. (Sometimes the term foster parent refers to a relative who cares for the children under agency guidelines, and sometimes these "kinship" foster parents are also provided financial support.)
When children are placed into foster care or other non-parental care, agencies and families usually do their best to keep siblings together. Brothers and sisters usually provide each other with someone to navigate social challenges and provide continuity over time. Studies have shown that siblings placed together show more closeness to their foster caregivers and like living in the foster home more than those not placed with a sibling (Hegar and Rosenthal, 2011). Separating siblings can cause them to worry about each other or their birth families, and slows acceptance of their new home (Affronti, Rittner, & Semanchin Jones, 2015).
Siblings sometimes play more of a parental role themselves, especially when there are large age gaps or if there are very young children involved. These older siblings may take on some parental responsibilities during a divorce or when children are sent to live with others. "Parentified" siblings may have trouble navigating the complexities of parental roles when they themselves are often still very young. These experiences can actually be traumatic and lead to compulsive disorders as well as lifelong issues with relationships and self-care (Lamothe 2017)
Changes in the traditional family structure raise questions about how such societal shifts affect children. U.S. Census statistics have long shown that children living in homes with both parents grow up with more financial and educational advantages than children who are raised in single-parent homes (U.S. Census 1997). Parental marital status seems to be a significant indicator of advancement in a child’s life. Children living with a divorced parent typically have more advantages than children living with a parent who never married; this is particularly true of children who live with divorced fathers. This correlates with the statistic that never-married parents are typically younger, have fewer years of schooling, and have lower incomes (U.S. Census 1997). Six in ten children living with only their mother live near or below the poverty level. Of those being raised by single mothers, 69 percent live in or near poverty compared to 45 percent for divorced mothers (U.S. Census 1997). Though other factors such as age and education play a role in these differences, it can be inferred that marriage between parents is generally beneficial for children.
### Cohabitation
Living together before or in lieu of marriage is a growing option for many couples. Cohabitation is when a man and woman live together in a sexual relationship without being married. In 2018, 15 percent of young adults ages 25-34 live with an unmarried partner, up from 12 percent 10 years ago (Gurrentz 2018). This surge in cohabitation is likely due to the decrease in social stigma pertaining to the practice. 69 percent of surveyed Americans believe it is acceptable for adults to live together if they are not currently married or do not plan to get married, while 16 percent say it is acceptable only if they plan to get married. (Horowitz 2019).
Cohabitating couples may choose to live together in an effort to spend more time together or to save money on living costs. Many couples view cohabitation as a “trial run” for marriage. 66 percent of married couples who cohabited but were not engaged saw cohabitation as a step toward marriage. And 44 percent of cohabiting adults who are not yet engaged or married see moving in with their partner as a step toward marriage (Horowitz 2019).
While couples may use this time to “work out the kinks” of a relationship before they wed, the most recent research has found that cohabitation has little effect on the success of a marriage. In fact, those who do not cohabitate before marriage have slightly better rates of remaining married for more than ten years (Jayson 2010). Cohabitation may contribute to the increase in the number of men and women who delay marriage. The median age for marriage is the highest it has ever been since the U.S. Census kept records—age twenty-six for women and age twenty-eight for men (U.S. Census 2010).
### Same-Sex Couples
The number of same-sex couples has grown significantly in the past decade. The U.S. Census Bureau reported 594,000 same-sex couple households in the United States, a 50 percent increase from 2000. This increase is a result of more coupling, the growing social acceptance of LGBTQ people, and a subsequent increase in people’s willingness to share more about their identity. Nationally, same-sex couple households make up 1.5 percent of the total partner-headed households in the United States (U.S. Census Bureau 2020). When the 2015 Obergefell vs. Hodges Supreme Court decision legalized same-sex marriage throughout the United States, all federally mandated spousal rights and benefits began apply to same-sex married couples. These have impacts on Social Security and veterans benefits, family leave, and so on. For example, when same-sex marriage was not legal, an LGBTQ person couldn't take the same type of family leave as an opposite sex spouse could if their partner became ill, and could even be prohibited from visiting their partner in the hospital.
In terms of demographics, same-sex couples are not very different from opposite-sex couples. Same-sex couple households have an average age of 52 and an average annual household income of about $107,000; opposite-sex couple households have an average age of 59 and an average household income of $97,000. Same-sex couples are less likely to have children under 18-years-old, with a rate of 14 percent compared to 38 percent of opposite-sex couples; note these include both married and unmarried couples (Census Bureau 2020).
In an analysis of 81 parenting studies, sociologists found no quantifiable data to support the notion that opposite-sex parenting is any better than same-sex parenting. Children of lesbian couples, however, were shown to have slightly lower rates of behavioral problems and higher rates of self-esteem (Biblarz and Stacey 2010). Prior to the nationwide legalization, studies also showed that the rate of suicide among high school students declined in states where same-sex marriage was legal. Suicide is the second-highest cause of death among high school students, and it is a tragic outcome for LGBTQ teenagers who feel unaccepted or vulnerable. The evidence indicates that the legalization of same-sex marriage had positive outcomes for the emotional and mental wellbeing of LGBTQ people (Johns Hopkins University 2017).
### Staying Single
About three-in-ten American adults report that they are single, meaning that they are neither married nor in a committed relationship. That group varies greatly by age and gender. Half of men below age 30 are single, compared with about a quarter of men between ages 30-64. About 30 percent of women under 30 are single, and that drops to 19 percent for women between 30 and 60 years-old. There are also differences among racial lines, with White and Hispanic adults less likely to be single than are Black people. Single individuals are found in higher concentrations in large cities or metropolitan areas, with New York City being one of the highest.
Although both single men and single women report social pressure to get married, women are subject to greater scrutiny. Single women are often portrayed as unhappy or in some way lacking something they should have. Single men, on the other hand, are typically portrayed as lifetime bachelors who cannot settle down or simply “have not found the right girl.” Single women report feeling insecure and displaced in their families when their single status is disparaged (Roberts 2007). However, single women older than thirty-five years old report feeling secure and happy with their unmarried status, as many women in this category have found success in their education and careers. In general, women feel more independent and more prepared to live a large portion of their adult lives without a spouse or domestic partner than they did in the 1960s (Roberts 2007).
The decision to marry or not to marry can be based on a variety of factors including religion and cultural expectations. Asian individuals are the most likely to marry, while African Americans are the least likely to marry (Venugopal 2011). Additionally, individuals who place no value on religion are more likely to be unmarried than those who place a high value on religion. For Black women, however, the importance of religion made no difference in marital status (Bakalar 2010). In general, being single is not a rejection of marriage; rather, it is a lifestyle that does not necessarily include marriage.
### Theoretical Perspectives on Marriage and Family
Sociologists study families on both the macro and micro level to determine how families function. Sociologists may use a variety of theoretical perspectives to explain events that occur within and outside of the family.
### Functionalism
When considering the role of family in society, functionalists uphold the notion that families are an important social institution and that they play a key role in stabilizing society. They also note that family members take on status roles in a marriage or family. The family—and its members—perform certain functions that facilitate the prosperity and development of society.
Sociologist George Murdock conducted a survey of 250 societies and determined that there are four universal residual functions of the family: sexual, reproductive, educational, and economic (Lee 1985). According to Murdock, the family (which for him includes the state of marriage) regulates sexual relations between individuals. He does not deny the existence or impact of premarital or extramarital sex, but states that the family offers a socially legitimate sexual outlet for adults (Lee 1985). This outlet gives way to reproduction, which is a necessary part of ensuring the survival of society.
Once children are produced, the family plays a vital role in training them for adult life. As the primary agent of socialization and enculturation, the family teaches young children the ways of thinking and behaving that follow social and cultural norms, values, beliefs, and attitudes. Parents teach their children manners and civility. A well-mannered child reflects a well-mannered parent.
Parents also teach children gender roles. Gender roles are an important part of the economic function of a family. In each family, there is a division of labor that consists of instrumental and expressive roles. Men tend to assume the instrumental roles in the family, which typically involve work outside of the family that provides financial support and establishes family status. Women tend to assume the expressive roles, which typically involve work inside of the family which provides emotional support and physical care for children (Crano and Aronoff 1978). According to functionalists, the differentiation of the roles on the basis of sex ensures that families are well balanced and coordinated. When family members move outside of these roles, the family is thrown out of balance and must recalibrate in order to function properly. For example, if the father assumes an expressive role such as providing daytime care for the children, the mother must take on an instrumental role such as gaining paid employment outside of the home in order for the family to maintain balance and function.
### Conflict Theory
Conflict theorists are quick to point out that U.S. families have been defined as private entities, the consequence of which has been to leave family matters to only those within the family. Many people in the United States are resistant to government intervention in the family: parents do not want the government to tell them how to raise their children or to become involved in domestic issues. Conflict theory highlights the role of power in family life and contends that the family is often not a haven but rather an arena where power struggles can occur. This exercise of power often entails the performance of family status roles. Conflict theorists may study conflicts as simple as the enforcement of rules from parent to child, or they may examine more serious issues such as domestic violence (spousal and child), sexual assault, marital rape, and incest.
The first study of marital power was performed in 1960. Researchers found that the person with the most access to value resources held the most power. As money is one of the most valuable resources, men who worked in paid labor outside of the home held more power than women who worked inside the home (Blood and Wolfe 1960). Conflict theorists find disputes over the division of household labor to be a common source of marital discord. Household labor offers no wages and, therefore, no power. Studies indicate that when men do more housework, women experience more satisfaction in their marriages, reducing the incidence of conflict (Coltrane 2000). In general, conflict theorists tend to study areas of marriage and life that involve inequalities or discrepancies in power and authority, as they are reflective of the larger social structure.
### Symbolic Interactionism
Interactionists view the world in terms of symbols and the meanings assigned to them (LaRossa and Reitzes 1993). The family itself is a symbol. To some, it is a father, mother, and children; to others, it is any union that involves respect and compassion. Interactionists stress that family is not an objective, concrete reality. Like other social phenomena, it is a social construct that is subject to the ebb and flow of social norms and ever-changing meanings.
Consider the meaning of other elements of family: “parent” was a symbol of a biological and emotional connection to a child; with more parent-child relationships developing through adoption, remarriage, or change in guardianship, the word “parent” today is less likely to be associated with a biological connection than with whoever is socially recognized as having the responsibility for a child’s upbringing. Similarly, the terms “mother” and “father” are no longer rigidly associated with the meanings of caregiver and breadwinner. These meanings are more free-flowing through changing family roles.
Interactionists also recognize how the family status roles of each member are socially constructed, playing an important part in how people perceive and interpret social behavior. Interactionists view the family as a group of role players or “actors” that come together to act out their parts in an effort to construct a family. These roles are up for interpretation. In the late nineteenth and early twentieth century, a “good father,” for example, was one who worked hard to provide financial security for his children. Today, a “good father” is one who takes the time outside of work to promote his children’s emotional well-being, social skills, and intellectual growth—in some ways, a much more daunting task.
### Summary
People's concepts of marriage and family in the United States are changing. Increases in cohabitation, same-sex partners, and singlehood are altering of our ideas of marriage. Similarly, single parents, same-sex parents, cohabitating parents, and unwed parents are changing our notion of what it means to be a family. While most children still live in opposite-sex, two-parent, married households, that is no longer viewed as the only type of nuclear family.
### Section Quiz
### Short Answer
### Further Research
For more statistics on marriage and family, see the Forum on Child and Family Statistics at http://openstax.org/l/child_family_statistics, as well as the American Community Survey, the Current Population Survey, and the U.S. Census decennial survey at the U.S. Census Bureau's web site.
### References
Affronti, M., Rittner, B., & Semanchin Jones, A. M. 2015. “Functional adaptation to foster care: Foster care alumni speak out.” Journal of Public Child Welfare, 9, 1–21. doi: 10.1080/15548732.2014.978930
Bakalar, Nicholas. 2010. “Education, Faith, and a Likelihood to Wed.” New York Times, March 22. Retrieved February 14, 2012 (http://www.nytimes.com/2010/03/23/health/23stat.html).
Biblarz, Tim. J., and Judith Stacey. 2010. “How Does the Gender of Parents Matter?” Journal of Marriage and Family 72:3–22.
Blood, Robert Jr. and Donald Wolfe. 1960. Husbands and Wives: The Dynamics of Married Living. Glencoe, IL: The Free Press.
Childstats.gov. 2019. “Family Structure and Child Living Arrangements.” (https://www.childstats.gov/americaschildren19/family1.asp)
Coltrane, Scott. 2000. “Research on Household Labor: Modeling and Measuring the Social Embeddedness of Routine Family Work.” Journal of Marriage and the Family 62:1209–1233.
Crano, William, and Joel Aronoff. 1978. “A Cross-Cultural Study of Expressive and Instrumental Role Complementarity in the Family.” American Sociological Review 43:463–471.
De Toledo, Sylvie, and Deborah Edler Brown. 1995. Grandparents as Parents: A Survival Guide for Raising a Second Family. New York: Guilford Press.
Gurrentz, Benjamin. 2018. “Cohabitation Is Up, Marriage is Down for Young Adults.” U.S. Census Bureau. (https://www.census.gov/library/stories/2018/11/cohabitaiton-is-up-marriage-is-down-for-young-adults.html)
Hegar, R. L., & Rosenthal, J. A. 2011. “Foster children placed with or separated from siblings: Outcomes based on a national sample.” Children and Youth Services Review, 33(7), 1245–1253. doi: 10.1016/j. childyouth.2011.02.020
Hurley, Dan. 2005. “Divorce Rate: It’s Not as High as You Think.” New York Times, April 19. Retrieved February 14, 2012 (http://www.nytimes.com/2005/04/19/health/19divo.html).
Jayson, Sharon. 2010. “Report: Cohabiting Has Little Effect on Marriage Success.” USA Today, October 14. Retrieved February 14, 2012 (http://www.usatoday.com/news/health/2010-03-02-cohabiting02_N.htm).
Johns Hopkins University. 2017. “Legalization of same-sex marriage linked to reduction of suicide attempts among high school students.” JHU Hub Reports. (https://hub.jhu.edu/2017/02/20/same-sex-marriage-suicide-attempts/)
LaRossa, Ralph, and Donald Reitzes. 1993. “Symbolic Interactionism and Family Studies.” Sourcebook of Family Theories and Methods: A Contextual Approach. New York: Plenum Press.
Lee, Gary. 1982. Family Structure and Interaction: A Comparative Analysis. Minneapolis, MN: University of Minnesota Press.
Livingston, Gretchen. 2018. “About One-Third of U.S. Children Are Living with An Unmarried Parent.” Pew Research Center. (https://www.pewresearch.org/fact-tank/2018/04/27/about-one-third-of-u-s-children-are-living-with-an-unmarried-parent/)
Roberts, Sam. 2007. “51% of Women Are Now Living Without a Spouse.” New York Times, January 16. Retrieved from February 14, 2012 (http://www.nytimes.com/2007/01/16/us/16census.html?pagewanted=all0).
Tayor, Danielle. 2020. “Same-Sex Couples Are More Likel to Adopt or Foster Children.” U.S. Census Bureau. (https://www.census.gov/library/stories/2020/09/fifteen-percent-of-same-sex-couples-have-children-in-their-household.html)
U.S. Census Bureau. 1997. “Children With Single Parents – How They Fare.” Retrieved January 16, 2012 (http://www.census.gov/prod/3/97pubs/cb-9701.pdf).
U.S. Census Bureau. 2009. “American Community Survey (ACS).” Retrieved January 16, 2012 (http://www.census.gov/acs/www/).
U.S. Census Bureau. 2010. “Current Population Survey (CPS).” Retrieved January 16, 2012 (http://www.census.gov/population/www/cps/cpsdef.html).
U.S. Census Bureau. 2011. “America’s Children: Key National Indicators of Well-Being. Forum on Child and Family Statistics. Retrieved January 16, 2012 (http://www.childstats.gov/americaschildren/famsoc1.asp).
Venugopal, Arun. 2011. “New York Leads in Never-Married Women.” WNYC, December 10. Retrieved February 14, 2012 (http://www.wnyc.org/blogs/wnyc-news-blog/2011/sep/22/new-york-never-married-women/).
Waite, Linda, and Lee Lillard. 1991. “Children and Marital Disruption.” American Journal of Sociology 96(4):930–953. |
# Relationships, Marriage, and Family
## Challenges Families Face
As the structure of family changes over time, so do the challenges families face. Events like divorce and remarriage present new difficulties for families and individuals. Other long-standing domestic issues such as abuse continue to strain the health and stability of today’s families.
### Divorce and Remarriage
Divorce, while fairly common and accepted in modern U.S. society, was once a word that would only be whispered and was accompanied by gestures of disapproval. In 1960, divorce was generally uncommon, affecting only 9.1 out of every 1,000 married persons. That number more than doubled (to 20.3) by 1975 and peaked in 1980 at 22.6. Over the last quarter century, divorce rates have dropped steadily and are now similar to those in 1970 (Wang 2020). The dramatic increase in divorce rates after the 1960s has been associated with the liberalization of divorce laws, as well as the shift in societal makeup due to women increasingly entering the workforce (Michael 1978). The decrease in divorce rates can be attributed to three probable factors: First, an increase in the age at which people get married, and second, an increased level of education among those who marry—both of which have been found to promote greater marital stability. The third factor is that the marriage rate itself is going down, and with it the divorce rate. In 2019, there were 16.3 new marriages for every 1,000 women age 15 and over in the United States, down from 17.6 in 2009 (Anderson 2020).
Divorce does not occur equally among all people in the United States; some segments of the U.S. population are more likely to divorce than others. According to the American Community Survey (ACS), men and women in the Northeast and Midwest have the lowest rates of divorce. The South generally has the highest rate of divorce. Divorce rates are likely higher in the South because marriage rates are higher and marriage occurs at younger-than-average ages in this region. In the Northeast, the marriage rate is lower and first marriages tend to be delayed; therefore, the divorce rate is lower (Reynolds 2020). Note that these are generalizations. For example, the District of Columbia has a high marriage rate but among the lowest divorce rate (Anderson 2020).
So what causes divorce? While more young people are choosing to postpone or opt out of marriage, those who enter into the union do so with the expectation that it will last. A great deal of marital problems can be related to stress, especially financial stress. According to researchers participating in the University of Virginia’s National Marriage Project, couples who enter marriage without a strong asset base (like a home, savings, and a retirement plan) are 70 percent more likely to be divorced after three years than are couples with at least $10,000 in assets. This is connected to factors such as age and education level that correlate with low incomes.
The addition of children to a marriage creates added financial and emotional stress. Research has established that marriages enter their most stressful phase upon the birth of the first child (Popenoe and Whitehead 2007). This is particularly true for couples who have multiples (twins, triplets, and so on). Married couples with twins or triplets are 17 percent more likely to divorce than those with children from single births (McKay 2010). Another contributor to the likelihood of divorce is a general decline in marital satisfaction over time. As people get older, they may find that their values and life goals no longer match up with those of their spouse (Popenoe and Whitehead 2004).
Divorce is thought to have a cyclical pattern. Children of divorced parents are 40 percent more likely to divorce than children of married parents. And when we consider children whose parents divorced and then remarried, the likelihood of their own divorce rises to 91 percent (Wolfinger 2005). This might result from being socialized to a mindset that a broken marriage can be replaced rather than repaired (Wolfinger 2005). That sentiment is also reflected in the finding that when both partners of a married couple have been previously divorced, their marriage is 90 percent more likely to end in divorce (Wolfinger 2005).
About 15 percent of all married couples involve one partner who is in their second marriage while the other partner is in their first marriage. About 9 percent of married couples are both in their second marriage. (U.S. Census Bureau 2015). The vast majority (91 percent) of remarriages occur after divorce; only 9 percent occur after death of a spouse (Kreider 2006). Most men and women remarry within five years of a divorce, with the median length for men (three years) being lower than for women (4.4 years). This length of time has been fairly consistent since the 1950s. The majority of those who remarry are between the ages of twenty-five and forty-four (Kreider 2006). The general pattern of remarriage also shows that White people are more likely to remarry than Black people.
Marriage the second time around (or third or fourth) can be a very different process than the first. Remarriage lacks many of the classic courtship rituals of a first marriage. In a second marriage, individuals are less likely to deal with issues like parental approval, premarital sex, or desired family size (Elliot 2010). In a survey of households formed by remarriage, a mere 8 percent included only biological children of the remarried couple. Of the 49 percent of homes that include children, 24 percent included only the woman’s biological children, 3 percent included only the man’s biological children, and 9 percent included a combination of both spouse’s children (U.S. Census Bureau 2006).
### Children of Divorce and Remarriage
Divorce and remarriage can be stressful on partners and children alike. Divorce is often justified by the notion that children are better off in a divorced family than in a family with parents who do not get along. However, long-term studies determine that to be generally untrue. Research suggests that while marital conflict does not provide an ideal childrearing environment, going through a divorce can be damaging. Children are often confused and frightened by the threat to their family security. They may feel responsible for the divorce and attempt to bring their parents back together, often by sacrificing their own well-being (Amato 2000). Only in high-conflict homes do children benefit from divorce and the subsequent decrease in conflict. The majority of divorces come out of lower-conflict homes, and children from those homes are more negatively impacted by the stress of the divorce than the stress of unhappiness in the marriage (Amato 2000). Studies also suggest that stress levels for children are not improved when a child acquires a stepfamily through marriage. Although there may be increased economic stability, stepfamilies typically have a high level of interpersonal conflict (McLanahan and Sandefur 1994).
Children’s ability to deal with a divorce may depend on their age. Research has found that divorce may be most difficult for school-aged children, as they are old enough to understand the separation but not old enough to understand the reasoning behind it. Older teenagers are more likely to recognize the conflict that led to the divorce but may still feel fear, loneliness, guilt, and pressure to choose sides. Infants and preschool-age children may suffer the heaviest impact from the loss of routine that the marriage offered (Temke 2006).
Proximity to parents also makes a difference in a child’s well-being after divorce. Boys who live or have joint arrangements with their fathers show less aggression than those who are raised by their mothers only. Similarly, girls who live or have joint arrangements with their mothers tend to be more responsible and mature than those who are raised by their fathers only. Nearly three-fourths of the children of parents who are divorced live in a household headed by their mother, leaving many boys without a father figure residing in the home (U.S. Census Bureau 2011b). Still, researchers suggest that a strong parent-child relationship can greatly improve a child’s adjustment to divorce (Temke 2006).
There is empirical evidence that divorce has not discouraged children in terms of how they view marriage and family. A blended family has additional stress resulting from combining children from the current and previous relationships. The blended family may also have a parent that has different discipline techniques. In a survey conducted by researchers from the University of Michigan, about three-quarters of high school seniors said it was “extremely important” to have a strong marriage and family life. And over half believed it was “very likely” that they would be in a lifelong marriage (Popenoe and Whitehead 2007). These numbers have continued to climb over the last twenty-five years.
### Violence and Abuse
Violence and abuse are among the most disconcerting of the challenges that today’s families face. Abuse can occur between spouses, between parent and child, as well as between other family members. The frequency of violence among families is a difficult to determine because many cases of spousal abuse and child abuse go unreported. In any case, studies have shown that abuse (reported or not) has a major impact on families and society as a whole.
### Domestic Violence
Domestic violence is a significant social problem in the United States. It is often characterized as violence between household or family members, specifically spouses. To include unmarried, cohabitating, and same-sex couples, family sociologists have created the term intimate partner violence (IPV). (Note that healthcare and support personnel, researchers, or victims may use these terms or related ones interchangeably to refer to the same general issue of violence, aggression, and abuse.) Women are the primary victims of intimate partner violence. It is estimated that one in five women has experienced some form of IPV in her lifetime (compared to one in seven men) (Catalano 2007). IPV may include physical violence, such as punching, kicking, or other methods of inflicting physical pain; sexual violence, such as rape or other forced sexual acts; threats and intimidation that imply either physical or sexual abuse; and emotional abuse, such as harming another’s sense of self-worth through words or controlling another’s behavior. IPV often starts as emotional abuse and then escalates to other forms or combinations of abuse (Centers for Disease Control 2012). IPV includes stalking as well as technological violence (sometimes called cyber aggression), which is committed through communications/social networks or which uses cameras or other technologies to harm victims or control their behavior (Watkins 2016).
Beyond its tragic outcomes and damaging long-term effects, sociologists and other researchers seeking to understand and prevent IPV and support victims may find a wide variance in the data.
On a global scale, intimate partners kill over 130 women each day. The UN Office of Drugs and Crime reported that, “women continue to pay the highest price as a result of gender inequality, discrimination and negative stereotypes... They are also the most likely to be killed by intimate partners and family” (Doom 2018).
The types of violence can vary significantly according to gender. In 2010, of IPV acts that involved physical actions against women, 57 percent involved physical violence only; 9 percent involved rape and physical violence; 14 percent involved physical violence and stalking; 12 percent involved rape, physical violence, and stalking; and 4 percent involved rape only (CDC 2011). This is vastly different than IPV abuse patterns for men, which show that nearly all (92 percent) physical acts of IVP take the form of physical violence and fewer than 1 percent involve rape alone or in combination (Catalano 2007). Perpetrators of IPV work to establish and maintain dependence in order to hold power and control over their victims, making them feel stupid, crazy, or ugly—in some way worthless.
IPV affects different segments of the population at different rates. The rate of IPV for Native American and Alaskan Native women is higher than any other race (Bureau of Justice Statistics 2017). The rate of IPV for Black women (4.6 per 1,000 persons over the age of twelve) is higher than that for White women (3.1). These numbers have been fairly stable for both racial groups over the last ten years.
Accurate statistics on IPV are difficult to determine, as it is estimated that more than half of nonfatal IPV goes unreported. It is not until victims choose to report crimes that patterns of abuse are exposed. Most victims studied stated that abuse had occurred for at least two years prior to their first report (Carlson, Harris, and Holden 1999). Also, studies and research methods apply a range of categories, which makes comparative or reinforcing data difficult to obtain. For example, some studies may only ask about IPV in two categories (for example, physical and sexual violence only) and may find fewer respondents reporting IPV than do studies that add psychological abuse, stalking, and technological violence.
Sometimes abuse is reported to police by a third party, but it still may not be confirmed by victims. A study of domestic violence incident reports found that even when confronted by police about abuse, 29 percent of victims denied that abuse occurred. Surprisingly, 19 percent of their assailants were likely to admit to abuse (Felson, Ackerman, and Gallagher 2005). According to the National Criminal Victims Survey, victims cite varied reasons why they are reluctant to report abuse, as shown in the table below.
IPV against LGBTQ people is generally higher than it is against non-LGBTQ people. Gay men report experiencing IPV in their lifetimes less often (26 percent) than straight men (29 percent) or bisexual men (37 percent). 44 percent of lesbian women report experiencing some type of IPV in their lifetime, compared to 35 percent of straight women. 61 percent of bisexual women report experiencing IPV, a much higher rate than any other sexual orientation frequently studied.
Studies regarding intimate partner violence against transgender people are relatively limited, but several are ongoing. A meta-analysis of available information indicated that physical IPV had occurred in the lifetimes of 38 percent of transgender people, and 25 percent of transgender people had experienced sexual IPV in their lifetimes. Compared with cisgender individuals, transgender individuals were 1.7 times more likely to experience any IPV (Peitzmeier 2020).
Many college students encounter IPV, as well. Overall, psychological violence seems to be the type of IPV college students face most frequently, followed by physical and/or sexual violence (Cho & Huang, 2017). Of high schoolers who report being in a dating relationship, 10% experience physical violence by a boyfriend or girlfriend, 7% experience forced sexual intercourse, and 11% experience sexual dating violence. Seven percent of women and four percent of men who experience IPV are victimized before age 18 (NCJRS 2017). IPV victimization during young adulthood, including the college years, is likely to lead to continuous victimization in adulthood, possibly throughout a lifetime (Greenman & Matsuda, 2016)
### Child Abuse
Children are among the most helpless victims of abuse. In 2010, there were more than 3.3 million reports of child abuse involving an estimated 5.9 million children (Child Help 2011). Three-fifths of child abuse reports are made by professionals, including teachers, law enforcement personnel, and social services staff. The rest are made by anonymous sources, other relatives, parents, friends, and neighbors.
Child abuse may come in several forms, the most common being neglect (78.3 percent), followed by physical abuse (10.8 percent), sexual abuse (7.6 percent), psychological maltreatment (7.6 percent), and medical neglect (2.4 percent) (Child Help 2011). Some children suffer from a combination of these forms of abuse. The majority (81.2 percent) of perpetrators are parents; 6.2 percent are other relatives.
Infants (children less than one year old) were the most victimized population with an incident rate of 20.6 per 1,000 infants. This age group is particularly vulnerable to neglect because they are entirely dependent on parents for care. Some parents do not purposely neglect their children; factors such as cultural values, standard of care in a community, and poverty can lead to hazardous level of neglect. If information or assistance from public or private services are available and a parent fails to use those services, child welfare services may intervene (U.S. Department of Health and Human Services).
Infants are also often victims of physical abuse, particularly in the form of violent shaking. This type of physical abuse is referred to as shaken-baby syndrome, which describes a group of medical symptoms such as brain swelling and retinal hemorrhage resulting from forcefully shaking or causing impact to an infant’s head. A baby’s cry is the number one trigger for shaking. Parents may find themselves unable to soothe a baby’s concerns and may take their frustration out on the child by shaking him or her violently. Other stress factors, such as a poor economy, unemployment, and general dissatisfaction with parental life, may contribute this type of abuse. While there is no official central registry of shaken-baby syndrome statistics, it is estimated that each year 1,400 babies die or suffer serious injury from being shaken (Barr 2007).
Child abuse occurs at all socioeconomic and education levels and crosses ethnic and cultural lines. Just as child abuse is often associated with stresses felt by parents, including financial stress, parents who demonstrate resilience to these stresses are less likely to abuse (Samuels 2011). Young parents are typically less capable of coping with stresses, particularly the stress of becoming a new parent. Teenage mothers are more likely to abuse their children than their older counterparts. As a parent’s age increases, the risk of abuse decreases. Children born to mothers who are fifteen years old or younger are twice as likely to be abused or neglected by age five than are children born to mothers ages twenty to twenty-one (George and Lee 1997).
Drug and alcohol use is also a known contributor to child abuse. Children raised by substance abusers have a risk of physical abuse three times greater than other kids, and neglect is four times as prevalent in these families (Child Welfare Information Gateway 2011). Other risk factors include social isolation, depression, low parental education, and a history of being mistreated as a child. Approximately 30 percent of abused children will later abuse their own children (Child Welfare Information Gateway 2006).
The long-term effects of child abuse impact the physical, mental, and emotional wellbeing of a child. Injury, poor health, and mental instability occur at a high rate in this group, with 80 percent meeting the criteria of one or more psychiatric disorders, such as depression, anxiety, or suicidal behavior, by age twenty-one. Abused children may also suffer from cognitive and social difficulties. Behavioral consequences will affect most, but not all, of child abuse victims. Children of abuse are 25 percent more likely, as adolescents, to suffer from difficulties like poor academic performance and teen pregnancy, or to engage in behaviors like drug abuse and general delinquency. They are also more likely to participate in risky sexual acts that increase their chances of contracting a sexually transmitted disease (Child Welfare Information Gateway 2006). Other risky behaviors include drug and alcohol abuse. As these consequences can affect the health care, education, and criminal systems, the problems resulting from child abuse do not just belong to the child and family, but to society as a whole.
### Summary
Today’s families face a variety of challenges, specifically to marital stability. While divorce rates have decreased in the last twenty-five years, many family members, especially children, still experience the negative effects of divorce. Children are also negatively impacted by violence and abuse within the home, with nearly 6 million children abused each year.
### Section Quiz
### Short Answer
### Further Research
To find more information on child abuse, visit the U.S. Department of Health and Human Services web site to review documents provided by the Child Welfare Information Gateway.
### References
Amato, Paul. 2000. “What Children Learn From Divorce.” Journal of Family Issues 21(8):1061–1086.
American Community Survey. 2011. “Marital Events of Americans: 2009.” The U.S. Census Bureau. Retrieved January 16, 2012 (http://www.census.gov/prod/2011pubs/acs-13.pdf).
Anderson, Lydia and Scherer, Zachary. 2020. “See How Marriage and Divorce Rates In Your State Stack Up.” U.S. Census Bureau. (https://www.census.gov/library/stories/2020/12/united-states-marriage-and-divorce-rates-declined-last-10-years.html)
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# Religion
## Introduction
Why do sociologists study religion? For centuries, humankind has sought to understand and explain the “meaning of life.” Many philosophers believe this contemplation and the desire to understand our place in the universe are what differentiate humankind from other species. Religion, in one form or another, has been found in all human societies since human societies first appeared. Archaeological digs have revealed ritual objects, ceremonial burial sites, and other religious artifacts. Social conflict and even wars often result from religious disputes. To understand a culture, sociologists must study its religion.
What is religion? Pioneer sociologist Émile Durkheim described it with the ethereal statement that it consists of “things that surpass the limits of our knowledge” (1915). He went on to elaborate: Religion is “a unified system of beliefs and practices relative to sacred things, that is to say set apart and forbidden, beliefs and practices which unite into one single moral community, called a church, all those who adhere to them” (1915). Some people associate religion with places of worship (a synagogue or church), others with a practice (confession or meditation), and still others with a concept that guides their daily lives (like dharma or sin). All these people can agree that religion is a system of beliefs, values, and practices concerning what a person holds sacred or considers to be spiritually significant.
Does religion bring fear, wonder, relief, explanation of the unknown or control over freedom and choice? How do our religious perspectives affect our behavior? These are questions sociologists ask and are reasons they study religion. What are peoples' conceptions of the profane and the sacred? How do religious ideas affect the real-world reactions and choices of people in a society?
Religion can also serve as a filter for examining other issues in society and other components of a culture. For example, after the terrorist attacks of September 11, 2001, and later in during the rise and predominant of the terrorist group ISIS, it became important for teachers, church leaders, and the media to educate Americans about Islam to prevent stereotyping and to promote religious tolerance. Sociological tools and methods, such as surveys, polls, interviews, and analysis of historical data, can be applied to the study of religion in a culture to help us better understand the role religion plays in people’s lives and the way it influences society.
### References
Durkheim, Émile. 1947 [1915]. The Elementary Forms of Religious Life, translated by J. Swain. Glencoe, IL: Free Press. |
# Religion
## The Sociological Approach to Religion
From the Latin religio (respect for what is sacred) and religare (to bind, in the sense of an obligation), the term religion describes various systems of belief and practice that define what people consider to be sacred or spiritual (Fasching and deChant 2001; Durkheim 1915). Throughout history, and in societies across the world, leaders have used religious narratives, symbols, and traditions in an attempt to give more meaning to life and understand the universe. Some form of religion is found in every known culture, and it is usually practiced in a public way by a group. The practice of religion can include feasts and festivals, intercession with God or gods, marriage and funeral services, music and art, meditation or initiation, sacrifice or service, and other aspects of culture.
While some people think of religion as something individual because religious beliefs can be highly personal, religion is also a social institution. Social scientists recognize that religion exists as an organized and integrated set of beliefs, behaviors, and norms centered on basic social needs and values. Moreover, religion is a cultural universal found in all social groups. For instance, in every culture, funeral rites are practiced in some way, although these customs vary between cultures and within religious affiliations. Despite differences, there are common elements in a ceremony marking a person’s death, such as announcement of the death, care of the deceased, disposition, and ceremony or ritual. These universals, and the differences in the way societies and individuals experience religion, provide rich material for sociological study.
In studying religion, sociologists distinguish between what they term the experience, beliefs, and rituals of a religion. Religious experience refers to the conviction or sensation that we are connected to “the divine.” This type of communion might be experienced when people pray or meditate. Religious beliefs are specific ideas members of a particular faith hold to be true, such as that Jesus Christ was the son of God, or that reincarnation exists. Another illustration of religious beliefs is the creation stories we find in different religions. Religious rituals are behaviors or practices that are either required or expected of the members of a particular group, such as bar mitzvah or confession of sins (Barkan and Greenwood 2003).
### The History of Religion as a Sociological Concept
In the wake of nineteenth century European industrialization and secularization, three social theorists attempted to examine the relationship between religion and society: Émile Durkheim, Max Weber, and Karl Marx. They are among the founding thinkers of modern sociology.
As stated earlier, French sociologist Émile Durkheim (1858–1917) defined religion as a “unified system of beliefs and practices relative to sacred things” (1915). To him, sacred meant extraordinary—something that inspired wonder and that seemed connected to the concept of “the divine.” Durkheim argued that “religion happens” in society when there is a separation between the profane (ordinary life) and the sacred (1915). A rock, for example, isn’t sacred or profane as it exists. But if someone makes it into a headstone, or another person uses it for landscaping, it takes on different meanings—one sacred, one profane.
Durkheim is generally considered the first sociologist who analyzed religion in terms of its societal impact. Above all, he believed religion is about community: It binds people together (social cohesion), promotes behavior consistency (social control), and offers strength during life’s transitions and tragedies (meaning and purpose). By applying the methods of natural science to the study of society, Durkheim held that the source of religion and morality is the collective mind-set of society and that the cohesive bonds of social order result from common values in a society. He contended that these values need to be maintained to maintain social stability.
But what would happen if religion were to decline? This question led Durkheim to posit that religion is not just a social creation but something that represents the power of society: When people celebrate sacred things, they celebrate the power of their society. By this reasoning, even if traditional religion disappeared, society wouldn’t necessarily dissolve.
Whereas Durkheim saw religion as a source of social stability, German sociologist and political economist Max Weber (1864–1920) believed it was a precipitator of social change. He examined the effects of religion on economic activities and noticed that heavily Protestant societies—such as those in the Netherlands, England, Scotland, and Germany—were the most highly developed capitalist societies and that their most successful business leaders were Protestant. In his writing The Protestant Ethic and the Spirit of Capitalism (1905), he contends that the Protestant work ethic influenced the development of capitalism. Weber noted that certain kinds of Protestantism supported the pursuit of material gain by motivating believers to work hard, be successful, and not spend their profits on frivolous things. (The modern use of “work ethic” comes directly from Weber’s Protestant ethic, although it has now lost its religious connotations.)
German philosopher, journalist, and revolutionary socialist Karl Marx (1818–1883) also studied the social impact of religion. He believed religion reflects the social stratification of society and that it maintains inequality and perpetuates the status quo. For him, religion was just an extension of working-class (proletariat) economic suffering. He famously argued that religion “is the opium of the people” (1844).
For Durkheim, Weber, and Marx, who were reacting to the great social and economic upheaval of the late nineteenth century and early twentieth century in Europe, religion was an integral part of society. For Durkheim, religion was a force for cohesion that helped bind the members of society to the group, while Weber believed religion could be understood as something separate from society. Marx considered religion inseparable from the economy and the worker. Religion could not be understood apart from the capitalist society that perpetuated inequality. Despite their different views, these social theorists all believed in the centrality of religion to society.
### Theoretical Perspectives on Religion
Modern-day sociologists often apply one of three major theoretical perspectives. These views offer different lenses through which to study and understand society: functionalism, symbolic interactionism, and conflict theory. Let’s explore how scholars applying these paradigms understand religion.
### Functionalism
Functionalists contend that religion serves several functions in society. Religion, in fact, depends on society for its existence, value, and significance, and vice versa. From this perspective, religion serves several purposes, like providing answers to spiritual mysteries, offering emotional comfort, and creating a place for social interaction and social control.
In providing answers, religion defines the spiritual world and spiritual forces, including divine beings. For example, it helps answer questions like, “How was the world created?” “Why do we suffer?” “Is there a plan for our lives?” and “Is there an afterlife?” As another function, religion provides emotional comfort in times of crisis. Religious rituals bring order, comfort, and organization through shared familiar symbols and patterns of behavior.
One of the most important functions of religion, from a functionalist perspective, is the opportunities it creates for social interaction and the formation of groups. It provides social support and social networking and offers a place to meet others who hold similar values and a place to seek help (spiritual and material) in times of need. Moreover, it can foster group cohesion and integration. Because religion can be central to many people’s concept of themselves, sometimes there is an “in-group” versus “out-group” feeling toward other religions in our society or within a particular practice. On an extreme level, the Inquisition, the Salem witch trials, and anti-Semitism are all examples of this dynamic. Finally, religion promotes social control: It reinforces social norms such as appropriate styles of dress, following the law, and regulating sexual behavior.
### Conflict Theory
Conflict theorists view religion as an institution that helps maintain patterns of social inequality. For example, the Vatican has a tremendous amount of wealth, while the average income of Catholic parishioners is small. According to this perspective, religion has been used to support the “divine right” of oppressive monarchs and to justify unequal social structures, like India’s caste system.
Conflict theorists are critical of the way many religions promote the idea that believers should be satisfied with existing circumstances because they are divinely ordained. This power dynamic has been used by Christian institutions for centuries to keep poor people poor and to teach them that they shouldn’t be concerned with what they lack because their “true” reward (from a religious perspective) will come after death. Conflict theorists also point out that those in power in a religion are often able to dictate practices, rituals, and beliefs through their interpretation of religious texts or via proclaimed direct communication from the divine.
The feminist perspective is a conflict theory view that focuses specifically on gender inequality. In terms of religion, feminist theorists assert that, although women are typically the ones to socialize children into a religion, they have traditionally held very few positions of power within religions. A few religions and religious denominations are more gender equal, but male dominance remains the norm of most.
### Symbolic Interactionism
Rising from the concept that our world is socially constructed, symbolic interactionism studies the symbols and interactions of everyday life. To interactionists, beliefs and experiences are not sacred unless individuals in a society regard them as sacred. The Star of David in Judaism, the cross in Christianity, and the crescent and star in Islam are examples of sacred symbols. Interactionists are interested in what these symbols communicate. Because interactionists study one-on-one, everyday interactions between individuals, a scholar using this approach might ask questions focused on this dynamic. The interaction between religious leaders and practitioners, the role of religion in the ordinary components of everyday life, and the ways people express religious values in social interactions—all might be topics of study to an interactionist.
### Summary
Religion describes the beliefs, values, and practices related to sacred or spiritual concerns. Social theorist Émile Durkheim defined religion as a “unified system of beliefs and practices relative to sacred things” (1915). Max Weber believed religion could be a force for social change. Karl Marx viewed religion as a tool used by capitalist societies to perpetuate inequality. Religion is a social institution, because it includes beliefs and practices that serve the needs of society. Religion is also an example of a cultural universal, because it is found in all societies in one form or another. Functionalism, conflict theory, and interactionism all provide valuable ways for sociologists to understand religion.
### Section Quiz
### Short Answer
### Further Research
For more discussion on the study of sociology and religion, check out The Immanent Frame is a forum for the exchange of ideas about religion, secularism, and society by leading thinkers in the social sciences and humanities.
Read more about functionalist views on religion here. Read more about women in the clergy here.
Some would argue that the Protestant work ethic is still alive and well in the United States. Read British historian Niall Ferguson’s view here.
### References
Barkan, Steven E., and Susan Greenwood. 2003. “Religious Attendance and Subjective Well-Being among Older Americans: Evidence from the General Social Survey.” Review of Religious Research 45:116–129.
Durkheim, Émile. 1933 [1893]. Division of Labor in Society. Translated by George Simpson. New York: Free Press.
Durkheim, Émile. 1947 [1915]. The Elementary Forms of Religious Life. Translated by J. Swain. Glencoe, IL: Free Press.
Ellway, P. 2005. “The Rational Choice Theory of Religion: Shopping for Faith or Dropping your Faith?” Retrieved February 21, 2012 (http://www.csa.com/discoveryguides/religion/overview.php).
Fasching, Darrel, and Dell deChant. 2001. Comparative Religious Ethics: A Narrative Approach. Hoboken, NJ: Wiley-Blackwel.
Finke, R., and R. Stark. 1988. “Religious Economies and Sacred Canopies: Religious Mobilization in American Cities, 1906.” American Sociological Review 53:41–49.
Greeley, Andrew. 1989. “Protestant and Catholic: Is the Analogical Imagination Extinct?” American Sociological Review 54:485–502.
Hechter, M. 1997. “Sociological Rational Choice Theory.” Annual Review of Sociology 23:191–214. Retrieved January 20, 2012 (http://personal.lse.ac.uk/KANAZAWA/pdfs/ARS1997.pdf).
Hightower, Jim. 1975. Eat Your Heart Out: Food Profiteering in America. New York: Crown Publishers, Inc.
Marx, Karl. 1973 [1844]. Contribution to Critique of Hegel's Philosophy of Right. Cambridge, England: Cambridge University Press.
Ritzer, George. 1993. The McDonaldization of Society. Thousand Oaks, CA: Pine Forge.
Weber, Max. 2002 [1905]. The Protestant Ethic and the Spirit of Capitalism and Other Writings, translated by Peter R. Baehr and Gordon C. Wells. New York: Penguin. |
# Religion
## World Religions
The major religions of the world (Hinduism, Buddhism, Islam, Christianity, Taoism, and Judaism) differ in many respects, including how each religion is organized and the belief system each upholds. Other differences include the nature of belief in a higher power, the history of how the world and the religion began, and the use of sacred texts and objects.
### Types of Religious Organizations
Religions organize themselves—their institutions, practitioners, and structures—in a variety of fashions. For instance, when the Roman Catholic Church emerged, it borrowed many of its organizational principles from the ancient Roman military and turned senators into cardinals, for example. Sociologists use different terms, like ecclesia, denomination, and sect, to define these types of organizations. Scholars are also aware that these definitions are not static. Most religions transition through different organizational phases. For example, Christianity began as a cult, transformed into a sect, and today exists as an ecclesia.
Cults are new religious movements and are often characterized as small, secretive, and highly controlling of members and may have a charismatic leader. In the United States today this term often carries pejorative connotations. However, almost all religions began as cults and gradually progressed to levels of greater size and organization. The term cult is sometimes used interchangeably with the term new religious movement (NRM). The new term may be an attempt to lessen the negativity that the term ‘cult’ has amassed.
Controversy exists over whether some groups are cults, perhaps due in part to media sensationalism over groups like polygamous Mormons or the Peoples Temple followers who died at Jonestown, Guyana. Some groups that are controversially labeled as cults today include the Church of Scientology and the Hare Krishna movement.
A sect is an offshoot of a larger religious group that has distinct beliefs and practices that deviate from that group. Most of the well-known Christian denominations in the United States today began as sects. For example, the Methodists and Baptists protested against their parent Anglican Church in England, just as Henry VIII protested against the Catholic Church by forming the Anglican Church. From “protest” comes the term Protestant.
Occasionally, a sect is a breakaway group that may be in tension with larger society. They sometimes claim to be returning to “the fundamentals” or to contest the veracity of a particular doctrine. When membership in a sect increases over time, it may grow into a denomination. Often a sect begins as an offshoot of a denomination, when a group of members believes they should separate from the larger group.
Some sects do not grow into denominations. Sociologists call these established sects. Established sects, such as the Amish or Jehovah’s Witnesses fall halfway between sect and denomination on the ecclesia–cult continuum because they have a mixture of sect-like and denomination-like characteristics.
A denomination is a large, mainstream religious organization, but it does not claim to be official or state sponsored. It is one religion among many. For example, Baptist, African Methodist Episcopal, Catholic, and Seventh-day Adventist are all Christian denominations.
The term ecclesia, originally referring to a political assembly of citizens in ancient Athens, Greece, now refers to a congregation. In sociology, the term is used to refer to a religious group that most all members of a society belong to. It is considered a nationally recognized, or official, religion that holds a religious monopoly and is closely allied with state and secular powers. The United States does not have an ecclesia by this standard; in fact, this is the type of religious organization that many of the first colonists came to America to escape.
There are many countries in Europe, Asia, Central and South America, and Africa that are considered to have an official state-church. Most of their citizens share similar beliefs, and the state-church has significant involvement in national institutions, which includes restricting the behavior of those with different belief systems. The state-church of England is the Church of England or the Anglican Church established in the 16th century by King Henry VIII. In Saudi Arabia, Islamic law is enforced, and public display of any other religion is illegal. Using this definition then, it can be said that the major Abrahamic systems of Christianity, Judaism, and Islam, are ecclesia; in some regions, they are considered a state-church.
One way to remember these religious organizational terms is to think of cults, sects, denominations, and ecclesia representing a continuum, with increasing influence on society, where cults are least influential and ecclesia are most influential.
### Types of Religions
Scholars from a variety of disciplines have strived to classify religions. One widely accepted categorization that helps people understand different belief systems considers what or who people worship (if anything). Using this method of classification, religions might fall into one of these basic categories, as shown in .
Note that some religions may be practiced—or understood—in various categories. For instance, the Christian notion of the Holy Trinity (God, Jesus, Holy Spirit) defies the definition of monotheism, which is a religion based on belief in a single deity, to some scholars. Similarly, many Westerners view the multiple manifestations of Hinduism’s godhead as polytheistic, which is a religion based on belief in multiple deities,, while Hindus might describe those manifestations are a monotheistic parallel to the Christian Trinity. Some Japanese practice Shinto, which follows animism, which is a religion that believes in the divinity of nonhuman beings, like animals, plants, and objects of the natural world, while people who practice totemism believe in a divine connection between humans and other natural beings.
It is also important to note that every society also has nonbelievers, such as atheists, who do not believe in a divine being or entity, and agnostics, who hold that ultimate reality (such as God) is unknowable. While typically not an organized group, atheists and agnostics represent a significant portion of the population. It is important to recognize that being a nonbeliever in a divine entity does not mean the individual subscribes to no morality. Indeed, many Nobel Peace Prize winners and other great humanitarians over the centuries would have classified themselves as atheists or agnostics.
### The World’s Religions and Philosophies
Religions have emerged and developed across the world. Some have been short-lived, while others have persisted and grown. In this section, we will explore seven of the world’s major religions.
### Hinduism
The oldest religion in the world, Hinduism originated in the Indus River Valley about 4,500 years ago in what is now modern-day northwest India and Pakistan. It arose contemporaneously with ancient Egyptian and Mesopotamian cultures. With roughly one billion followers, Hinduism is the third-largest of the world’s religions. Hindus believe in a divine power that can manifest as different entities. Three main incarnations—Brahma, Vishnu, and Shiva—are sometimes compared to the manifestations of the divine in the Christian Trinity.
Multiple sacred texts, collectively called the Vedas, contain hymns and rituals from ancient India and are mostly written in Sanskrit. Hindus generally believe in a set of principles called dharma, which refer to one’s duty in the world that corresponds with “right” actions. Hindus also believe in karma, or the notion that spiritual ramifications of one’s actions are balanced cyclically in this life or a future life (reincarnation).
### Buddhism
Buddhism was founded by Siddhartha Gautama around 500 B.C.E. Siddhartha was said to have given up a comfortable, upper-class life to follow one of poverty and spiritual devotion. At the age of thirty-five, he famously meditated under a sacred fig tree and vowed not to rise before he achieved enlightenment (bodhi). After this experience, he became known as Buddha, or “enlightened one.” Followers were drawn to Buddha’s teachings and the practice of meditation, and he later established a monastic order.
Buddha’s teachings encourage Buddhists to lead a moral life by accepting the four Noble Truths: 1) life is suffering, 2) suffering arises from attachment to desires, 3) suffering ceases when attachment to desires ceases, and 4) freedom from suffering is possible by following the “middle way.” The concept of the “middle way” is central to Buddhist thinking, which encourages people to live in the present and to practice acceptance of others (Smith 1991). Buddhism also tends to deemphasize the role of a godhead, instead stressing the importance of personal responsibility (Craig 2002).
### Confucianism
Confucianism was developed by Kung Fu-Tzu (Confucius), who lived in the sixth and fifth centuries B.C.E. An extraordinary teacher, his lessons—which were about self-discipline, respect for authority and tradition, and jen (the kind treatment of every person)—were collected in a book called the Analects.
Many consider Confucianism more of a philosophy or social system than a religion because it focuses on sharing wisdom about moral practices but doesn’t involve any type of specific worship; nor does it have formal objects. In fact, its teachings were developed in context of problems of social anarchy and a near-complete deterioration of social cohesion. Dissatisfied with the social solutions put forth, Kung Fu-Tzu developed his own model of religious morality to help guide society (Smith 1991).
### Taoism
In Taoism, the purpose of life is inner peace and harmony. Tao is usually translated as “way” or “path.” The founder of the religion is generally recognized to be a man named Laozi, who lived sometime in the sixth century B.C.E. in China. Taoist beliefs emphasize the virtues of compassion and moderation.
The central concept of tao can be understood to describe a spiritual reality, the order of the universe, or the way of modern life in harmony with the former two. The ying-yang symbol and the concept of polar forces are central Taoist ideas (Smith 1991). Some scholars have compared this Chinese tradition to its Confucian counterpart by saying that “whereas Confucianism is concerned with day-to-day rules of conduct, Taoism is concerned with a more spiritual level of being” (Feng and English 1972).
### Judaism
After their Exodus from Egypt in the thirteenth century B.C.E., Jews, a nomadic society, became monotheistic, worshipping only one God. The Jews’ covenant, or promise of a special relationship with Yahweh (God), is an important element of Judaism. Abraham, a key figure in the foundation of the Jewish faith, is also recognized as a foundation of Christianity and Islam, resulting in the three religions and a few others being referred to as “Abrahamic.” The sacred Jewish text is the Torah, which Christians also follow as the first five books of the Bible. Talmud refers to a collection of sacred Jewish oral interpretation of the Torah. Jews emphasize moral behavior and action in this world as opposed to beliefs or personal salvation in the next world. Since Moses was a leader of the Jewish people when he recorded the Ten Commandments, their culture is interwoven with that of other religions and of governments who adhere to “Judeo-Christian values.”
Jewish people may identify as an ethnic group as well as a religion (Glauz-Todrank 2014). After numerous invasions and wars in the Jewish homeland, culminating in the destruction of the Second Temple, Jewish people relocated to other parts of the world in what is known as the Jewish Diaspora. Large populations settled in Europe, and eventually migrated to the United States. Though a contemporary Jewish person's ancestors may hail from Eastern Europe, the Middle East, or the Iberian Peninsula, many identify themselves as people of Jewish origin, rather than indicating the nation from which their ancestors emigrated (Chervyakov 2010). Today, Jewish people are the second-largest religious group in the United States at 1.9% (Pew Research Center 2018), and the United States is also home to the second largest population of Jewish people, with Israel having the largest.
### Islam
Islam is monotheistic religion, and it follows the teaching of the prophet Muhammad, born in Mecca, Saudi Arabia, in 570 C.E. Muhammad is seen only as a prophet, not as a divine being, and he is believed to be the messenger of Allah (God), who is divine. The followers of Islam are called Muslims.
Islam means “peace” and “submission.” The sacred text for Muslims is the Qur’an (or Koran). As with Christianity’s Old Testament, many of the Qur’an stories are shared with the Jewish faith. Divisions exist within Islam, but all Muslims are guided by five beliefs or practices, often called “pillars”: 1) Allah is the only god, and Muhammad is his prophet, 2) daily prayer, 3) helping those in poverty, 4) fasting as a spiritual practice, and 5) pilgrimage to the holy center of Mecca.
About one-fifth of the world’s population identifies as Muslim. While there is a significant concentration of Muslim people in the Middle East, they span the globe. The most country with the most Muslim people is is Indonesia, an island country in Southeast Asia. In the United States, Muslim people make up the third-largest religious group after Christian and Jewish people, and that population is expected to become larger than the U.S. Jewish population by about 2040 (Pew Research Center 2018).
### Christianity
Today the largest religion in the world, Christianity began 2,000 years ago in Palestine, with Jesus of Nazareth, a leader who taught his followers about caritas (charity) or treating others as you would like to be treated yourself.
The sacred text for Christians is the Bible. While Jews, Christians, and Muslims share many of same historical religious stories, their beliefs verge. In their shared sacred stories, it is suggested that the son of God—a messiah—will return to save God’s followers. While Christians believe that he already appeared in the person of Jesus Christ, Jews and Muslims disagree. While they recognize Christ as an important historical figure, their traditions don’t believe he’s the son of God, and their faiths see the prophecy of the messiah’s arrival as not yet fulfilled.
The largest group of Christians in the United States are members of the Protestant religions, including members of the Baptist, Episcopal, Lutheran, Methodist, Pentecostal, and other churches. However, more people identify as Catholic than any one of those individual Protestant religions (Pew Research Center, 2020).
Different Christian groups have variations among their sacred texts. For instance, The Church of Jesus Christ of Latter-day Saints, an established Christian sect, also uses the Book of Mormon, which they believe details other parts of Christian doctrine and Jesus’ life that aren’t included in the Bible. Similarly, the Catholic Bible includes the Apocrypha, a collection that, while part of the 1611 King James translation, is no longer included in Protestant versions of the Bible. Although monotheistic, many Christians describe their god through three manifestations that they call the Holy Trinity: the father (God), the son (Jesus), and the Holy Spirit. The Holy Spirit is a term Christians often use to describe religious experience, or how they feel the presence of the sacred in their lives. One foundation of Christian doctrine is the Ten Commandments, which decry acts considered sinful, including theft, murder, and adultery.
### Summary
Sociological terms for different kinds of religious organizations are, in order of decreasing influence in society, ecclesia, denomination, sect, and cult. Religions can be categorized according to what or whom its followers worship. Some of the major, and oldest, of the world’s religions and related philosophies include Hinduism, Buddhism, Confucianism, Taoism, Judaism, Islam, and Christianity. In the United States, the most widespread religions are Christianity, Judaism, and Islam.
### Section Quiz
### Short Answer
### Further Research
PBS’s Frontline explores “the life of Jesus and the rise of Christianity” in this in-depth documentary. View the piece in its entirety here: .
For more insight on Confucianism, read the Analects by Confucius. For a primer on Judaism, read Judaism 101.
Sorting through the different Christian denominations can be a daunting task. To help clarify these groups, go to this page with information on Christian denominations.
### References
Chernyakov, Valeriy and Gitelman, Zvi and Shapiro, Vladimir. 2010. “Religion and ethnicity: Judaism in the ethnic consciousness of contemporary Russian Jews.” Ethnic and Racial Studies, Volume 20. (https://www.tandfonline.com/doi/pdf/10.1080/01419870.1997.9993962)
Craig, Mary, transl. 2002. The Pocket Dalai Lama. Boston, MA: Shambhala.
Feng, Gia-fu, and Jane English, transl. 1972. “Introduction” in Tao Te Ching. New York: Random House.
Glauz-Todrank, Annalise. 2014. “Race, Religion, or Ethnicity?: Situating Jews in the American Scene.” Religon Compass, Volume 8, Issue 10. (https://doi.org/10.1111/rec3.12134)
Holy Bible: 1611 Edition, King James Version. 1982 [1611]. Nashville, TN: Thomas Nelson.
Pew Research Center. 2020. “New Estimates Show U.S. Muslim Population Continues to Grow.” (https://www.pewresearch.org/fact-tank/2018/01/03/new-estimates-show-u-s-muslim-population-continues-to-grow/)
Smith, Huston. 1991 [1958]. The World’s Religions. San Francisco, CA: Harper Collins. |
# Religion
## Religion in the United States
In examining the state of religion in the United States today, we see the complexity of religious life in our society, plus emerging trends like the rise of the megachurch, secularization, and the role of religion in social change.
### Religion and Social Change
Religion has historically been an impetus for and a barrier against social change. With Gutenberg’s invention of the printing press, spreading ideas became far easier to share. Many pamphlets for all sorts of interests were printed, but one of Gutenberg's greatest contributions may have been mass producing the Christian Bible. The translation of sacred texts into everyday, nonscholarly language empowered people to shape their religions. However, printers did not just work for the Church. They printed many other texts, including those that were not aligned with Church doctrine. Martin Luther had his complaints against the Church (the 95 Theses) printed in 1517, which allowed them to be distributed throughout Europe. His convictions eventually led to the Protestant Reformation, which revolutionized not only the Church, but much of Western civilization. Disagreements between religious groups and instances of religious persecution have led to wars and genocides. The United States is no stranger to religion as an agent of social change. In fact, many of the United States' early European arrivals were acting largely on religious convictions when they were driven to settle in the United States.
### Liberation Theology
Liberation theology began as a movement within the Roman Catholic Church in the 1950s and 1960s in Latin America, and it combines Christian principles with political activism. It uses the church to promote social change via the political arena, and it is most often seen in attempts to reduce or eliminate social injustice, discrimination, and poverty. A list of proponents of this kind of social justice (although some pre-date liberation theory) could include Francis of Assisi, Leo Tolstoy, Martin Luther King Jr., and Desmond Tutu.
Although begun as a moral reaction against the poverty caused by social injustice in that part of the world, today liberation theology is an international movement that encompasses many churches and denominations. Liberation theologians discuss theology from the point of view of the poor and the oppressed, and some interpret the scriptures as a call to action against poverty and injustice. In Europe and North America, feminist theology has emerged from liberation theology as a movement to bring social justice to women.
### Megachurches
A megachurch is a Christian church that has a very large congregation averaging more than 2,000 people who attend regular weekly services. As of 2009, the largest megachurch in the United States was in Houston Texas, boasting an average weekly attendance of more than 43,000 (Bogan 2009). Megachurches exist in other parts of the world, especially in South Korea, Brazil, and several African countries, but the rise of the megachurch in the United States is a fairly recent phenomenon that has developed primarily in California, Florida, Georgia, and Texas.
Since 1970 the number of megachurches in this country has grown from about fifty to more than 1,000, most of which are attached to the Southern Baptist denomination (Bogan 2009). Approximately six million people are members of these churches (Bird and Thumma 2011). The architecture of these church buildings often resembles a sport or concert arena. The church may include jumbotrons (large-screen televisual technology usually used in sports arenas to show close-up shots of an event). Worship services feature contemporary music with drums and electric guitars and use state-of-the-art sound equipment. The buildings sometimes include food courts, sports and recreation facilities, and bookstores. Services such as child care and mental health counseling are often offered.
Typically, a single, highly charismatic pastor leads the megachurch; at present, most are male. Some megachurches and their preachers have a huge television presence, and viewers all around the country watch and respond to their shows and fundraising.
Besides size, U.S. megachurches share other traits, including conservative theology, evangelism, use of technology and social networking (Facebook, Twitter, podcasts, blogs), hugely charismatic leaders, few financial struggles, multiple sites, and predominantly white membership. They list their main focuses as youth activities, community service, and study of the Scripture (Hartford Institute for Religion Research b).
### Secularization
Historical sociologists Émile Durkheim, Max Weber, and Karl Marx and psychoanalyst Sigmund Freud anticipated secularization and claimed that the modernization of society would bring about a decrease in the influence of religion. Weber believed membership in distinguished clubs would outpace membership in Protestant sects as a way for people to gain authority or respect.
Conversely, some people suggest secularization is a root cause of many social problems, such as divorce, drug use, and educational downturn. One-time presidential contender Michele Bachmann even linked Hurricane Irene and the 2011 earthquake felt in Washington D.C. to politicians’ failure to listen to God (Ward 2011). Similar statements have been made about Hurricane Harvey being the result of Houston’s progressivism and for the city electing a lesbian mayor.
While some the United States seems to be increasingly secular, that change is occurring with a concurrent rise in fundamentalism. Compared to other democratic, industrialized countries, the United States is generally perceived to be a fairly religious nation. Whereas 65 percent of U.S. adults in a 2009 Gallup survey said religion was an important part of their daily lives, the numbers were lower in Spain (49 percent), Canada (42 percent), France (30 percent), the United Kingdom (27 percent), and Sweden (17 percent) (Crabtree and Pelham 2009).
Secularization interests social observers because it entails a pattern of change in a fundamental social institution. Much has been made about the rising number of people who identify as having no religious affiliation, which in a 2019 Pew Poll reached a new high of 26 percent, up from 17 percent in 2009 (Pew Research Center, 2020). But the motivations and meanings of having “no religion” vary significantly. A person who is a part of a religion may make a difficult decision to formally leave it based on disagreements with the organization or the tenets of the faith. Other people may simply “drift away,” and decide to no longer identify themselves as members of a religion. Some people are not raised as a part of a religion, and therefore make a decision whether or not to join one later in life. And finally, a growing number of people identify as spiritual but not religious (SBNR) and they may pray, meditate, and even celebrate holidays in ways quite similar to people affiliated with formal religions; they may also find spirituality through other avenues that range from nature to martial arts. Sociologists and other social scientists may study these motivations and their impact on aspects of individuals’ lives, as well as cultural and group implications.
In addition to the identification and change regarding people’s religious affiliation, religious observance is also interesting. Researchers analyze the depth of involvement in formal institutions, like attending worship, and informal or individual practices. As shown in , of the religions surveyed, members of the Jehovah's Witness religion attend religious services more regularly than members of other religions in the United States. A number of Protestant religions also have relatively high attendance. Regular attendance at services may play a role in building social structure and acceptance of new people into the general community.
### Summary
Liberation theology combines Christian principles with political activism to address social injustice, discrimination, and poverty. Megachurches are those with a membership of more than 2,000 regular attendees, and they are a vibrant, growing and highly influential segment of U.S. religious life. While the numbers of people who identify as having no religious affiliation is rising in the United States, individual motivations and ways of identifying may vary significantly.
### Section Quiz
### Short Answer
### Further Research
What is a megachurch and how are they changing the face of religion? Read “Exploring the Megachurch Phenomena: Their Characteristics and Cultural Context”.
Curious about the LGBT religious movement? Visit the Gay and Lesbian Alliance Against Defamation (GLAAD) and Human Rights Campaign (HRC) web sites for current news about the growing inclusion of LGBT citizens into their respective religious communities, both in the pews and from the pulpit.
How do Christians feel about gay marriage? How many Mormons are there in the United States? Check out the Pew Forum on Religion and Public Life, a research institute examining U.S. religious trends.
### References
Barrick, Audrey. 2011. “Church Trial Set for Lesbian Methodist Minister.” Christian Post, Feb 15. Retrieved January 22, 2012 (http://www.christianpost.com/news/church-trial-set-for-lesbian-methodist-minister-48993).
Beck, Edward L. 2010. “Are Gay Priests the Problem?” ABC News/Good Morning America, April 15. Retrieved January 22, 2012 (http://abcnews.go.com/GMA/Spirituality/gay-priests-problem/story?id=10381964).
Bird, Warren, and Scott Thumma. 2011. “A New Decade of Megachurches: 2011 Profile of Large Attendance Churches in the United States.” Hartford Institute for Religion Research. Retrieved February 21, 2012 (http://hirr.hartsem.edu/megachurch/megachurch-2011-summary-report.htm).
Bogan, Jesse. 2009. “America’s Biggest Megachurches.” Forbes.com, June 26. Retrieved February 21, 2012 (http://www.forbes.com/2009/06/26/americas-biggest-megachurches-business-megachurches.html).
Crabtree, Steve, and Brett Pelham. 2009. “What Alabamians and Iranians Have in Common.” Gallup World, February 9. Retrieved February 21, 2012 (http://www.gallup.com/poll/114211/alabamians-iranians-common.aspx).
Hartford Institute for Religion Research a. “Database of Megachurches in the US.” Retrieved February 21, 2012 (http://hirr.hartsem.edu/megachurch/database.html).
Hartford Institute for Religion Research b. “Megachurch Definition.” Retrieved February 21, 2012 (http://hirr.hartsem.edu/megachurch/definition.html).
Human Rights Campaign. 2019. “Stances of Faiths on LGBTQ Issues.” (Series of web-based articles.) (https://www.hrc.org/resources/stances-of-faiths-on-lgbt-issues-episcopal-church)
McKenna, Josephine. 2014. “Catholic Bishops Narrowly Reject a Wider Welcome to Gays, Divorced Catholics.” Religion News Service. Retrieved Oct. 27, 2014 (http://www.religionnews.com/2014/10/18/gays-missing-final-message-vaticans-heated-debate-family/).
NBC New York, 2020. “Episcopal Bishop to Resign Over Same-Sex Marriage Stance.” (https://www.nbcnewyork.com/news/local/episcopal-bishop-to-resign-over-same-sex-marriage-stance/2686504/)
Newport, Frank. 2003. “Americans Approve of Displays of Religious Symbols.” Gallup, October 3. Retrieved February 21, 2012 (http://www.gallup.com/poll/9391/americans-approve-public-displays-religious-symbols.aspx).
Pasha-Robinson, Lucy. 2017. “Gay People To Blame for Hurricane Harvey, Say Evangelical Christian Leaders.” The Independent. (https://www.independent.co.uk/news/world/americas/gay-people-hurricane-harvey-blame-christian-leaders-texas-flooding-homosexuals-lgbt-a7933026.html)
Pew Research Center. 2020. “Religious Landscape Study.” (https://www.pewforum.org/religious-landscape-study/)
Pew Research Forum. 2011. “The Future of the Global Muslim Population.” The Pew Forum on Religion and Public Life, January 27. Retrieved February 21, 2012 (http://www.pewforum.org/The-Future-of-the-Global-Muslim-Population.aspx).
Ward, Jon. 2011. “Michele Bachman Says Hurricane and Earthquake Are Divine Warnings to Washington.” Huffington Post, August 29. Retrieved February 21, 2012 (http://www.huffingtonpost.com/2011/08/29/michele-bachmann-hurricane-irene_n_940209.html). |
# Education
## Introduction
“What the educator does in teaching is to make it possible for the students to become themselves” (Paulo Freire, Pedagogy of the Oppressed).
David Simon, in his book Social Problems and the Sociological Imagination: A Paradigm for Analysis (1995), points to the notion that social problems are, in essence, contradictions—that is, statements, ideas, or features of a situation that are opposed to one another. Consider then, that one of the greatest expectations in U.S. society is that to attain any form of success in life, a person needs an education. In fact, a college degree is rapidly becoming an expectation at many levels of success, not merely an enhancement to our occupational choices. And, as you might expect, the number of people graduating from college in the United States continues to rise dramatically.
The contradiction, however, lies in the fact that the more impactful a college degree has become, the harder it has become to achieve it. The cost of getting a college degree has risen sharply since the mid-1980s, while many important forms of government support have barely increased.
The net result is that those who do graduate from college are likely to begin a career in debt. As of 2009, a typical student’s loans amounted to around $23,000. Ten years later, the average amount of debt for students who took loans grew to over $30,000. The overall national student loan debt topped $1.6 trillion in 2020, according to the Federal Reserve. These rising costs and risky debt burdens have led to a number of diverse proposals for solutions. Some call for cancelling current college debt and making more colleges free to qualifying students. Others advocate for more focused and efficient education in order to achieve needed career requirements more quickly. Employers, seeking both to widen their applicant pool and increase equity among their workforce, have increasingly sought ways to eliminate unnecessary degree requirements: If a person has the skills and knowledge to do the job, they have more access to it (Kerr 2020).
Is a college degree still worth it? Lifetime earnings among those with a college degree are, on average, still much higher than for those without. A 2019 Federal Reserve report indicated that, on average, college graduates earn $30,000 per year more than non-college graduates. Also, that wage gap has nearly doubled in the past 40 years (Abel 2019).
Is the wage advantage enough to overcome the potential debt? And what’s behind those averages? Remember, since the $30,000 is an average, it also confirms what we see from other data: That certain people and certain college majors earn far more than others. As a result, earning a college degree in a field that has a smaller wage advantage over non-college graduates might not seem “worth it.”
But is college worth more than money?
A student earning Associate’s and Bachelor’s degrees generally will often take a wide array of courses, including many outside of their major. The student is exposed to a fairly broad range of topics, from mathematics and the physical sciences to history and literature, the social sciences, and music and art through introductory and survey-styled courses. It is in this period that the student’s world view is, it is hoped, expanded. Then, when they begin the process of specialization, it is with a much broader perspective than might be otherwise. This additional “cultural capital” can further enrich the life of the student, enhance their ability to work with experienced professionals, and build wisdom upon knowledge. Over two thousand years ago, Socrates said, “The unexamined life is not worth living.” The real value of an education, then, is to enhance our skill at self-examination. Education, its impact, and its costs are important not just to sociologists, but to policymakers, employers, and of course to parents.
### References
Abel, Jaison R. and Dietz, Richard. 2019 “Despite Rising Costs, College Is Still a Good Investment.” New York Federal Reserve, Liberty Street Economics. (https://libertystreeteconomics.newyorkfed.org/2019/06/despite-rising-costs-college-is-still-a-good-investment.html)
Kerr, Emma. 2020. “See 10 Average Years of Student Loan Debt.” US News and World Reports. (https://www.usnews.com/education/best-colleges/paying-for-college/articles/see-how-student-loan-borrowing-has-risen-in-10-years)
Leonhardt, David. 2014. “Is College Worth It? Clearly , New Data Say.” The New York Times. Retrieved December 12, 2014. (http://www.nytimes.com/2014/05/27/upshot/is-college-worth-it-clearly-new-data-say.html?_r=0&abt=0002&abg=1).
Lorin Janet, and Jeanna Smialek. 2014. “College Graduates Struggle to Find Eployment Worth a Degree.” Bloomberg. Retrieved December 12, 2014. (http://www.bloomberg.com/news/2014-06-05/college-graduates-struggle-to-find-employment-worth-a-degree.html).
New Oxford English Dictionary. “contradiction.” New Oxford English Dictionary. Retrieved December 12, 2014. (http://www.oxforddictionaries.com/us/definition/american_english/contradiction?searchDictCode=all).
Plumer, Brad. 2013. “Only 27 percent of college graduates have a job related ot their major.” The Washington Post. Retrieved December 12, 2014. (http://www.washingtonpost.com/blogs/wonkblog/wp/2013/05/20/only-27-percent-of-college-grads-have-a-job-related-to-their-major/).
Simon, R David. 1995. Social Problems and the Sociological Imagination: A Paradigm for Analysis. New York: McGraw-Hill Education. |
# Education
## Education around the World
Education is a social institution through which members of a society are taught basic academic knowledge, learning skills, and cultural norms. Every nation in the world is equipped with some form of education system, though those systems vary greatly. The major factors that affect education systems are the resources and money that are utilized to support those systems in different nations. As you might expect, a country’s wealth has much to do with the amount of money spent on education. Countries that do not have such basic amenities as running water are unable to support robust education systems or, in many cases, any formal schooling at all. The result of this worldwide educational inequality is a social concern for many countries, including the United States.
International differences in education systems are not solely a financial issue. The value placed on education, the amount of time devoted to it, and the distribution of education within a country also play a role in those differences. For example, students in South Korea spend 220 days a year in school, compared to the 180 days a year of their United States counterparts (Pellissier 2010).
Then there is the issue of educational distribution and changes within a nation. The Program for International Student Assessment (PISA) is administered to samples of fifteen-year-old students worldwide. In 2010, the results showed that students in the United States had fallen from fifteenth to twenty-fifth in the rankings for science and math (National Public Radio 2010). The same program showed that by 2018, U.S. student achievement had remained on the same level for mathematics and science, but had shown improvements in reading. In 2018, about 4,000 students from about 200 high schools in the United States took the PISA test (OECD 2019).
Analysts determined that the nations and city-states at the top of the rankings had several things in common. For one, they had well-established standards for education with clear goals for all students. They also recruited teachers from the top 5 to 10 percent of university graduates each year, which is not the case for most countries (National Public Radio 2010).
Finally, there is the issue of social factors. One analyst from the Organization for Economic Cooperation and Development, the organization that created the PISA test, attributed 20 percent of performance differences and the United States’ low rankings to differences in social background. Researchers noted that educational resources, including money and quality teachers, are not distributed equitably in the United States. In the top-ranking countries, limited access to resources did not necessarily predict low performance. Analysts also noted what they described as “resilient students,” or those students who achieve at a higher level than one might expect given their social background. In Shanghai and Singapore, the proportion of resilient students is about 70 percent. In the United States, it is below 30 percent. These insights suggest that the United States’ educational system may be on a descending path that could detrimentally affect the country’s economy and its social landscape (National Public Radio 2010).
### Formal and Informal Education
As already mentioned, education is not solely concerned with the basic academic concepts that a student learns in the classroom. Societies also educate their children, outside of the school system, in matters of everyday practical living. These two types of learning are referred to as formal education and informal education.
Formal education describes the learning of academic facts and concepts through a formal curriculum. Arising from the tutelage of ancient Greek thinkers, centuries of scholars have examined topics through formalized methods of learning. Education in earlier times was only available to the higher classes; they had the means for access to scholarly materials, plus the luxury of leisure time that could be used for learning. The Industrial Revolution and its accompanying social changes made education more accessible to the general population. Many families in the emerging middle class found new opportunities for schooling.
The modern U.S. educational system is the result of this progression. Today, basic education is considered a right and responsibility for all citizens. Expectations of this system focus on formal education, with curricula and testing designed to ensure that students learn the facts and concepts that society believes are basic knowledge.
In contrast, informal education describes learning about cultural values, norms, and expected behaviors by participating in a society. This type of learning occurs both through the formal education system and at home. Our earliest learning experiences generally happen via parents, relatives, and others in our community. Through informal education, we learn important life skills that help us get through the day and interact with each other, including how to dress for different occasions, how to perform regular tasks such as shopping for and preparing food, and how to keep our bodies clean. Many professional tasks and local customs are learned informally, as well.
Cultural transmission refers to the way people come to learn the values, beliefs, and social norms of their culture. Both informal and formal education include cultural transmission. For example, a student will learn about cultural aspects of modern history in a U.S. History classroom. In that same classroom, the student might learn the cultural norm for asking a classmate out on a date through passing notes and whispered conversations.
### Access to Education
Another global concern in education is universal access. This term refers to people’s equal ability to participate in an education system. On a world level, access might be more difficult for certain groups based on class or gender (as was the case in the United States earlier in the nation’s history, a dynamic we still struggle to overcome). The modern idea of universal access arose in the United States as a concern for people with disabilities. In the United States, one way in which universal education is supported is through federal and state governments covering the cost of free public education. Of course, the way this plays out in terms of school budgets and taxes makes this an often-contested topic on the national, state, and community levels.
A precedent for universal access to education in the United States was set with the 1972 U.S. District Court for the District of Columbia’s decision in Mills v. Board of Education of the District of Columbia. This case was brought on the behalf of seven school-age children with special needs who argued that the school board was denying their access to free public education. The school board maintained that the children’s “exceptional” needs, which included intellectual disabilities, precluded their right to be educated for free in a public school setting. The board argued that the cost of educating these children would be too expensive and that the children would therefore have to remain at home without access to education.
This case was resolved in a hearing without any trial. The judge, Joseph Cornelius Waddy, upheld the students’ right to education, finding that they were to be given either public education services or private education paid for by the Washington, D.C., board of education. He noted that
Today, the optimal way to include people with disabilities students in standard classrooms is still being researched and debated. “Inclusion” is a method that involves complete immersion in a standard classroom, whereas “mainstreaming” balances time in a special-needs classroom with standard classroom participation. There continues to be social debate surrounding how to implement the ideal of universal access to education.
### Summary
Educational systems around the world have many differences, though the same factors—including resources and money—affect every educational system. Educational distribution is a major issue in many nations, including in the United States, where the amount of money spent per student varies greatly by state. Education happens through both formal and informal systems; both foster cultural transmission. Universal access to education is a worldwide concern.
### Section Quiz
### Short Answer
### Further Research
Though it’s a struggle, education is continually being improved in the developing world. To learn how educational programs are being fostered worldwide, explore the Education section of the Center for Global Development’s website.
### References
Darling-Hammond, Linda. 2010. "What We Can Learn from Finland's Successful School Reform." NEA Today Magazine. Retrieved December 12, 2014. (http://www.nea.org/home/40991.htm)..
Durkheim, Émile. 1898 [1956]. Education and Sociology. New York: Free Press.
Educationdata.org. 2019. “U.S. Public Education Statistics.” (https://educationdata.org/public-education-spending-statistics)
Gross-Loh, Christine. 2014. "Finnish Education Chief: 'We Created a School System Based on Equality.'" The Atlantic. Retrieved December 12, 2014. (http://www.theatlantic.com/education/archive/2014/03/finnish-education-chief-we-created-a-school-system-based-on-equality/284427/?single_page=true).
Mills v. Board of Education, 348 DC 866 (1972).
National Center for Public Policy and Higher Education. 2006. Measuring UP: The National Report Card on Higher Education. Retrieved December 9, 2011 (http://www.eric.ed.gov/PDFS/ED493360.pdf).
National Public Radio. 2010. “Study Confirms U.S. Falling Behind in Education.” All Things Considered, December 10. Retrieved December 9, 2011 (https://www.npr.org/2010/12/07/131884477/Study-Confirms-U-S-Falling-Behind-In-Education).
OECD. 2019. “PISA Results from 2018: Country Note: USA.” (https://www.oecd.org/pisa/publications/PISA2018_CN_USA.pdf)
Pellissier, Hank. 2010. “High Test Scores, Higher Expectations, and Presidential Hype.” Great Schools. Retrieved January 17, 2012 (http://www.greatschools.org/students/academic-skills/2427-South-Korean-schools.gs).
Rampell, Catherine. 2009. “Of All States, New York’s Schools Spend Most Money Per Pupil.” Economix. Retrieved December 15, 2011 (http://economix.blogs.nytimes.com/2009/07/27/of-all-states-new-york-schools-spend-most-money-per-pupil/).
U.S. Census Bureau. 2014. "Public Education Finances 2012." Retrieved December 12, 2014. (http://www2.census.gov/govs/school/12f33pub.pdf).
World Bank. 2011. “Education in Afghanistan.” Retrieved December 14, 2011 (http://go.worldbank.org/80UMV47QB0). |
# Education
## Theoretical Perspectives on Education
While it is clear that education plays an integral role in individuals’ lives as well as society as a whole, sociologists view that role from many diverse points of view. Functionalists believe that education equips people to perform different functional roles in society. Conflict theorists view education as a means of widening the gap in social inequality. Feminist theorists point to evidence that sexism in education continues to prevent women from achieving a full measure of social equality. Symbolic interactionists study the dynamics of the classroom, the interactions between students and teachers, and how those affect everyday life. In this section, you will learn about each of these perspectives.
### Functionalism
Functionalists view education as one of the more important social institutions in a society. They contend that education contributes two kinds of functions: manifest (or primary) functions, which are the intended and visible functions of education; and latent (or secondary) functions, which are the hidden and unintended functions.
### Manifest Functions
There are several major manifest functions associated with education. The first is socialization. Beginning in preschool and kindergarten, students are taught to practice various societal roles. The French sociologist Émile Durkheim (1858–1917), who established the academic discipline of sociology, characterized schools as “socialization agencies that teach children how to get along with others and prepare them for adult economic roles” (Durkheim 1898). Indeed, it seems that schools have taken on this responsibility in full.
This socialization also involves learning the rules and norms of the society as a whole. In the early days of compulsory education, students learned the dominant culture. Today, since the culture of the United States is increasingly diverse, students may learn a variety of cultural norms, not only that of the dominant culture.
School systems in the United States also transmit the core values of the nation through manifest functions like social control. One of the roles of schools is to teach students conformity to law and respect for authority. Obviously, such respect, given to teachers and administrators, will help a student navigate the school environment. This function also prepares students to enter the workplace and the world at large, where they will continue to be subject to people who have authority over them. Fulfillment of this function rests primarily with classroom teachers and instructors who are with students all day.
Education also provides one of the major methods used by people for upward social mobility. This function is referred to as social placement. College and graduate schools are viewed as vehicles for moving students closer to the careers that will give them the financial freedom and security they seek. As a result, college students are often more motivated to study areas that they believe will be advantageous on the social ladder. A student might value business courses over a class in Victorian poetry because she sees business class as a stronger vehicle for financial success.
### Latent Functions
Education also fulfills latent functions. As you well know, much goes on in a school that has little to do with formal education. For example, you might notice an attractive fellow student when he gives a particularly interesting answer in class—catching up with him and making a date speaks to the latent function of courtship fulfilled by exposure to a peer group in the educational setting.
The educational setting introduces students to social networks that might last for years and can help people find jobs after their schooling is complete. Of course, with social media such as Facebook and LinkedIn, these networks are easier than ever to maintain. Another latent function is the ability to work with others in small groups, a skill that is transferable to a workplace and that might not be learned in a homeschool setting.
The educational system, especially as experienced on university campuses, has traditionally provided a place for students to learn about various social issues. There is ample opportunity for social and political advocacy, as well as the ability to develop tolerance to the many views represented on campus. In 2011, the Occupy Wall Street movement swept across college campuses all over the United States, leading to demonstrations in which diverse groups of students were unified with the purpose of changing the political climate of the country.
Functionalists recognize other ways that schools educate and enculturate students. One of the most important U.S. values students in the United States learn is that of individualism—the valuing of the individual over the value of groups or society as a whole. In countries such as Japan and China, where the good of the group is valued over the rights of the individual, students do not learn as they do in the United States that the highest rewards go to the “best” individual in academics as well as athletics. One of the roles of schools in the United States is fostering self-esteem; conversely, schools in Japan focus on fostering social esteem—the honoring of the group over the individual.
In the United States, schools also fill the role of preparing students for competition in life. Obviously, athletics foster a competitive nature, but even in the classroom students compete against one another academically. Schools also fill the role of teaching patriotism. Students recite the Pledge of Allegiance each morning and take history classes where they learn about national heroes and the nation’s past.
Another role of schools, according to functionalist theory, is that of sorting, or classifying students based on academic merit or potential. The most capable students are identified early in schools through testing and classroom achievements. Such students are placed in accelerated programs in anticipation of successful college attendance.
Functionalists also contend that school, particularly in recent years, is taking over some of the functions that were traditionally undertaken by family. Society relies on schools to teach about human sexuality as well as basic skills such as budgeting and job applications—topics that at one time were addressed by the family.
### Conflict Theory
Conflict theorists do not believe that public schools reduce social inequality. Rather, they believe that the educational system reinforces and perpetuates social inequalities that arise from differences in class, gender, race, and ethnicity. Where functionalists see education as serving a beneficial role, conflict theorists view it more negatively. To them, educational systems preserve the status quo and push people of lower status into obedience.
The fulfillment of one’s education is closely linked to social class. Students of low socioeconomic status are generally not afforded the same opportunities as students of higher status, no matter how great their academic ability or desire to learn. Picture a student from a working-class home who wants to do well in school. On a Monday, he’s assigned a paper that’s due Friday. Monday evening, he has to babysit his younger sister while his divorced mother works. Tuesday and Wednesday, he works stocking shelves after school until 10:00 p.m. By Thursday, the only day he might have available to work on that assignment, he’s so exhausted he can’t bring himself to start the paper. His mother, though she’d like to help him, is so tired herself that she isn’t able to give him the encouragement or support he needs. And since English is her second language, she has difficulty with some of his educational materials. They also lack a computer and printer at home, which most of his classmates have, so they have to rely on the public library or school system for access to technology. As this story shows, many students from working-class families have to contend with helping out at home, contributing financially to the family, poor study environments and a lack of support from their families. This is a difficult match with education systems that adhere to a traditional curriculum that is more easily understood and completed by students of higher social classes.
Such a situation leads to social class reproduction, extensively studied by French sociologist Pierre Bourdieu. He researched how cultural capital, or cultural knowledge that serves (metaphorically) as currency that helps us navigate a culture, alters the experiences and opportunities available to French students from different social classes. Members of the upper and middle classes have more cultural capital than do families of lower-class status. As a result, the educational system maintains a cycle in which the dominant culture’s values are rewarded. Instruction and tests cater to the dominant culture and leave others struggling to identify with values and competencies outside their social class. For example, there has been a great deal of discussion over what standardized tests such as the SAT truly measure. Many argue that the tests group students by cultural ability rather than by natural intelligence.
The cycle of rewarding those who possess cultural capital is found in formal educational curricula as well as in the hidden curriculum, which refers to the type of nonacademic knowledge that students learn through informal learning and cultural transmission. This hidden curriculum reinforces the positions of those with higher cultural capital and serves to bestow status unequally.
Conflict theorists point to tracking, a formalized sorting system that places students on “tracks” (advanced versus low achievers) that perpetuate inequalities. While educators may believe that students do better in tracked classes because they are with students of similar ability and may have access to more individual attention from teachers, conflict theorists feel that tracking leads to self-fulfilling prophecies in which students live up (or down) to teacher and societal expectations (Education Week 2004).
To conflict theorists, schools play the role of training working-class students to accept and retain their position as lower members of society. They argue that this role is fulfilled through the disparity of resources available to students in richer and poorer neighborhoods as well as through testing (Lauen and Tyson 2008).
IQ tests have been attacked for being biased—for testing cultural knowledge rather than actual intelligence. For example, a test item may ask students what instruments belong in an orchestra. To correctly answer this question requires certain cultural knowledge—knowledge most often held by more affluent people who typically have more exposure to orchestral music. Though experts in testing claim that bias has been eliminated from tests, conflict theorists maintain that this is impossible. These tests, to conflict theorists, are another way in which education does not provide opportunities, but instead maintains an established configuration of power.
### Feminist Theory
Feminist theory aims to understand the mechanisms and roots of gender inequality in education, as well as their societal repercussions. Like many other institutions of society, educational systems are characterized by unequal treatment and opportunity for women. Almost two-thirds of the world’s 862 million illiterate people are women, and the illiteracy rate among women is expected to increase in many regions, especially in several African and Asian countries (UNESCO 2005; World Bank 2007).
Women in the United States have been relatively late, historically speaking, to be granted entry to the public university system. In fact, it wasn’t until the establishment of Title IX of the Education Amendments in 1972 that discriminating on the basis of sex in U.S. education programs became illegal. In the United States, there is also a post-education gender disparity between what male and female college graduates earn. A study released in May 2011 showed that, among men and women who graduated from college between 2006 and 2010, men out-earned women by an average of more than $5,000 each year. First-year job earnings for men averaged $33,150; for women the average was $28,000 (Godofsky, Zukin, and van Horn 2011). Similar trends are seen among salaries of professionals in virtually all industries.
When women face limited opportunities for education, their capacity to achieve equal rights, including financial independence, are limited. Feminist theory seeks to promote women’s rights to equal education (and its resultant benefits) across the world.
### Symbolic Interactionism
Symbolic interactionism sees education as one way that labeling theory is seen in action. A symbolic interactionist might say that this labeling has a direct correlation to those who are in power and those who are labeled. For example, low standardized test scores or poor performance in a particular class often lead to a student who is labeled as a low achiever. Such labels are difficult to “shake off,” which can create a self-fulfilling prophecy (Merton 1968).
In his book High School Confidential, Jeremy Iversen details his experience as a Stanford graduate posing as a student at a California high school. One of the problems he identifies in his research is that of teachers applying labels that students are never able to lose. One teacher told him, without knowing he was a bright graduate of a top university, that he would never amount to anything (Iversen 2006). Iversen obviously didn’t take this teacher’s false assessment to heart. But when an actual seventeen-year-old student hears this from a person with authority over her, it’s no wonder that the student might begin to “live down to” that label.
The labeling with which symbolic interactionists concern themselves extends to the very degrees that symbolize completion of education. Credentialism embodies the emphasis on certificates or degrees to show that a person has a certain skill, has attained a certain level of education, or has met certain job qualifications. These certificates or degrees serve as a symbol of what a person has achieved, and allows the labeling of that individual.
Indeed, as these examples show, labeling theory can significantly impact a student’s schooling. This is easily seen in the educational setting, as teachers and more powerful social groups within the school dole out labels that are adopted by the entire school population.
### Summary
The major sociological theories offer insight into how we understand education. Functionalists view education as an important social institution that contributes both manifest and latent functions. Functionalists see education as serving the needs of society by preparing students for later roles, or functions, in society. Conflict theorists see schools as a means for perpetuating class, racial-ethnic, and gender inequalities. In the same vein, feminist theory focuses specifically on the mechanisms and roots of gender inequality in education. The theory of symbolic interactionism focuses on education as a means for labeling individuals.
### Section Quiz
### Short Answer
### Further Research
Can tracking actually improve learning? This 2009 article from explores the debate with evidence from Kenya.
The National Center for Fair & Open Testing (FairTest) is committed to ending the bias and other flaws seen in standardized testing. Their mission is to ensure that students, teachers, and schools are evaluated fairly. You can learn more about their mission, as well as the latest in news on test bias and fairness, at their website.
### References
American Federation for Children. 2017. “Why I Support School Choice, An Advocate’s Story. (https://www.federationforchildren.org/school-choice-advocates-story/)
Berlinsky-Schine, Laura. 2020. “What Is Grade Inflation?” College Vine. (https://blog.collegevine.com/what-is-grade-inflation/)
Boleslavsky, Raphael and Christopher Cotton. 2014. “Unrecognised Benefits of Grade Inflation.” VOXEU. (https://voxeu.org/article/unrecognised-benefits-grade-inflation)
Education Week. 2004. “Tracking.” Education Week, August 4. Retrieved February 24, 2012 (http://www.edweek.org/ew/issues/tracking/).
Godofsky, Jessica, Cliff Zukin, and Carl Van Horn. 2011. Unfulfilled Expectations: Recent College Graduates Struggle in a Troubled Economy. New Brunswick, NJ: Rutgers University.
Greason, Grace. 2020. “Make Harvard Grade Again.” Harvard Political Review. March 21, 2020. (https://harvardpolitics.com/make-harvard-grade-again/)
Iversen, Jeremy. 2006. High School Confidential. New York: Atria.
Jaschik, Scott. 2016. “Grade Inflation, Higher and Higher.” Inside Higher Ed. (https://www.insidehighered.com/news/2016/03/29/survey-finds-grade-inflation-continues-rise-four-year-colleges-not-community-college)
Lauen, Douglas Lee and Karolyn Tyson. 2008. “Perspectives from the Disciplines: Sociological Contribution to Education Policy Research and Debate.” AREA Handbook on Education Policy Research. Retrieved February 24, 2012.
Murphy, James S. 2017. “Should We Be Worried About High School Grade Inflation.” Inside Higher Ed. (https://www.insidehighered.com/views/2017/09/15/analysis-college-boards-study-grade-inflation-essay)
National Public Radio. 2004. “Princeton Takes Steps to Fight ‘Grade Inflation.’” Day to Day, April 28.
Mansfield, Harvey C. 2001. “Grade Inflation: It’s Time to Face the Facts.” The Chronicle of Higher Education 47(30): B24.
Merton, Robert K. 1968. Social Theory and Social Structure. New York: Free Press.
UNESCO. 2005. Towards Knowledge Societies: UNESCO World Report. Paris: UNESCO Publishing.
Swift SA, Moore DA, Sharek ZS, Gino F (2013) Inflated Applicants: Attribution Errors in Performance Evaluation by Professionals. PLoS ONE 8(7): e69258. (https://doi.org/10.1371/journal.pone.0069258)
World Bank. 2007. World Development Report. Washington, DC: World Bank. |
# Education
## Issues in Education
As schools strive to fill a variety of roles in their students’ lives, many issues and challenges arise. Students walk a minefield of bullying, violence in schools, the results of declining funding, changes due to the COVID-19 pandemic, and other problems that affect their education. When Americans are asked about their opinion of public education on the Gallup poll each year, reviews are mixed at best (Saad 2008). Schools are no longer merely a place for learning and socializing. With the landmark Brown v. Board of Education of Topeka ruling in 1954, schools became a repository of much political and legal action that is at the heart of several issues in education.
### Equal Education
Until the 1954 Brown v. Board of Education ruling, schools had operated under the precedent set by Plessy v. Ferguson in 1896, which allowed racial segregation in schools and private businesses (the case dealt specifically with railroads) and introduced the much maligned phrase “separate but equal” into the U.S. lexicon. The 1954 Brown v. Board decision overruled this, declaring that state laws that had established separate schools for Black and White students were, in fact, unequal and unconstitutional.
While the ruling paved the way toward civil rights, it was also met with contention in many communities. In Arkansas in 1957, the governor mobilized the state National Guard to prevent Black students from entering Little Rock Central High School. President Eisenhower, in response, sent members of the 101st Airborne Division from Kentucky to uphold the students’ right to enter the school. In 1963, almost ten years after the ruling, Governor George Wallace of Alabama used his own body to block two Black students from entering the auditorium at the University of Alabama to enroll in the school. Wallace’s desperate attempt to uphold his policy of “segregation now, segregation tomorrow, segregation forever,” stated during his 1963 inauguration (PBS 2000) became known as the “Stand in the Schoolhouse Door.” He refused to grant entry to the students until a general from the Alabama National Guard arrived on President Kennedy’s order.
Presently, students of all races and ethnicities are permitted into schools, but there remains a troubling gap in the equality of education they receive. The long-term socially embedded effects of racism—and other discrimination and disadvantage—have left a residual mark of inequality in the nation’s education system. Students from wealthy families and those of lower socioeconomic status do not receive the same opportunities.
Today’s public schools, at least in theory, are positioned to help remedy those gaps. Predicated on the notion of universal access, this system is mandated to accept and retain all students regardless of race, religion, social class, and the like. Moreover, public schools are held accountable to equitable per-student spending (Resnick 2004). Private schools, usually only accessible to students from high-income families, and schools in more affluent areas generally enjoy access to greater resources and better opportunities. In fact, some of the key predictors for student performance include socioeconomic status and family background. Children from families of lower socioeconomic status often enter school with learning deficits they struggle to overcome throughout their educational tenure. These patterns, uncovered in the landmark Coleman Report of 1966, are still highly relevant today, as sociologists still generally agree that there is a great divide in the performance of white students from affluent backgrounds and their nonwhite, less affluent, counterparts (Coleman 1966).
The findings in the Coleman Report were so powerful that they brought about two major changes to education in the United States. The federal Head Start program, which is still active and successful today, was developed to give low-income students an opportunity to make up the preschool deficit discussed in Coleman’s findings. The program provides academic-centered preschool to students of low socioeconomic status.
### Transfers and Busing
In the years following Brown v. Board of Education, the Southern states were not alone in their resistance to change. In New York City, schools in lower-income neighborhoods had less experienced teachers, inadequate facilities, and lower spending per student than did schools in higher-income neighborhoods, even though all of the schools were in the same district. In 1958, Activist Mae Mallory, with the support of grassroots advocate Ella Baker and the NAACP, led a group of parents who kept their children out of school, essentially boycotting the district. She and the rest of the group, known as the Harlem Nine, were publicly chastised and pursued by the judicial system. After several decisions and appeals, the culminating legal decision found that the city was effectively segregating schools, and that students in certain neighborhoods were still receiving a “discriminatorily inferior education.” New York City, the nation’s largest school district, enacted an open transfer policy that laid the groundwork for further action (Jeffries 2012).
With the goal of further desegregating education, courts across the United States ordered some school districts to begin a program that became known as “busing.” This program involved bringing students to schools outside their neighborhoods (and therefore schools they would not normally have the opportunity to attend) to bring racial diversity into balance. This practice was met with a great deal of public resistance from people on both sides dissatisfied with White students traveling to inner city schools and minority students being transported to schools in the suburbs.
### No Child Left Behind and Every Student Succeeds
In 2001, the Bush administration passed the No Child Left Behind Act, which requires states to test students in grades three through eight. The results of those tests determine eligibility to receive federal funding. Schools that do not meet the standards set by the Act run the risk of having their funding cut. Sociologists and teachers alike have contended that the impact of the No Child Left Behind Act is far more negative than positive, arguing that a “one size fits all” concept cannot apply to education.
As a result of widespread criticism, many of the national aspects of the act were gradually altered, and in 2015 they were essentially eliminated. That year, Congress passed the Every Student Succeeds Act (ESSA). The law decreases the federal role in education. Annual testing is still required, but the achievement and improvement accountability is shifted to the states, which must submit plans and goals regarding their approaches to the U.S. Department of Education for approval. While this aspect of ESSA was delayed for several years under the Trump administration, the Department of Education announced in April, 2020 that Massachusetts had become the first to have its plans approved. The COVID-19 pandemic delayed many states’ further action in terms of ESSA approval.
### New Views On Standardized Tests
The funding tie-in of the No Child Left Behind Act has led to the social phenomenon commonly called “teaching to the test,” which describes when a curriculum focuses on equipping students to succeed on standardized tests, to the detriment of broader educational goals and concepts of learning. At issue are two approaches to classroom education: the notion that teachers impart knowledge that students are obligated to absorb, versus the concept of student-centered learning that seeks to teach children not facts, but problem solving abilities and learning skills. Both types of learning have been valued in the U.S. school system. The former, to critics of “teaching to the test,” only equips students to regurgitate facts, while the latter, to proponents of the other camp, fosters lifelong learning and transferable work skills.
The Scholastic Aptitude Test (SAT) and the American College Testing (ACT) have for decades served as rites of passage for millions of high school students. Colleges utilize the scores as benchmarks in the admissions process. Since the tests have been important in college admissions, many families place significant emphasis on preparing for them.
However, the disparity in how much money families are able to spend on that preparation results in inequities. SAT/ACT-prep courses and tutors are expensive, and not everyone can afford them. As a result, the inequity found in K-12 education may extend to college.
For years, college admissions programs have been taking these disparities into account, and have based admissions on factors beyond standardized test scores. However, issues with the tests remain. In 2020, a slate of highly selective colleges eliminated their standardized test requirement for admission, and, in 2021 several colleges expanded and extended their “test-optional” approach.
### Students With Disabilities
Since the 1978 implementation of what would become the Individuals with Disabilities Education Act (IDEA), states and local districts have continually increased their investment in the quality of education for students with disabilities. The Act’s reauthorization, coupled with No Child Left Behind, added requirements and guidance for states and school districts. Until that point in time, students with intellectual or other disabilities had been steadily improving their achievement, graduation rates, and success in post-high school endeavors. However, significant disparities existed (and persist today) based on race, ethnicity, and also on geography. Beyond the quality of education for students with disabilities, the disparity was often most noticeable in the classification of those students. States varied on which disabilities received services, and how much support was provided.
Many students with dyslexia, ADHD, and other disorders are either not diagnosed, not taken seriously, or not given as much support as they require in order to succeed. This can extend into adulthood. For example, ADHD was for years considered only a children’s disease, something that people “grew out of.” But the disorder can impact people at any age, something that many educators and even some doctors are not aware of.
No Child Left Behind’s focus on standards and standardized testing extended to students with disabilities as well. A core goal was that students with disabilities would work toward the same standards and take the same tests (with accommodations, if needed) as did students without disabilities. The outcomes were mixed. Test performance for students with disabilities increased, but so did drop outs. There was also evidence that some schools were less welcoming to students with disabilities, as a way to increase average scores (National Council on Disabilities 2004).
In general, programs have improved to the point that students with disabilities are graduating from high school at a national average of about 73 percent. This is lower than the average graduation rate for students in all populations, which is 88 percent, but it is a vast improvement over previous decades (NCES 2020). However, several issues remain. First, students from lower-income and areas and states with lower education budgets still are offered far fewer services; they graduate high school at a much lower rate than the average. Second, because identification remains a major gap, many students with disabilities may be in the “mainstream” population but are not supported as well as they should be. Even when this group gets to college, they may be starting with a lower level of preparation (Samuels 2019).
### School Choice
As we have seen, education is not equal, and people have varied needs. Parents, guardians, and child advocates work to obtain the best schooling for children, which may take them outside the traditional environment.
Public school alternatives to traditional schools include vocational schools, special education schools, magnet schools, charter schools, alternative schools, early college schools, and virtual schools. Private school options may include religious and non-religious options, as well as boarding schools. In some locations, a large number of students engage in these options. For example, in North Carolina, one in five students does not attend a traditional public school (Hui 2019).
Homeschooling refers to children being educated in their own homes, typically by a parent, instead of in a traditional public or private school system. Proponents of this type of education argue that it provides an outstanding opportunity for student-centered learning while circumventing problems that plague today’s education system. Opponents counter that homeschooled children miss out on the opportunity for social development that occurs in standard classroom environments and school settings.
School choice advocates promote the idea that more choice allows parents and students a more effective educational experience that is right for them. They may choose a nontraditional school because it is more aligned with their philosophy, because they’ve been bullied or had other trouble in their neighborhood school, or because they want to prepare for a specific career (American Federation for Children 2017). School choice opponents may argue that while the alternative schools may be more effective for those students who need them and are fortunate enough to get in, the money would be better spent in general public schools.
### Remote and Hybrid Schooling
The COVID-19 pandemic was among the most disruptive events in American education. You likely have your own stories, successes, failures, and preferences based on your experiences as students, parents, and family members. Educators at every level went through stages of intense stress, lack of information, and difficult choices. In many cities and states, families, school districts, governments, and health departments found themselves on different sides of debates. Countless arguments raged over attendance, mental health, instructional quality, safety, testing, academic integrity, and the best ways to move forward as the situation began to improve.
College students and their families went through similar disruptions and debates, compounded by the fact that many students felt that the high costs of particular colleges were not worth it. Overall college enrollment dipped significantly during the pandemic (Koenig 2020).
At the time of this writing, the sociological and educational impact of the pandemic is difficult to assess, though many are studying it. Overall data indicates that most outcomes are negative. Students underperformed, stress and mental health problems increased, and overall plans and pathways were interrupted. Perhaps most damaging was that the pandemic amplified many of the other challenges in education, meaning that under-resourced districts and underserved students were impacted even more severely than others. On the other hand, once instructors and students adapted to the technological and social differences, many began to employ new techniques to ensure more caretaking, connection, differentiated instruction, and innovation. Most agree that education will be changed for years following the pandemic, but it might not all be for the worse.
### Summary
As schools continue to fill many roles in the lives of students, challenges arise. Historical issues include the racial desegregation of schools, marked by the 1954 Brown v. Board of Education of Topeka ruling. In today’s diverse educational landscape, socioeconomic status and diversity remain at the heart of issues in education. Students with disabilities have improved outcomes compared to previous decades, but issues with identifying and serving varied needs remain. Other educational issues that impact society include school choice and standardized testing.
### Section Quiz
### Short Answer
### Further Research
Whether or not students in public schools are entitled to free speech is a subject of much debate. In the public school system, there can be a clash between the need for a safe learning environment and the guarantee to free speech granted to U.S. citizens. You can learn more about this complicated issue on this web page about the First Amendment in schools.
### References
CBS News. 2011. “NYC Charter School's $125,000 Experiment.” CBS, March 10. Retrieved December 14, 2011 (http://www.cbsnews.com/stories/2011/03/10/60minutes/main20041733.shtml).
Chapman, Ben, and Rachel Monahan. 2012. "Talking Pineapple Question on State Exam Stumps...Everyone!" Retrieved December 12, 2014. (http://www.nydailynews.com/new-york/talking-pineapple-question-state-exam-stumps-article-1.1064657).
Coleman, James S. 1966. Equality of Educational Opportunity Study. Washington, DC: United States Department of Health, Education, and Welfare.
The Common Core State Standards Initiative. 2014. "About the Standards." Retrieved December 12, 2014. (http://www.corestandards.org/about-the-standards/).
CREDO, Stanford University. "Multiple Choice: Charter School Performance in 16 States," published in 2009. Accessed on December 31, 2014 (http://credo.stanford.edu/reports/MULTIPLE_CHOICE_CREDO.pdf.
Holt, Emily W., Daniel J. McGrath, and Marily M. Seastrom. 2006. “Qualifications of Public Secondary School History Teachers, 1999-2001.” Washington, DC: U.S. Department of Education, National Center for Education Statistics.
Hui, Keung. 2019. “1 in 5 NC Students Don’t Attend Traditional Public Schools.” The News and Observer. July 18 2019. (https://www.newsobserver.com/news/politics-government/article232761337.html)
Jaschik, Scott. 2021. “From Year 1 To Year 2.” Inside Higher Ed. (https://www.insidehighered.com/admissions/article/2021/02/01/colleges-went-test-optional-one-year-are-now-extending-time)
Jeffries, Hasan Kwame and Jones, Patrick D. 2012 “Desegregating New York: The Case of the 'Harlem Nine'”. OAH Magazine of History, Volume 26, Issue 1, January 2012, Pages 51–53, (https://doi.org/10.1093/oahmag/oar061)
Koenig, Rebecca. 2020. “Colleges Lost Nearly Half a Million Enrollments This Fall.” EdSurge. December 2020. (https://www.edsurge.com/news/2020-12-17-colleges-lost-nearly-half-a-million-student-enrollments-this-fall)
Lewin, Tamar. 2011. “College Graduates Debt Burden Grew, Yet Again, in 2010.” The New York Times, November 2. Retrieved January 17, 2012 (http://www.nytimes.com/2011/11/03/education/average-student-loan-debt-grew-by-5-percent-in-2010.html).
Morse et al. v. Frederick, 439 F. 3d 1114 (2007).
National Center for Education Statistics. 2008. “1.5 Million Homeschooled Students in the United States in 2007.” Retrieved January 17, 2012 (http://nces.ed.gov/pubs2009/2009030.pdf).
National Council on Disability. 2004. “Improving Educational Outcomes for Students with Disabilities.” (https://files.eric.ed.gov/fulltext/ED485691.pdf)
NCES. 2020. “The Condition of Education: Students With Disabilities.” National Center for Education Statistics. (https://nces.ed.gov/programs/coe/indicator_cgg.asp)
PBS. 2000. Wallace Quotes. Retrieved December 15, 2011 (http://www.pbs.org/wgbh/amex/wallace/sfeature/quotes.html).
Resnick, Michael A. 2004. “Public Education—An American Imperative: Why Public Schools Are Vital to the Well-Being of Our Nation.” . Alexandria, VA: National School Boards Association.
Saad, Lydia. 2008. “U.S. Education System Garners Split Reviews.” Gallup. Retrieved January 17, 2012 (http://www.gallup.com/poll/109945/us-education-system-garners-split-reviews.aspx).
Samuels, Christina A. 2019. “Special Education Is Broken.” EdWeek, January 2019. (https://www.edweek.org/teaching-learning/special-education-is-broken/2019/01) |
# Government and Politics
## Introduction
On November 6, 2018, Florida residents voted overwhelmingly to restore voting rights to people convicted of most felonies after they had completed their sentences. Rather than undergoing the complex process of passing a law through legislative representatives, the people voted directly on the matter as part of their ballot, a process typically referred to as a referendum. The two-thirds majority in favor of the referendum seemed to make the voters' intention clear, but their intentions would not be carried as directly as they thought.
Many believe that voting is a privilege to be granted to "upstanding" citizens. The 14th Amendment gives government the right to restrict voting for those who have "participated in rebellion or other crime." As of 2021, 48 states had some type of restrictions for people with felony convictions, though the vast majority of those permit people to vote upon completion of their sentence (ACLU 2021). At the time of the 2018 referendum, Florida had almost 1.7 million people unable to vote due to felony convictions, which was roughly ten percent of its total population; to put it another way, Florida had more disenfranchised people than any other state (Lewis 2018). Many statewide Florida elections are decided by only a few percentage points. For example, the last three elections for governor were decided by less than two percent of the vote.
Disenfranchisement laws affect people of certain races, ethnicities, and socioeconomic status more significantly than other groups. For example, in Florida, 23 percent of Black people were unable to vote because of felony convictions (Brennan Center 2020).
Despite the overwhelming majority of citizens who supported the change, the Florida governor and legislature effectively blocked the referendum's implementation. In early 2019, less than two weeks after the resolution went into effect, the government passed a law indicating that voting would only be allowed for convicted felons who served their sentences and had also paid all fines and penalties owed to the state. The effect was significant: Fines associated with sentences can be quite large, and people with felony convictions have major issues with employment. The law severely diminished the referendum's effect. By the time of the 2020 Presidential election, about 700,000 people with felony convictions, who had served their sentences, still could not vote.
Many in Florida felt that their referendum clearly indicated the people's choice, and their power had been taken. On the other hand, the legislators indicated that they were obtaining money owed to the state, and that the brief, 140-word referendum didn't specify the method of implementation. Florida is going through a conflict that has faced the nation from its earliest days: Who has the right to make decisions? Who has the power?
### References
ACLU. 2020. "State Disenfranchisement Laws (Map)." American Civil Liberties Union. (https://www.aclu.org/issues/voting-rights/voter-restoration/felony-disenfranchisement-laws-map)
Brennan Center for Justice. 2019. "Voter Restoration Efforts in Florida." (https://www.brennancenter.org/our-work/research-reports/voting-rights-restoration-efforts-florida)
Lewis, Sarah. A. 2018. "The Disenfranchisement of Ex-Felons in Florida: A Brief History." University of Florida. (https://scholarship.law.ufl.edu/cgi/viewcontent.cgi?article=1846&context=facultypub) |
# Government and Politics
## Power and Authority
The world has almost 200 countries. Many of those countries have states or provinces with their own governments. In some countries such as the United States and Canada, Native Americans and First Nations have their own systems of government in some relationship with the federal government. Just considering those thousands of different entities, it's easy to see what differentiates governments. What about what they have in common? Do all of them serve the people? Protect the people? Increase prosperity?
The answer to those questions might be a matter of opinion, perspective, and circumstance. However, one reality seems clear: Something all governments have in common is that they exert control over the people they govern. The nature of that control—what we will define as power and authority—is an important feature of society.
Sociologists have a distinctive approach to studying governmental power and authority that differs from the perspective of political scientists. For the most part, political scientists focus on studying how power is distributed in different types of political systems. They would observe, for example, that the United States’ political system is divided into three distinct branches (legislative, executive, and judicial), and they would explore how public opinion affects political parties, elections, and the political process in general. Sociologists, however, tend to be more interested in the influences of governmental power on society and in how social conflicts arise from the distribution of power. Sociologists also examine how the use of power affects local, state, national, and global agendas, which in turn affect people differently based on status, class, and socioeconomic standing.
### What Is Power?
For centuries, philosophers, politicians, and social scientists have explored and commented on the nature of power. Pittacus (c. 640–568 B.C.E.) opined, “The measure of a man is what he does with power,” and Lord Acton perhaps more famously asserted, “Power tends to corrupt; absolute power corrupts absolutely” (1887). Indeed, the concept of power can have decidedly negative connotations, and the term itself is difficult to define.
Many scholars adopt the definition developed by German sociologist Max Weber, who said that
power is the ability to exercise one’s will over others (Weber 1922). Power affects more than personal relationships; it shapes larger dynamics like social groups, professional organizations, and governments. Similarly, a government’s power is not necessarily limited to control of its own citizens. A dominant nation, for instance, will often use its clout to influence or support other governments or to seize control of other nation states. Efforts by the U.S. government to wield power in other countries have included joining with other nations to form the Allied forces during World War II, entering Iraq in 2002 to topple Saddam Hussein’s regime, and imposing sanctions on the government of North Korea in the hopes of constraining its development of nuclear weapons.
Endeavors to gain power and influence do not necessarily lead to violence, exploitation, or abuse. Leaders such as Martin Luther King Jr. and Mohandas Gandhi, for example, commanded powerful movements that effected positive change without military force. Both men organized nonviolent protests to combat corruption and injustice and succeeded in inspiring major reform. They relied on a variety of nonviolent protest strategies, such as rallies, sit-ins, marches, petitions, and boycotts.
Modern technology has made such forms of nonviolent reform easier to implement. Often, protesters can use cell phones and the Internet to disseminate information and plans to masses of protesters in a rapid and efficient manner. Some governments like Myanmar, China, and Russia tamp down communication and protest through platform bans or Internet blocks (see the Media and Technology chapter for more information). But in the Arab Spring uprisings of 2010-11, for example, Twitter feeds and other social media helped protesters coordinate their movements, share ideas, and bolster morale, as well as gain global support for their causes. Social media was also important in getting accurate accounts of the demonstrations out to the world, in contrast to many earlier situations in which government control of the media censored news reports. Notice that in these examples, the users of power were the citizens rather than the governments. They found they had power because they were able to exercise their will over their own leaders. Thus, government power does not necessarily equate to absolute power.
### Types of Authority
The protesters in Tunisia and the civil rights protesters of Martin Luther King, Jr.’s day had influence apart from their position in a government. Their influence came, in part, from their ability to advocate for what many people held as important values. Government leaders might have this kind of influence as well, but they also have the advantage of wielding power associated with their position in the government. As this example indicates, there is more than one type of authority in a community.
Authority refers to accepted power—that is, power that people agree to follow. People listen to authority figures because they feel that these individuals are worthy of respect. Generally speaking, people perceive the objectives and demands of an authority figure as reasonable and beneficial, or true.
Not all authority figures are police officers, elected officials or government authorities. Besides formal offices, authority can arise from tradition and personal qualities. Economist and sociologist Max Weber realized this when he examined individual action as it relates to authority, as well as large-scale structures of authority and how they relate to a society’s economy. Based on this work, Weber developed a classification system for authority. His three types of authority are traditional authority, charismatic authority and legal-rational authority (Weber 1922).
### Traditional Authority
According to Weber, the power of traditional authority is accepted because that has traditionally been the case; its legitimacy exists because it has been accepted for a long time. Britain’s Queen Elizabeth, for instance, occupies a position that she inherited based on the traditional rules of succession for the monarchy. People adhere to traditional authority because they are invested in the past and feel obligated to perpetuate it. In this type of authority, a ruler typically has no real force to carry out his will or maintain his position but depends primarily on a group’s respect.
A more modern form of traditional authority is patrimonialism, which is traditional domination facilitated by an administration and military that are purely personal instruments of the master (Eisenberg 1998). In this form of authority, all officials are personal favorites appointed by the ruler. These officials have no rights, and their privileges can be increased or withdrawn based on the caprices of the leader. The political organization of ancient Egypt typified such a system: when the royal household decreed that a pyramid be built, every Egyptian was forced to work toward its construction.
Traditional authority can be intertwined with race, class, and gender. In most societies, for instance, men are more likely to be privileged than women and thus are more likely to hold roles of authority. Similarly, members of dominant racial groups or upper-class families also win respect more readily. In the United States, the Kennedy family, which has produced many prominent politicians, exemplifies this model.
### Charismatic Authority
Followers accept the power of charismatic authority because they are drawn to the leader’s personal qualities. The appeal of a charismatic leader can be extraordinary, and can inspire followers to make unusual sacrifices or to persevere in the midst of great hardship and persecution. Charismatic leaders usually emerge in times of crisis and offer innovative or radical solutions. They may even offer a vision of a new world order. Hitler’s rise to power in the postwar economic depression of Germany is an example.
Charismatic leaders tend to hold power for short durations, and according to Weber, they are just as likely to be tyrannical as they are heroic. Diverse male leaders such as Hitler, Napoleon, Jesus Christ, César Chávez, Malcolm X, and Winston Churchill are all considered charismatic leaders. Because so few women have held dynamic positions of leadership throughout history, the list of charismatic female leaders is comparatively short. Many historians consider figures such as Joan of Arc, Margaret Thatcher, and Mother Teresa to be charismatic leaders.
### Rational-Legal Authority
According to Weber, power made legitimate by laws, written rules, and regulations is termed rational-legal authority. In this type of authority, power is vested in a particular rationale, system, or ideology and not necessarily in the person who implements the specifics of that doctrine. A nation that follows a constitution applies this type of authority. On a smaller scale, you might encounter rational-legal authority in the workplace via the standards set forth in the employee handbook, which provides a different type of authority than that of your boss.
Of course, ideals are seldom replicated in the real world. Few governments or leaders can be neatly categorized. Some leaders, like Mohandas Gandhi for instance, can be considered charismatic and legal-rational authority figures. Similarly, a leader or government can start out exemplifying one type of authority and gradually evolve or change into another type.
### Summary
Sociologists examine government and politics in terms of their impact on individuals and larger social systems. Power is an entity or individual’s ability to control or direct others, while authority is influence that is predicated on perceived legitimacy. Max Weber studied power and authority, differentiating between the two concepts and formulating a system for classifying types of authority.
### Section Quiz
### Short Answer
### Further Research
Want to learn more about sociologists at work in the real world? Read this overview of sociological perspectives on disenfranchisement of people convicted of felonies.
### References
Acton, Lord. 2010 [1887]. Essays on Freedom and Power. Auburn, AL: Ludwig von Mises Institute.
Catrer, Chelsea, and Fantz, Ashley. 2014. “ISIS Video Shows Beheading of American Journalist Steven Sotloft.” CNN, September 9. Retrieved October 5, 2014 (http://www.cnn.com/2014/09/02/world/meast/isis-american-journalist-sotloff/)
Eisenberg, Andrew. 1998. “Weberian Patrimonialism and Imperial Chinese History.” Theory and Society 27(1):83–102.
Hosenball, Mark, and Westall, Slyvia. 2014. “Islamic State Video Shows Second British Hostage Beheaded.” Reuters, October 4. Retrieved October 5, 2014 (http://www.reuters.com/article/2014/10/04/us-mideast-crisis-henning-behading-idUSKCN0HS1XX20141004)
NPR. 2014. “Debate: Does U.S. Military Intervention in the Middle East help or Hurt?” October 7. Retrieved October 7, 2014 (http://www.npr.org/2014/10/07/353294026/debate-does-u-s-military-intervention-in-the-middle-east-help-or-hurt)
Mullen, Jethro. 2014. “U.S.-led airstrikes on ISIS in Syria: What you need to know.” CNN, September 24. Retrieved October 5, 2014 (http://www.cnn.com/2014/09/23/world/meast/syria-isis-airstrikes-explainer/)
Mullen, Jethro (2014). “U.S.-led airstrikes on ISIS in Syria: Who's in, who's not”. CNN, October 2, 2014. Retrieved October 5, 2014 (http://www.cnn.com/2014/09/23/world/meast/syria-airstrikes-countries-involved/)
Pollock, John. 2011. “How Egyptian and Tunisian Youth Hijacked the Arab Spring.” Technology Review, September/October. Retrieved January 23, 2012 (http://www.technologyreview.com/web/38379/).
Weber, Max. 1978 [1922]. Economy and Society: An Outline of Interpretive Sociology. Berkeley: University of California Press.
Weber, Max. 1947 [1922]. The Theory of Social and Economic Organization. Translated by A. M. Henderson and T. Parsons. New York: Oxford University Press. |
# Government and Politics
## Forms of Government
Most people generally agree that anarchy, or the absence of organized government, does not facilitate a desirable living environment for society, but it is much harder for individuals to agree upon the particulars of how a population should be governed. Throughout history, various forms of government have evolved to suit the needs of changing populations and mindsets, each with pros and cons. Today, members of Western society hold that democracy is the most just and stable form of government, although former British Prime Minister Winston Churchill once declared to the House of Commons, “Indeed it has been said that democracy is the worst form of government except for all those other forms that have been tried from time to time” (Shapiro 2006).
### Monarchy
Even though people in the United States tend to be most aware of Great Britain’s royals, many other nations also recognize kings, queens, princes, princesses, and other figures with official royal titles. The power held by these positions varies from one country to another. Strictly speaking, a monarchy is a government in which a single person (a monarch) rules until he or she dies or abdicates the throne. Usually, a monarch claims the rights to the title by way of hereditary succession or as a result of some sort of divine appointment or calling. As mentioned above, the monarchies of most modern nations are ceremonial remnants of tradition, and individuals who hold titles in such sovereignties are often aristocratic figureheads.
A few nations today, however, are run by governments wherein a monarch has absolute or unmitigated power. Such nations are called absolute monarchies. Although governments and regimes are constantly changing across the global landscape, it is generally safe to say that most modern absolute monarchies are concentrated in the Middle East and Africa. The small, oil-rich nation of Oman, for instance, is an example of an absolute monarchy. In this nation, Sultan Qaboos bin Said ruled from the 1970s until his death in 2020, when his cousin, Haitham bin Tariq, became Sultan. The Sultan creates all laws, appoints all judges, and has no formal check on their power. Living conditions and opportunities for Oman’s citizens have improved to the point that the UN ranked the nation as the most improved in the world in the past (UNDP 2010), but many citizens who live under the reign of an absolute ruler must contend with oppressive or unfair policies that are installed based on the unchecked whims or political agendas of that leader.
In today’s global political climate, monarchies far more often take the form of constitutional monarchies, governments of nations that recognize monarchs but require these figures to abide by the laws of a greater constitution. Many countries that are now constitutional monarchies evolved from governments that were once considered absolute monarchies. In most cases, constitutional monarchies, such as Great Britain and Canada, feature elected prime ministers whose leadership role is far more involved and significant than that of its titled monarchs. In spite of their limited authority, monarchs endure in such governments because people enjoy their ceremonial significance and the pageantry of their rites.
### Oligarchy
The power in an oligarchy is held by a small, elite group. Unlike in a monarchy, members of an oligarchy do not necessarily achieve their statuses based on ties to noble ancestry. Rather, they may ascend to positions of power because of military might, economic power, or similar circumstances.
The concept of oligarchy is somewhat elusive; rarely does a society openly define itself as an oligarchy. Generally, the word carries negative connotations and conjures notions of a corrupt group whose members make unfair policy decisions in order to maintain their privileged positions. Many modern nations that claim to be democracies are really oligarchies. In fact, some prominent journalists, such as Paul Krugman, who won a Nobele laureate prize in economics, have labeled the United States an oligarchy, pointing to the influence of large corporations and Wall Street executives on U.S. policy (Krugman 2011). Other political analysts assert that all democracies are really just “elected oligarchies,” or systems in which citizens must vote for an individual who is part of a pool of candidates who come from the society’s elite ruling class (Winters 2011).
Oligarchies have existed throughout history, and today many consider Russia an example of oligarchic political structure. After the fall of communism, groups of business owners captured control of this nation’s natural resources and have used the opportunity to expand their wealth and political influence. Once an oligarchic power structure has been established, it can be very difficult for middle- and lower-class citizens to advance their socioeconomic status.
### Dictatorship
Power in a dictatorship is held by a single person (or a very small group) that wields complete and absolute authority over a government and population. Like some absolute monarchies, dictatorships may be corrupt and seek to limit or even eradicate the liberties of the general population. Dictators use a variety of means to perpetuate their authority. Economic and military might, as well as intimidation and brutality are often foremost among their tactics; individuals are less likely to rebel when they are starving and fearful. Many dictators start out as military leaders and are conditioned to the use of violence against opposition.
Some dictators also possess the personal appeal that Max Weber identified with a charismatic leader. Subjects of such a dictator may believe that the leader has special ability or authority and may be willing to submit to his or her authority. The late Kim Jong-Il, North Korean dictator, and his successor, Kim Jong-Un, exemplify this type of charismatic dictatorship.
Some dictatorships do not align themselves with any particular belief system or ideology; the goal of this type of regime is usually limited to preserving the authority of the dictator. A totalitarian dictatorship is even more oppressive and attempts to control all aspects of its subjects’ lives; including occupation, religious beliefs, and number of children permitted in each family. Citizens may be forced to publicly demonstrate their faith in the regime by participating in marches and demonstrations.
Some “benevolent” dictators, such as Napoleon and Anwar Sadat, are credited with advancing their people’s standard of living or exercising a moderate amount of evenhandedness. Others grossly abuse their power. Joseph Stalin, Adolf Hitler, Saddam Hussein, Cambodia’s Pol Pot, and Zimbabwe’s Robert Mugabe, for instance, are heads of state who earned a reputation for leading through fear and intimidation.
### Democracy
A democracy is a form of government that strives to provide all citizens with an equal voice, or vote, in determining state policy, regardless of their level of socioeconomic status. Another important fundamental of the democratic state is the establishment and governance of a just and comprehensive constitution that delineates the roles and responsibilities of leaders and citizens alike.
Democracies, in general, ensure certain basic rights for their citizens. First and foremost, citizens are free to organize political parties and hold elections. Leaders, once elected, must abide by the terms of the given nation’s constitution and are limited in the powers they can exercise, as well as in the length of the duration of their terms. Most democratic societies also champion freedom of individual speech, the press, and assembly, and they prohibit unlawful imprisonment. Of course, even in a democratic society, the government constrains citizens' total freedom to act however they wish. A democratically elected government does this by passing laws and writing regulations that, at least ideally, reflect the will of the majority of its people.
Although the United States champions the democratic ideology, it is not a “pure” democracy. In a purely democratic society, all citizens would vote on all proposed legislation, and this is not how laws are passed in the United States. There is a practical reason for this: a pure democracy would be hard to implement. Thus, the United States is a constitution-based federal republic in which citizens elect representatives to make policy decisions on their behalf. The term representative democracy, which is virtually synonymous with republic, can also be used to describe a government in which citizens elect representatives to promote policies that favor their interests. In the United States, representatives are elected at local and state levels, and the votes of the Electoral College determine who will hold the office of president. Each of the three branches of the U.S. government—the executive, judicial, and legislative—is held in check by the other branches.
### Summary
Nations are governed by different political systems, including monarchies, oligarchies, dictatorships, and democracies. Generally speaking, citizens of nations wherein power is concentrated in one leader or a small group are more likely to suffer violations of civil liberties and experience economic inequality. Many nations that are today organized around democratic ideals started out as monarchies or dictatorships but have evolved into more egalitarian systems. Democratic ideals, although hard to implement and achieve, promote basic human rights and justice for all citizens.
### Section Quiz
### Short Answer
### Further Research
The Tea Party is among the highest-profile grassroots organizations active in U.S. politics today. What is its official platform? Examine the Tea Party website to find out more information.
### References
Balz, Dan. 2014. "For GOP, demographic opportunities, challenges await". The Washington Post. Retrieved December 11, 2014. (http://www.washingtonpost.com/politics/for-gop-demographic-opportunities-challenges-await/2014/11/29/407118ae-7720-11e4-9d9b-86d397daad27_story.html)
Dunbar, John (2012). “The Citizen’s United Decision and Why It Matters” The Center for Public Integrity. October 18, 2012. Retrieved October 2, 2014 (http://www.publicintegrity.org/2012/10/18/11527/citizens-united-decision-and-why-it-matters)
Krugman, Paul. 2011. “Oligarchy, American Style.” New York Times, November 3. Retrieved February 14, 2012 (http://www.nytimes.com/2011/11/04/opinion/oligarchy-american-style.html).
O'Dell, Rob and Penzenstadler, Nick. 2019. "You elected them to write new laws. They're letting corporations do it instead." USA Today. (https://www.usatoday.com/in-depth/news/investigations/2019/04/03/abortion-gun-laws-stand-your-ground-model-bills-conservatives-liberal-corporate-influence-lobbyists/3162173002/)
PBS Online. “Gilded Age.” 1999. The American Experience. Retrieved February 14, 2012 (http://www.pbs.org/wgbh/amex/carnegie/gildedage.html).
Represent.US. 2014. "The U.S. Is an Oligarchy? The Research Explained." (https://bulletin.represent.us/u-s-oligarchy-explain-research/)
Schulz, Thomas. 2011. “The Second Gilded Age: Has America Become an Oligarchy?” Spiegel Online International, October 28. Retrieved February 14, 2012 (http://www.spiegel.de/international/spiegel/0,1518,793896,00.html).
UNDP. 2010. "Five Arab Countries Among Top Leaders in Long-Term Gains." United Nations. (http://hdr.undp.org/en/mediacentre/news/announcements/title,21573,en.html)
Winters, Jeffrey. 2011. “Oligarchy and Democracy.” American Interest, November/December. Retrieved February 17, 2012 (http://www.the-american-interest.com/article.cfm?piece=1048).
Zucman, Gabriel. 2019. "Global Wealth Inequality." Annual Review of Economics. May 2019. (https://gabriel-zucman.eu/files/Zucman2019.pdf) |
# Government and Politics
## Politics in the United States
When describing a nation’s politics, we should define the term. We may associate the term with freedom, power, corruption, or rhetoric. Political science looks at politics as the interaction between citizens and their government. Sociology studies politics as a means to understand the underlying social norms and values of a group. A society’s political structure and practices provide insight into the distribution of power and wealth, as well as larger philosophical and cultural beliefs. A cursory sociological analysis of U.S. politics might suggest that Americans' desire to promote equality and democracy on a theoretical level is at odds with the nation’s real-life capitalist orientation.
Lincoln's famous phrase “of the people, by the people, for the people” is at the heart of the U.S. system and sums up its most essential aspect: that citizens willingly and freely elect representatives they believe will look out for their best interests. Although many Americans take free elections for granted, it is a vital foundation of any democracy. When the U.S. government was formed, however, African Americans and women were denied the right to vote. Each of these groups struggled to secure the same suffrage rights as their White male counterparts, yet this history fails to inspire some Americans to show up at the polls and cast their ballots. Problems with the democratic process, including limited voter turnout, require us to more closely examine complex social issues that influence political participation.
### Voter Participation
Voter participation is essential to the success of the U.S. political system. Although many Americans are quick to complain about laws and political leadership, in any given election year roughly half the population does not vote (United States Elections Project 2010). Some years have seen even lower turnouts; in 2010, for instance, only 37.8 percent of the population participated in the electoral process (United States Elections Project 2011). Poor turnout can skew election results, particularly if one age or socioeconomic group is more diligent in its efforts to make it to the polls.
Certain voting advocacy groups work to improve turnout. Vote.org focuses on absentee voting, mail-in voting, and similar practices. Native Vote is an organization that strives to inform Native Americans about upcoming elections and encourages their participation. National Council of La Raza and Voto Latino strive to improve voter turnout among the Latino population. William Frey, author of Diversity Explosion, points out that the number of Hispanic people, Asian people, and multiracial populations is expected to double in the next forty years (Balz 2014).
### Race, Gender, and Class Issues
Although recent records have shown more minorities voting now than ever before, this trend is still fairly new. Historically, African Americans and other minorities have been underrepresented at the polls. Black men were not allowed to vote at all until after the Civil War, and Black women gained the right to vote along with other women only with the ratification of the Nineteenth Amendment in 1920. For years, African Americans who were brave enough to vote were discouraged by discriminatory legislation, passed in many southern states, which required poll taxes and literacy tests of prospective voters. Literacy tests were not outlawed until 1965, when President Lyndon Johnson signed the Voting Rights Act.
The 1960s saw other important reforms in U.S. voting. Shortly before the Voting Rights Act was passed, the 1964 U.S. Supreme Court case Reynolds v. Sims changed the nature of elections. This landmark decision reaffirmed the notion of “one person, one vote,” a concept holding that all people’s votes should be counted equally. Before this decision, unequal distributions of population enabled small groups of people in sparsely populated rural areas to have as much voting power as the denser populations of urban areas. After Reynolds v. Sims, districts were redrawn so that they would include equal numbers of voters.
Unfortunately, in June 2013 the Supreme Court repealed several important aspects of the 1965 Voting Rights Act, ruling that southern states no longer need the stricter scrutiny that was once required to prohibit racial discrimination in voting practices in the South. Following this decision, several states moved forward with voter identification laws that had previously been banned by federal courts. Officials in Texas, Mississippi, and Alabama claim that new identification (ID) laws are needed to reduce voter fraud. Opponents point to the Department of Justice statistics indicating that only twenty-six voters, of 197 million voters in federal elections, were found guilty of voter fraud between 2002 and 2005. "Contemporary voter identification laws are trying to solve a problem that hasn’t existed in over a century” (Campbell, 2012). Opponents further note that new voter ID laws disproportionately affect minorities and the poor, potentially prohibiting them from exercising their right to vote.
Evidence suggests that legal protection of voting rights does not directly translate into equal voting power. Relative to their presence in the U.S. population, women and racial/ethnic minorities are underrepresented in the U.S. Congress. White men still dominate both houses. And until the inauguration of Barack Obama in 2009, all U.S. presidents had been White men.
Like race and ethnicity, social class also has influenced voting practices. Voting rates among lower-educated, lower-paid workers are lower than for people with higher socioeconomic status that fosters a system in which people with more power and access to resources have the means to perpetuate their power. Several explanations have been offered to account for this difference (Raymond 2010). Workers in low-paying service jobs might find it harder to get to the polls because they lack flexibility in their work hours and quality daycare to look after children while they vote. Because a larger share of racial and ethnic minorities is employed in such positions, social class may be linked to race and ethnicity influencing voting rates. New requirements for specific types of voter identification in some states are likely to compound these issues, because it may take additional time away from work, as well as additional child care or transportation, for voters to get the needed IDs. The impact on minorities and the impoverished may cause a further decrease in voter participation. Attitudes play a role as well. Some people of low socioeconomic status or minority race/ethnicity doubt their vote will count or voice will be heard because they have seen no evidence of their political power in their communities. Many believe that what they already have is all they can achieve.
As suggested earlier, money can carry a lot of influence in U.S. democracy. But there are other means to make one’s voice heard. Free speech can be influential, and people can participate in the democratic system through volunteering with political advocacy groups, writing to elected officials, sharing views in a public forum such as a blog or letter to the editor, forming or joining cause-related political organizations and interest groups, participating in public demonstrations, and even running for a local office.
### The Judicial System
The third branch of the U.S. government is the judicial system, which consists of local, state, and federal courts. The U.S. Supreme Court is the highest court in the United States, and it has the final say on decisions about the constitutionality of laws that citizens challenge. As noted earlier, some rulings have a direct impact on the political system, such as recent decisions about voter identification and campaign financing. Other Supreme Court decisions affect different aspects of society, and they are useful for sociological study because they help us understand cultural changes. One example is a recent and highly controversial case that dealt with the religious opposition of Hobby Lobby Stores Inc. to providing employees with specific kinds of insurance mandated by the Patient Protection and Affordable Care Act. Another example is same-sex marriage cases, which were expected to be heard by the Court; however, the Court denied review of these cases in the fall of 2014. For now, the rulings of federal district courts stand, and states can continue to have differing outcomes on same-sex marriage for their citizens.
### Summary
The success and validity of U.S. democracy hinges on free, fair elections that are characterized by the support and participation of diverse citizens. In spite of their importance, elections have low participation. In the past, the voice of minority groups was nearly imperceptible in elections, but recent trends have shown increased voter turnout across many minority races and ethnicities. In the past, the creation and sustenance of a fair voting process has necessitated government intervention, particularly on the legislative level. The Reynolds v. Sims case, with its landmark “one person, one vote” ruling, is an excellent example of such action.
### Section Quiz
### Short Answer
### Further Research
The 1965 Voting Rights Act was preceded by Lyndon Johnson’s signing of the 1964 Civil Rights Act. Both articles were instrumental in establishing equal rights for African Americans. Check out Cornell University’s website on this civil rights to learn more about this civil rights legislation.
### References
Bingham, Amy. 2012. “Voter Fraud: Non-Existent Problem or Election-Threatening Epidemic?” ABC News, September 12. Retrieved October 2, 2014 (http://abcnews.go.com/Politics/OTUS/voter-fraud-real-rare/story?id=17213376)
Cooper, Michael. 2013. “After Ruling, States Rush to Enact Voting Laws” The New York Times, July 5. Retrieved October 1, 2014 (http://www.nytimes.com/2013/07/06/us/politics/after-Supreme-Court-ruling-states-rush-to-enact-voting-laws.html?pagewanted=all&_r=0)
Dinan, Stephen. 2013. “Supreme Court Says Voting Rights Act of 1965 is No Longer Relevant” The Washington Times, June 25. Retrieved October 1, 2014 (http://www.washingtontimes.com/news/2013/jun/25/court-past-voting-discrimination-no-longer-held/?page=all)
IT Chicago-Kent School of Law. 2014. U.S. Supreme Court Media OYEZ. Retrieved October 7, 2014 (http://www.oyez.org/)
Lopez, Mark Hugo and Paul Taylor. 2009. “Dissecting the 2008 Electorate: the Most Diverse in U.S. History.” Pew Research Center. April 30. Retrieved April 24, 2012 (http://pewresearch.org/assets/pdf/dissecting-2008-electorate.pdf).
Raymond, Jose. 2010. “Why Poor People Don’t Vote.” Change.org, June 6. Retrieved February 17, 2012.
United States Elections Project. 2010. “2008 General Election Turnout Rates.” October 6. Retrieved February 14, 2012 (http://elections.gmu.edu/Turnout_2008G.html).
United States Elections Project. 2011. “2010 General Election Turnout Rates.” December 12. Retrieved February 14, 2012 (http://elections.gmu.edu/Turnout_2010G.html). |
# Government and Politics
## Theoretical Perspectives on Government and Power
Sociologists rely on organizational frameworks or paradigms to make sense of their study of sociology; already there are many widely recognized schemas for evaluating sociological data and observations. Each paradigm looks at the study of sociology through a unique lens. The sociological examination of government and power can thus be evaluated using a variety of perspectives that help the evaluator gain a broader perspective. Functionalism, conflict theory, and symbolic interactionism are a few of the more widely recognized philosophical stances in practice today.
### Functionalism
According to functionalism, the government has four main purposes: planning and directing society, meeting social needs, maintaining law and order, and managing international relations. According to functionalism, all aspects of society serve a purpose.
Functionalists view government and politics as a way to enforce norms and regulate conflict. Functionalists see active social change, such as the sit-in on Wall Street, as undesirable because it forces change and, as a result, undesirable things that might have to be compensated for. Functionalists seek consensus and order in society. Dysfunction creates social problems that lead to social change. For instance, functionalists would see monetary political contributions as a way of keeping people connected to the democratic process. This would be in opposition to a conflict theorist who would see this financial contribution as a way for the rich to perpetuate their own wealth.
### Conflict Theory
Conflict theory focuses on the social inequalities and power difference within a group, analyzing society through this lens. Philosopher and social scientist Karl Marx was a seminal force in developing the conflict theory perspective; he viewed social structure, rather than individual personality characteristics, as the cause of many social problems, such as poverty and crime. Marx believed that conflict between groups struggling to either attain wealth and power or keep the wealth and power they had was inevitable in a capitalist society, and conflict was the only way for the underprivileged to eventually gain some measure of equality.
C. Wright Mills (1956) elaborated on some of Marx’s concepts, coining the phrase power elite to describe what he saw as the small group of powerful people who control much of a society. Mills believed the power elite use government to develop social policies that allow them to keep their wealth. Contemporary theorist G. William Domhoff (2011) elaborates on ways in which the power elite may be seen as a subculture whose members follow similar social patterns such as joining elite clubs, attending select schools, and vacationing at a handful of exclusive destinations.
### Conflict Theory in Action
Even before there were modern nation-states, political conflicts arose among competing societies or factions of people. Vikings attacked continental European tribes in search of loot, and, later, European explorers landed on foreign shores to claim the resources of indigenous groups. Conflicts also arose among competing groups within individual sovereignties, as evidenced by the bloody French Revolution. Nearly all conflicts in the past and present, however, are spurred by basic desires: the drive to protect or gain territory and wealth, and the need to preserve liberty and autonomy.
According to sociologist and philosopher Karl Marx, such conflicts are necessary, although ugly, steps toward a more egalitarian society. Marx saw a historical pattern in which revolutionaries toppled elite power structures, after which wealth and authority became more evenly dispersed among the population, and the overall social order advanced. In this pattern of change through conflict, people tend to gain greater personal freedom and economic stability (1848).
Modern-day conflicts are still driven by the desire to gain or protect power and wealth, whether in the form of land and resources or in the form of liberty and autonomy. Internally, groups within the U.S. struggle within the system, by trying to achieve the outcomes they prefer. Political differences over budget issues, for example, led to the recent shutdown of the federal government, and alternative political groups, such as the Tea Party, are gaining a significant following.
The Arab Spring exemplifies oppressed groups acting collectively to change their governmental systems, seeking both greater liberty and greater economic equity. Some nations, such as Tunisia, have successfully transitioned to governmental change; others, like Egypt, have not yet reached consensus on a new government.
Unfortunately, the change process in some countries reached the point of active combat between the established government and the portion of the population seeking change, often called revolutionaries or rebels. Libya and Syria are two such countries; the multifaceted nature of the conflict, with several groups competing for their own desired ends, makes creation of a peaceful resolution more challenging.
Popular uprisings of citizens seeking governmental change have occurred this year in Bosnia, Brazil, Greece, Iran, Jordan, Portugal, Spain, Turkey, Ukraine, and most recently in Hong Kong. Although much smaller in size and scope, demonstrations occurred in the aftermath of the killing of George Floyd in the summer of 2020. Some of these and related demonstrations went on for months. Small numbers of these protests or protesters were violent, and many leaders in both the protest movement and government acknowledge that the protests had changed focus to reflect general anti-government sentiments, rather than focusing on racial justice.
### Symbolic Interactionism
Other sociologists study government and power by relying on the framework of symbolic interactionism, which is grounded in the works of Max Weber and George H. Mead.
Symbolic interactionism, as it pertains to government, focuses its attention on figures, emblems, or individuals that represent power and authority. Many diverse entities in larger society can be considered symbolic: trees, doves, wedding rings. Images that represent the power and authority of the United States include the White House, the eagle, and the American flag. The Seal of the President of the United States, along with the office in general, incites respect and reverence in many Americans.
Symbolic interactionists are not interested in large structures such as the government. As micro-sociologists, they are more interested in the face-to-face aspects of politics. In reality, much of politics consists of face-to-face backroom meetings and lobbyist efforts. What the public often sees is the front porch of politics that is sanitized by the media through gatekeeping.
Symbolic interactionists are most interested in the interaction between these small groups who make decisions, or in the case of some recent congressional committees, demonstrate the inability to make any decisions at all. The heart of politics is the result of interaction between individuals and small groups over periods of time. These meetings produce new meanings and perspectives that individuals use to make sure there are future interactions.
### Summary
Sociologists use frameworks to gain perspective on data and observations related to the study of power and government. Functionalism suggests that societal power and structure is predicated on cooperation, interdependence, and shared goals or values. Conflict theory, rooted in Marxism, asserts that societal structures are the result of social groups competing for wealth and influence. Symbolic interactionism examines a smaller realm of sociological interest: the individual’s perception of symbols of power and their subsequent reaction to the face-to-face interactions of the political realm.
### Section Quiz
### Short Answer
### Further Research
Functionalism is a complex philosophical theory that pertains to a variety of disciplines beyond sociology. Visit the entry devoted to functionalism on for a more comprehensive overview.
### References
Domhoff, G. William. 2011. “Who Rules America?” Sociology Department at University of California, Santa Cruz. Retrieved January 23, 2012 (http://www2.ucsc.edu/whorulesamerica/).
Marx, Karl. 1848. Manifesto of the Communist Party. Retrieved January 09, 2012 (http://www.marxists.org/archive/marx/works/1848/communist-manifesto/). |
# Work and the Economy
## Introduction to Work and the Economy
What if the U.S. economy thrived solely on basic bartering instead of its bustling agricultural and technological goods? Would you still see a busy building like the one shown in ?
In sociology, economy refers to the social institution through which a society’s resources are exchanged and managed. The earliest economies were based on trade, which is often a simple exchange in which people traded one item for another. While today’s economic activities are more complex than those early trades, the underlying goals remain the same: exchanging goods and services allows individuals to meet their needs and wants. In 1893, Émile Durkheim described what he called “mechanical” and “organic” solidarity that correlates to a society’s economy. Mechanical solidarity exists in simpler societies where social cohesion comes from sharing similar work, education, and religion. Organic solidarity arises out of the mutual interdependence created by the specialization of work. The complex U.S. economy, and the economies of other industrialized nations, meet the definition of organic solidarity. Most individuals perform a specialized task to earn money they use to trade for goods and services provided by others who perform different specialized tasks. In a simplified example, an elementary school teacher relies on farmers for food, doctors for healthcare, carpenters to build shelter, and so on. The farmers, doctors, and carpenters all rely on the teacher to educate their children. They are all dependent on each other and their work.
Economy is one of human society’s earliest social structures. Our earliest forms of writing (such as Sumerian clay tablets) were developed to record transactions, payments, and debts between merchants. As societies grow and change, so do their economies. The economy of a small farming community is very different from the economy of a large nation with advanced technology. In this chapter, we will examine different types of economic systems and how they have functioned in various societies.
Detroit, once the roaring headquarters of the country’s large and profitable automotive industry, had already been in a population decline for several decades as auto manufacturing jobs were being outsourced to other countries and foreign car brands began to take increasing portions of U.S. market share. According to State of Michigan population data (State of Michigan, n.d.), Detroit was home to approximately 1.85 million residents in 1950, which dwindled to slightly more than 700,000 in 2010 following the economic crash. The drastic reduction took its toll on the city. It is estimated that a third of the buildings in Detroit have been abandoned. The current average home price hovers around $7,000, while homes nationwide sell on average for around $200,000. The city has filed for bankruptcy, and its unemployment rate hovers around 30 percent.
### The Wage Gap in the United States
The Equal Pay Act, passed by the U.S. Congress in 1963, was designed to reduce the wage gap between men and women. The act in essence required employers to pay equal wages to men and women who were performing substantially similar jobs. However, more than fifty years later, women continue to make less money than their male counterparts. According to a report released by the White House in 2013, full-time working women made just 77 cents for every dollar a man made (National Equal Pay Taskforce 2013). Seven years later, the gap had only closed by four cents, with women making 81 cents for every dollar a man makes (Payscale 2020).
A part of the White House report read, “This significant gap is more than a statistic—it has real-life consequences. When women, who make up nearly half the workforce, bring home less money each day, it means they have less for the everyday needs of their families, and over a lifetime of work, far less savings for retirement.”
As shocking as it is, the gap actually widens when we add race and ethnicity to the picture. For example, African American women make on average 64 cents for every dollar a White male makes. Latina women make 56 cents, or 44 percent less, for every dollar a White man makes. African American and Latino men also make notably less than White men. Asian Americans tend to be the only minority that earns as much as or more than White men.
Certain professions have their own differences in wage gaps, even those whose participants have higher levels of education and supposedly a more merit-based method of promotion and credit. For example, U.S. and Canadian scientists have a significant wage gap that begins as soon as people enter the workforce. For example, of the PhD recipients that have jobs lined up after earning their degree, men reported an initial salary average of $92,000 per year, while women's was only $72,500. Men with permanent jobs in the life sciences reported an expected median salary of $87,000, compared with $80,000 for women. In mathematics and computer sciences, men reported an expected median salary of $125,000; for women, that figure was $101,500 (Woolston 2021).
### Recent Economic Conditions
In 2015, the United States continued its recovery from the “Great Recession,” arguably the worst economic downturn since the stock market collapse in 1929 and the Great Depression that ensued.
The 2008 recession was brought on by aggressive lending, extremely risky behavior by investment firms, and lax oversight by the government. During this time, banks provided mortgages to people with poor credit histories, sometimes with deceptively low introductory interest rates. When the rates rose, borrowers' mortgage payments increased to the point where they couldn't make payments. At the same time, investment firms had purchased these risky mortgages in the form of large bundled investments worth billions of dollars each (mortgage-backed securities or MBS). Rating agencies were supposed to rate mortgage securities according to their level of risk, but they typically rated all MBS as high-quality no matter what types of mortgages they contained. When the mortgages defaulted, the investment firms' holdings went down. The massive rate of loan defaults put a strain on the financial institutions that had made the loans as well as those that had purchased the MBS, and this stress rippled throughout the entire economy and around the globe.
With the entire financial system on the verge of permanent damage, the U.S. government bailed out many of these firms and provided support to other industries, such as airlines and automobile companies. But the Recession couldn't be stopped. The United States fell into a period of high and prolonged unemployment, extreme reductions in wealth (except at the very top), stagnant wages, and loss of value in personal property (houses and land).
Starting in 2009, however, employment began to tick back up as companies found their footing. By 2012, most of the country's employment rates were similar to the levels prior to the Great Recession. However, for most segments of the population, median income had not increased, and in fact it has receded in many cases. The size, income, and wealth of the middle class have been declining since the 1970s— effects that were perhaps hastened by the recession. Today, wealth is distributed inequitably at the top. Corporate profits have increased more than 141 percent, and CEO pay has risen by more than 298 percent.
Although wages had not increased, and certain parts of the economy, such as brick-and-mortar retail (department stores and similar chains) were doing poorly, the economy as a whole grew from the time after the Great Recession through 2020. Unemployment reached a historic low in late 2019. COVID-19 changed all that. As you may have experienced yourself, entire industries suffered incredible losses as they were forced to shut down or severely reduce operations. Some people were laid off from their jobs, while others had their hours or wages reduced. Unemployment skyrocketed again, reaching a new high of nearly 15 percent, only about six months after it had been at its record low. Industries as diverse as hospitality and mining reported massive decreases in employment, and part-time workers in particular were hard hit. By early 2021, the overall unemployment rate had returned to generally normal levels. The impact on those who had gone without work for so long, however, was significant (Congressional Research Service 2021).
### References
National Equal Pay Task Force. 2013. "Fifty Years After the Equal Pay Act: Assessing the Past, Taking Stock of the Future." Retrieved December 15, 2014. (http://www.whitehouse.gov/sites/default/files/equalpay/equal_pay_task_force_progress_report_june_2013_new.pdf).
Payscale.com. 2020. "State of the Gender Pay Gap 2020." Payscale.com. (https://www.payscale.com/data/gender-pay-gap)
State of Michigan, The. n.d. "Detrioit's Financial Crisis: What You Need to Know." Retrieved December 15, 2014. (http://www.michigan.gov/documents/detroitcantwait/DetroitFactSheet_412909_7.pdf).
U.S. Department of Agriculture. 2014. "Supplemental Nutrition Assistance Program Participation and Costs." Retrieved December 15, 2014. (http://www.fns.usda.gov/sites/default/files/pd/SNAPsummary.pdf).
Woolston, Chris. 2021. "Pay gap widens between men and women scientists in North America." Nature Career News. February 11 2021. (https://www.nature.com/articles/d41586-021-00387-3) |
# Work and the Economy
## Economic Systems
The dominant economic systems of the modern era are capitalism and socialism, and there have been many variations of each system across the globe. Countries have switched systems as their rulers and economic fortunes have changed. For example, Russia has been transitioning to a market-based economy since the fall of communism in that region of the world. Vietnam, where the economy was devastated by the Vietnam War, restructured to a state-run economy in response, and more recently has been moving toward a socialist-style market economy. In the past, other economic systems reflected the societies that formed them. Many of these earlier systems lasted centuries. These changes in economies raise many questions for sociologists. What are these older economic systems? How did they develop? Why did they fade away? What are the similarities and differences between older economic systems and modern ones?
### Economics of Agricultural, Industrial, and Postindustrial Societies
Our earliest ancestors lived as hunter-gatherers. Small groups of extended families roamed from place to place looking for subsistence. They would settle in an area for a brief time when there were abundant resources. They hunted animals for their meat and gathered wild fruits, vegetables, and cereals. They ate what they caught or gathered their goods as soon as possible, because they had no way of preserving or transporting it. Once the resources of an area ran low, the group had to move on, and everything they owned had to travel with them. Food reserves only consisted of what they could carry. Many sociologists contend that hunter-gatherers did not have a true economy, because groups did not typically trade with other groups due to the scarcity of goods.
### The Agricultural Revolution
The first true economies arrived when people started raising crops and domesticating animals. Although there is still a great deal of disagreement among archeologists as to the exact timeline, research indicates that agriculture began independently and at different times in several places around the world. The earliest agriculture was in the Fertile Crescent in the Middle East around 11,000–10,000 years ago. Next were the valleys of the Indus, Yangtze, and Yellow rivers in India and China, between 10,000 and 9,000 years ago. The people living in the highlands of New Guinea developed agriculture between 9,000 and 6,000 years ago, while people were farming in Sub-Saharan Africa between 5,000 and 4,000 years ago. Agriculture developed later in the western hemisphere, arising in what would become the eastern United States, central Mexico, and northern South America between 5,000 and 3,000 years ago (Diamond 2003).
Agriculture began with the simplest of technologies—for example, a pointed stick to break up the soil—but really took off when people harnessed animals to pull an even more efficient tool for the same task: a plow. With this new technology, one family could grow enough crops not only to feed themselves but also to feed others. Knowing there would be abundant food each year as long as crops were tended led people to abandon the nomadic life of hunter-gatherers and settle down to farm.
The improved efficiency in food production meant that not everyone had to toil all day in the fields. As agriculture grew, new jobs emerged, along with new technologies. Excess crops needed to be stored, processed, protected, and transported. Farming equipment and irrigation systems needed to be built and maintained. Wild animals needed to be domesticated and herds shepherded. Economies began to develop because people now had goods and services to trade. At the same time, farmers eventually came to labor for the ruling class.
As more people specialized in nonfarming jobs, villages grew into towns and then into cities. Urban areas created the need for administrators and public servants. Disputes over ownership, payments, debts, compensation for damages, and the like led to the need for laws and courts—and the judges, clerks, lawyers, and police who administered and enforced those laws.
At first, most goods and services were traded as gifts or through bartering between small social groups (Mauss 1922). Exchanging one form of goods or services for another was known as bartering. This system only works when one person happens to have something the other person needs at the same time. To solve this problem, people developed the idea of a means of exchange that could be used at any time: that is, money. Money refers to an object that a society agrees to assign a value to so it can be exchanged for payment. In early economies, money was often objects like cowry shells, rice, barley, or even rum. Precious metals quickly became the preferred means of exchange in many cultures because of their durability and portability. The first coins were minted in Lydia in what is now Turkey around 650–600 B.C.E. (Goldsborough 2010). Early legal codes established the value of money and the rates of exchange for various commodities. They also established the rules for inheritance, fines as penalties for crimes, and how property was to be divided and taxed (Horne 1915). A symbolic interactionist would note that bartering and money are systems of symbolic exchange. Monetary objects took on a symbolic meaning, one that carries into our modern-day use of cash, checks, and debit cards.
As city-states grew into countries and countries grew into empires, their economies grew as well. When large empires broke up, their economies broke up too. The governments of newly formed nations sought to protect and increase their markets. They financed voyages of discovery to find new markets and resources all over the world, which ushered in a rapid progression of economic development.
Colonies were established to secure these markets, and wars were financed to take over territory. These ventures were funded in part by raising capital from investors who were paid back from the goods obtained. Governments and private citizens also set up large trading companies that financed their enterprises around the world by selling stocks and bonds.
Governments tried to protect their share of the markets by developing a system called mercantilism. Mercantilism is an economic policy based on accumulating silver and gold by controlling colonial and foreign markets through taxes and other charges. The resulting restrictive practices and exacting demands included monopolies, bans on certain goods, high tariffs, and exclusivity requirements. Mercantilist governments also promoted manufacturing and, with the ability to fund technological improvements, they helped create the equipment that led to the Industrial Revolution.
### The Industrial Revolution
Until the end of the eighteenth century, most manufacturing was done by manual labor. This changed as inventors devised machines to manufacture goods. A small number of innovations led to a large number of changes in the British economy. In the textile industries, the spinning of cotton, worsted yarn, and flax could be done more quickly and less expensively using new machines with names like the Spinning Jenny and the Spinning Mule (Bond 2003). Another important innovation was made in the production of iron: Coke from coal could now be used in all stages of smelting rather than charcoal from wood, which dramatically lowered the cost of iron production while increasing availability (Bond 2003). James Watt ushered in what many scholars recognize as the greatest change, revolutionizing transportation and thereby the entire production of goods with his improved steam engine.
As people moved to cities to fill factory jobs, factory production also changed. Workers did their jobs in assembly lines and were trained to complete only one or two steps in the manufacturing process. These advances meant that more finished goods could be manufactured with more efficiency and speed than ever before.
The Industrial Revolution also changed agricultural practices. Until that time, many people practiced subsistence farming in which they produced only enough to feed themselves and pay their taxes. New technology introduced gasoline-powered farm tools such as tractors, seed drills, threshers, and combine harvesters. Farmers were encouraged to plant large fields of a single crop to maximize profits. With improved transportation and the invention of refrigeration, produce could be shipped safely all over the world.
The Industrial Revolution modernized the world. With growing resources came growing societies and economies. Between 1800 and 2000, the world’s population grew sixfold, while per capita income saw a tenfold jump (Maddison 2003).
While many people's lives were improving, the Industrial Revolution also birthed many societal problems. There were inequalities in the system. Owners amassed vast fortunes while laborers, including young children, toiled for long hours in unsafe conditions. Workers’ rights, wage protection, and safe work environments are issues that arose during this period and remain concerns today.
### Postindustrial Societies and the Information Age
Postindustrial societies, also known as information societies, have evolved in modernized nations. One of the most valuable goods of the modern era is information. Those who have the means to produce, store, and disseminate information are leaders in this type of society.
One way scholars understand the development of different types of societies (like agricultural, industrial, and postindustrial) is by examining their economies in terms of four sectors: primary, secondary, tertiary, and quaternary. Each has a different focus. The primary sector extracts and produces raw materials (like metals and crops). The secondary sector turns those raw materials into finished goods. The tertiary sector provides services: child care, healthcare, and money management. Finally, the quaternary sector produces ideas; these include the research that leads to new technologies, the management of information, and a society’s highest levels of education and the arts (Kenessey 1987).
In underdeveloped countries, the majority of the people work in the primary sector. As economies develop, more and more people are employed in the secondary sector. In well-developed economies, such as those in the United States, Japan, and Western Europe, the majority of the workforce is employed in service industries. In the United States, for example, almost 80 percent of the workforce is employed in the tertiary sector (U.S. Bureau of Labor Statistics 2011).
The rapid increase in computer use in all aspects of daily life is a main reason for the transition to an information economy. Fewer people are needed to work in factories because computerized robots now handle many of the tasks. Other manufacturing jobs have been outsourced to less-developed countries as a result of the developing global economy. The growth of the Internet has created industries that exist almost entirely online. Within industries, technology continues to change how goods are produced. For instance, the music and film industries used to produce physical products like CDs and DVDs for distribution. Now those goods are increasingly produced digitally and streamed or downloaded at a much lower physical manufacturing cost. Information and the means to use it creatively have become commodities in a postindustrial economy.
### Capitalism
Scholars don’t always agree on a single definition of capitalism. For our purposes, we will define capitalism as an economic system in which there is private ownership (as opposed to state ownership) and where there is an impetus to produce profit, and thereby wealth. This is the type of economy in place in the United States today. Under capitalism, people invest capital (money or property invested in a business venture) in a business to produce a product or service that can be sold in a market to consumers. The investors in the company are generally entitled to a share of any profit made on sales after the costs of production and distribution are taken out. These investors often reinvest their profits to improve and expand the business or acquire new ones. To illustrate how this works, consider this example. Sarah, Antonio, and Chris each invest $250,000 into a start-up company that offers an innovative baby product. When the company nets $1 million in profits its first year, a portion of that profit goes back to Sarah, Antonio, and Chris as a return on their investment. Sarah reinvests with the same company to fund the development of a second product line, Antonio uses his return to help another start-up in the technology sector, and Chris buys a small yacht for vacations.
To provide their product or service, owners hire workers to whom they pay wages. The cost of raw materials, the retail price they charge consumers, and the amount they pay in wages are determined through the law of supply and demand and by competition. When demand exceeds supply, prices tend to rise. When supply exceeds demand, prices tend to fall. When multiple businesses market similar products and services to the same buyers, there is competition. Competition can be good for consumers because it can lead to lower prices and higher quality as businesses try to get consumers to buy from them rather than from their competitors.
Wages tend to be set in a similar way. People who have talents, skills, education, or training that is in short supply and is needed by businesses tend to earn more than people without comparable skills. Competition in the workforce helps determine how much people will be paid. In times when many people are unemployed and jobs are scarce, people are often willing to accept less than they would when their services are in high demand. In this scenario, businesses are able to maintain or increase profits by not increasing workers' wages.
### Capitalism in Practice
As capitalists began to dominate the economies of many countries during the Industrial Revolution, the rapid growth of businesses and their tremendous profitability gave some owners the capital they needed to create enormous corporations that could monopolize an entire industry. Many companies controlled all aspects of the production cycle for their industry, from the raw materials, to the production, to the stores in which they were sold. These companies were able to use their wealth to buy out or stifle any competition.
In the United States, the predatory tactics used by these large monopolies caused the government to take action. Starting in the late 1800s, the government passed a series of laws that broke up monopolies and regulated how key industries—such as transportation, steel production, and oil and gas exploration and refining—could conduct business.
The United States is considered a capitalist country. However, the U.S. government has a great deal of influence on private companies through the laws it passes and the regulations enforced by government agencies. Through taxes, regulations on wages, guidelines to protect worker safety and the environment, plus financial rules for banks and investment firms, the government exerts a certain amount of control over how all companies do business. State and federal governments also own, operate, or control large parts of certain industries, such as the post office, schools, hospitals, highways and railroads, and many water, sewer, and power utilities. Debate over the extent to which the government should be involved in the economy remains an issue of contention today. Some criticize such involvements as socialism (a type of state-run economy), while others believe intervention is necessary to protect the rights of workers and the well-being of the general population.
### Socialism
Socialism is an economic system in which there is government ownership (often referred to as “state run”) of goods and their production, with an impetus to share work and wealth equally among the members of a society. Under socialism, everything that people produce, including services, is considered a social product. Everyone who contributes to the production of a good or to providing a service is entitled to a share in any benefits that come from its sale or use. To make sure all members of society get their fair share, governments must be able to control property, production, and distribution.
The focus in socialism is on benefitting society, whereas capitalism seeks to benefit the individual. Socialists claim that a capitalistic economy leads to inequality, with unfair distribution of wealth and individuals who use their power at the expense of society. Socialism strives, ideally, to control the economy to avoid the problems inherent in capitalism.
Within socialism, there are diverging views on the extent to which the economy should be controlled. One extreme believes all but the most personal items are public property. Other socialists believe only essential services such as healthcare, education, and utilities (electrical power, telecommunications, and sewage) need direct control. Under this form of socialism, farms, small shops, and businesses can be privately owned but are subject to government regulation.
The other area on which socialists disagree is on what level society should exert its control. In communist countries like the former Soviet Union, China, Vietnam, and North Korea, the national government exerts control over the economy centrally. They had the power to tell all businesses what to produce, how much to produce, and what to charge for it. Other socialists believe control should be decentralized so it can be exerted by those most affected by the industries being controlled. An example of this would be a town collectively owning and managing the businesses on which its residents depend.
Because of challenges in their economies, several of these communist countries have moved from central planning to letting market forces help determine many production and pricing decisions. Market socialism describes a subtype of socialism that adopts certain traits of capitalism, like allowing limited private ownership or consulting market demands. This could involve situations like profits generated by a company going directly to the employees of the company or being used as public funds (Gregory and Stuart 2003). Many Eastern European and some South American countries have mixed economies. Key industries are nationalized and directly controlled by the government; however, most businesses are privately owned and regulated by the government.
Organized socialism never became powerful in the United States. The success of labor unions and the government in securing workers’ rights, joined with the high standard of living enjoyed by most of the workforce, made socialism less appealing than the controlled capitalism practiced here.
### Socialism in Practice
As with capitalism, the basic ideas behind socialism go far back in history. Plato, in ancient Greece, suggested a republic in which people shared their material goods. Early Christian communities believed in common ownership, as did the systems of monasteries set up by various religious orders. Many of the leaders of the French Revolution called for the abolition of all private property, not just the estates of the aristocracy they had overthrown. Thomas More's Utopia, published in 1516, imagined a society with little private property and mandatory labor on a communal farm. A utopia has since come to mean an imagined place or situation in which everything is perfect. Most experimental utopian communities had the abolition of private property as a founding principle.
Modern socialism really began as a reaction to the excesses of uncontrolled industrial capitalism in the 1800s and 1900s. The enormous wealth and lavish lifestyles enjoyed by owners contrasted sharply with the miserable conditions of the workers.
Some of the first great sociological thinkers studied the rise of socialism. Max Weber admired some aspects of socialism, especially its rationalism and how it could help social reform, but he worried that letting the government have complete control could result in an "iron cage of future bondage" from which there is no escape (Greisman and Ritzer 1981).
Pierre-Joseph Proudhon (1809−1865) was another early socialist who thought socialism could be used to create utopian communities. In his 1840 book, What Is Property?, he famously stated that “property is theft” (Proudhon 1840). By this he meant that if an owner did not work to produce or earn the property, then the owner was stealing it from those who did. Proudhon believed economies could work using a principle called mutualism, under which individuals and cooperative groups would exchange products with one another on the basis of mutually satisfactory contracts (Proudhon 1840).
By far the most important influential thinker on socialism is Karl Marx. Through his own writings and those with his collaborator, industrialist Friedrich Engels, Marx used a scientific analytical process to show that throughout history, the resolution of class struggles caused changes in economies. He saw the relationships evolving from slave and owner, to serf and lord, to journeyman and master, to worker and owner. Neither Marx nor Engels thought socialism could be used to set up small utopian communities. Rather, they believed a socialist society would be created after workers rebelled against capitalistic owners and seized the means of production. They felt industrial capitalism was a necessary step that raised the level of production in society to a point it could progress to a socialist and then communist state (Marx and Engels 1848). These ideas form the basis of the sociological perspective of social conflict theory.
### Convergence Theory
We have seen how the economies of some capitalist countries such as the United States have features that are very similar to socialism. Some industries, particularly utilities, are either owned by the government or controlled through regulations. Public programs such as welfare, Medicare, and Social Security exist to provide public funds for private needs. We have also seen how several large communist (or formerly communist) countries such as Russia, China, and Vietnam have moved from state-controlled socialism with central planning to market socialism, which allows market forces to dictate prices and wages and for some business to be privately owned. In many formerly communist countries, these changes have led to economic growth compared to the stagnation they experienced under communism (Fidrmuc 2002).
In studying the economies of developing countries to see if they go through the same stages as previously developed nations did, sociologists have observed a pattern they call convergence. This describes the theory that societies move toward similarity over time as their economies develop.
Convergence theory explains that as a country's economy grows, its societal organization changes to become more like that of an industrialized society. Rather than staying in one job for a lifetime, people begin to move from job to job as conditions improve and opportunities arise. This means the workforce needs continual training and retraining. Workers move from rural areas to cities as they become centers of economic activity, and the government takes a larger role in providing expanded public services (Kerr et al. 1960).
Supporters of the theory point to Germany, France, and Japan—countries that rapidly rebuilt their economies after World War II. They point out how, in the 1960s and 1970s, East Asian countries like Singapore, South Korea, and Taiwan converged with countries with developed economies. They are now considered developed countries themselves.
To experience this rapid growth, the economies of developing countries must be able to attract inexpensive capital to invest in new businesses and to improve traditionally low productivity. They need access to new, international markets for buying the goods. If these characteristics are not in place, then their economies cannot catch up. This is why the economies of some countries are diverging rather than converging (Abramovitz 1986).
Another key characteristic of economic growth regards the implementation of technology. A developing country can bypass some steps of implementing technology that other nations faced earlier. Television and telephone systems are a good example. While developed countries spent significant time and money establishing elaborate system infrastructures based on metal wires or fiber-optic cables, developing countries today can go directly to cell phone and satellite transmission with much less investment.
Another factor affects convergence concerning social structure. Early in their development, countries such as Brazil and Cuba had economies based on cash crops (coffee or sugarcane, for instance) grown on large plantations by unskilled workers. The elite ran the plantations and the government, with little interest in training and educating the populace for other endeavors. This restricted economic growth until the power of the wealthy plantation owners was challenged (Sokoloff and Engerman 2000). Improved economies generally lead to wider social improvement. Society benefits from improved educational systems, and people have more time to devote to learning and leisure.
### Theoretical Perspectives on the Economy
Now that we’ve developed an understanding of the history and basic components of economies, let’s turn to theory. How might social scientists study these topics? What questions do they ask? What theories do they develop to add to the body of sociological knowledge?
### Functionalist Perspective
Someone taking a functional perspective will most likely view work and the economy as a well-oiled machine that is designed for maximum efficiency. The Davis-Moore thesis, for example, suggests that some social stratification is a social necessity. The need for certain highly skilled positions combined with the relative difficulty of the occupation and the length of time it takes to qualify will result in a higher reward for that job and will provide a financial motivation to engage in more education and a more difficult profession (Davis and Moore 1945). This theory can be used to explain the prestige and salaries that go with careers only available to those with doctorates or medical degrees.
The functionalist perspective would assume that the continued health of the economy is vital to the health of the nation, as it ensures the distribution of goods and services. For example, we need food to travel from farms (high-functioning and efficient agricultural systems) via roads (safe and effective trucking and rail routes) to urban centers (high-density areas where workers can gather). However, sometimes a dysfunction––a function with the potential to disrupt social institutions or organization (Merton 1968)––in the economy occurs, usually because some institutions fail to adapt quickly enough to changing social conditions. This lesson has been driven home recently with the bursting of the housing bubble. Due to risky lending practices and an underregulated financial market, we are recovering from the after-effects of the Great Recession, which Merton would likely describe as a major dysfunction.
Some of this is cyclical. Markets produce goods as they are supposed to, but eventually the market is saturated and the supply of goods exceeds the demands. Typically the market goes through phases of surplus, or excess, inflation, where the money in your pocket today buys less than it did yesterday, and recession, which occurs when there are two or more consecutive quarters of economic decline. The functionalist would say to let market forces fluctuate in a cycle through these stages. In reality, to control the risk of an economic depression (a sustained recession across several economic sectors), the U.S. government will often adjust interest rates to encourage more lending—and consequently more spending. In short, letting the natural cycle fluctuate is not a gamble most governments are willing to take.
### Conflict Perspective
For a conflict perspective theorist, the economy is not a source of stability for society. Instead, the economy reflects and reproduces economic inequality, particularly in a capitalist marketplace. The conflict perspective is classically Marxist, with the bourgeoisie (ruling class) accumulating wealth and power by exploiting and perhaps oppressing the proletariat (workers), and regulating those who cannot work (the aged, the infirm) into the great mass of unemployed (Marx and Engels 1848). From the symbolic (though probably made up) statement of Marie Antoinette, who purportedly said, “Let them eat cake” when told that the peasants were starving, to the Occupy Wall Street movement that began during the Great Recession, the sense of inequity is almost unchanged. Conflict theorists believe wealth is concentrated in the hands of those who do not deserve it. As of 2010, 20 percent of Americans owned 90 percent of U.S. wealth (Domhoff 2014). While the inequality might not be as extreme as in pre-revolutionary France, it is enough to make many believe that the United States is not the meritocracy it seems to be.
### Symbolic Interactionist Perspective
Those working in the symbolic interaction perspective take a microanalytical view of society. They focus on the way reality is socially constructed through day-to-day interaction and how society is composed of people communicating based on a shared understanding of symbols.
One important symbolic interactionist concept related to work and the economy is career inheritance. This concept means simply that children tend to enter the same or similar occupation as their parents, which is a correlation that has been demonstrated in research studies (Antony 1998). For example, the children of police officers learn the norms and values that will help them succeed in law enforcement, and since they have a model career path to follow, they may find law enforcement even more attractive. Related to career inheritance is career socialization—learning the norms and values of a particular job.
Finally, a symbolic interactionist might study what contributes to job satisfaction. Melvin Kohn and his fellow researchers (1990) determined that workers were most likely to be happy when they believed they controlled some part of their work, when they felt they were part of the decision-making processes associated with their work, when they have freedom from surveillance, and when they felt integral to the outcome of their work. Sunyal, Sunyal, and Yasin (2011) found that a greater sense of vulnerability to stress, the more stress experienced by a worker, and a greater amount of perceived risk consistently predicted a lower worker job satisfaction.
### Summary
Economy refers to the social institution through which a society’s resources (goods and services) are managed. The Agricultural Revolution led to development of the first economies that were based on trading goods. Mechanization of the manufacturing process led to the Industrial Revolution and gave rise to two major competing economic systems. Under capitalism, private owners invest their capital and that of others to produce goods and services they can sell in an open market. Prices and wages are set by supply and demand and competition. Under socialism, the means of production is commonly owned, and the economy is controlled centrally by government. Several countries’ economies exhibit a mix of both systems. Convergence theory seeks to explain the correlation between a country’s level of development and changes in its economic structure.
### Section Quiz
### Short Answer
### Further Research
Green jobs have the potential to improve not only your prospects of getting a good job, but the environment as well. Visit this web site to learn more about the green revolution in jobs
One alternative to traditional capitalism is to have the workers own the company for which they work. To learn more about company-owned businesses check out this website.
### References
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Abramovitz, Moses. 1986. “Catching Up, Forging Ahead and Falling Behind.” Journal of Economic History 46(2):385–406. Retrieved February 6, 2012 (http://www.jstor.org/pss/2122171).
Antony, James. 1998. “Exploring the Factors that Influence Men and Women to Form Medical Career Aspirations.” Journal of College Student Development 39:417–426.
Bond, Eric, Sheena Gingerich, Oliver Archer-Antonsen, Liam Purcell, and Elizabeth Macklem. 2003. The Industrial Revolution—Innovations. Retrieved February 6, 2012 (http://industrialrevolution.sea.ca/innovations.html).
Congressional Research Service. 2021. "Unemployment Rates During the COVID-19 Pandemic." January 2021. (https://fas.org/sgp/crs/misc/R46554.pdf)
Dalio, Ray. 2019. "Why and How Capitalism Needs To Be Reformed Parts 1&2." LinkedIn Personal Post. April 5 2019. (https://www.linkedin.com/pulse/why-how-capitalism-needs-reformed-parts-1-2-ray-dalio/)
Davis, Kingsley, and Wilbert Moore. 1945. “Some Principles of Stratification.” American Sociological Review 10:242–249.
Diamond, J., and P. Bellwood. 2003. “Farmers and Their Languages: The First Expansions.” Science April 25, pp. 597-603.
Domhoff, G. William. 2011. “Wealth Income and Power.” Who Rules America. Retrieved January 25, 2012 (http://www2.ucsc.edu/whorulesamerica/power/wealth.html).
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Fidrmuc, Jan. 2002. “Economic Reform, Democracy and Growth During Post-Communist Transition.” European Journal of Political Economy 19(30):583–604. Retrieved February 6, 2012 (http://siteresources.worldbank.org/INTDECINEQ/Resources/fidrmuc.pdf).
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U.S. Bureau of Labor Statistics. 2011. “Employment by Major Industry Sector.” Retrieved February 6, 2012 (http://www.bls.gov/emp/ep_table_201.htm). |
# Work and the Economy
## Globalization and the Economy
### What Is Globalization?
Globalization refers to the process of integrating governments, cultures, and financial markets through international trade into a single world market. Often, the process begins with a single motive, such as market expansion (on the part of a corporation) or increased access to healthcare (on the part of a nonprofit organization). But usually there is a snowball effect, and globalization becomes a mixed bag of economic, philanthropic, entrepreneurial, and cultural efforts. Sometimes the efforts have obvious benefits, even for those who worry about cultural colonialism, such as campaigns to bring clean-water technology to rural areas that do not have access to safe drinking water.
Other globalization efforts, however, are more complex. Let us look, for example, at the North American Free Trade Agreement (NAFTA). The agreement was among the countries of North America, including Canada, the United States, and Mexico, and allowed much freer trade opportunities without the kind of tariffs (taxes) and import laws that restrict international trade. Often, trade opportunities are misrepresented by politicians and economists, who sometimes offer them up as a panacea to economic woes. For example, trade can lead to both increases and decreases in job opportunities. This is because while easier, more lax export laws mean there is the potential for job growth in the United States, imports can mean the exact opposite. As the United States imports more goods from outside the country, jobs typically decrease, as more and more products are made overseas.
Many prominent economists believed that when NAFTA was created in 1994 it would lead to major gains in jobs. But by 2010, the evidence showed an opposite impact; the data showed 682,900 U.S. jobs lost across all states (Parks 2011). While NAFTA did increase the flow of goods and capital across the northern and southern U.S. borders, it also increased unemployment in Mexico, which spurred greater amounts of illegal immigration motivated by a search for work. NAFTA was renegotiated in 2018, and was formally replaced by the United States-Mexico-Canada Agreement in 2020.
There are several forces driving globalization, including the global economy and multinational corporations that control assets, sales, production, and employment (United Nations 1973). Characteristics of multinational corporations include the following: A large share of their capital is collected from a variety of different nations, their business is conducted without regard to national borders, they concentrate wealth in the hands of core nations and already wealthy individuals, and they play a key role in the global economy.
We see the emergence of global assembly lines, where products are assembled over the course of several international transactions. For instance, Apple designs its next-generation Mac prototype in the United States, components are made in various peripheral nations, they are then shipped to another peripheral nation such as Malaysia for assembly, and tech support is outsourced to India.
Globalization has also led to the development of global commodity chains, where internationally integrated economic links connect workers and corporations for the purpose of manufacture and marketing (Plahe 2005). For example, in maquiladoras, mostly found in northern Mexico, workers may sew imported precut pieces of fabric into garments.
Globalization also brings an international division of labor, in which comparatively wealthy workers from core nations compete with the low-wage labor pool of peripheral and semi-peripheral nations. This can lead to a sense of xenophobia, which is an illogical fear and even hatred of foreigners and foreign goods. Corporations trying to maximize their profits in the United States are conscious of this risk and attempt to “Americanize” their products, selling shirts printed with U.S. flags that were nevertheless made in Mexico.
### Aspects of Globalization
Globalized trade is nothing new. Societies in ancient Greece and Rome traded with other societies in Africa, the Middle East, India, and China. Trade expanded further during the Islamic Golden Age and after the rise of the Mongol Empire. The establishment of colonial empires after the voyages of discovery by European countries meant that trade was going on all over the world. In the nineteenth century, the Industrial Revolution led to even more trade of ever-increasing amounts of goods. However, the advance of technology, especially communications, after World War II and the Cold War triggered the explosive acceleration in the process occurring today.
One way to look at the similarities and differences that exist among the economies of different nations is to compare their standards of living. The statistic most commonly used to do this is the domestic process per capita. This is the gross domestic product, or GDP, of a country divided by its population. The table below compares the top 11 countries with the bottom 11 out of the 228 countries listed in the CIA World Factbook.
There are benefits and drawbacks to globalization. Some of the benefits include the exponentially accelerated progress of development, the creation of international awareness and empowerment, and the potential for increased wealth (Abedian 2002). However, experience has shown that countries can also be weakened by globalization. Some critics of globalization worry about the growing influence of enormous international financial and industrial corporations that benefit the most from free trade and unrestricted markets. They fear these corporations can use their vast wealth and resources to control governments to act in their interest rather than that of the local population (Bakan 2004). Indeed, when looking at the countries at the bottom of the list above, we are looking at places where the primary benefactors of mineral exploitation are major corporations and a few key political figures.
Other critics oppose globalization for what they see as negative impacts on the environment and local economies. Rapid industrialization, often a key component of globalization, can lead to widespread economic damage due to the lack of regulatory environment (Speth 2003). Further, as there are often no social institutions in place to protect workers in countries where jobs are scarce, some critics state that globalization leads to weak labor movements (Boswell and Stevis 1997). Finally, critics are concerned that wealthy countries can force economically weaker nations to open their markets while protecting their own local products from competition (Wallerstein 1974). This can be particularly true of agricultural products, which are often one of the main exports of poor and developing countries (Koroma 2007). In a 2007 article for the United Nations, Koroma discusses the difficulties faced by “least developed countries” (LDCs) that seek to participate in globalization efforts. These countries typically lack the infrastructure to be flexible and nimble in their production and trade, and therefore are vulnerable to everything from unfavorable weather conditions to international price volatility. In short, rather than offering them more opportunities, the increased competition and fast pace of a globalized market can make it more challenging than ever for LDCs to move forward (Koroma 2007).
The increasing use of outsourcing of manufacturing and service-industry jobs to developing countries has caused increased unemployment in some developed countries. Countries that do not develop new jobs to replace those that move, and train their labor force to do them, will find support for globalization weakening.
### Summary
Globalization refers to the process of integrating governments, cultures, and financial markets through international trade into a single world market. There are benefits and drawbacks to globalization. Often the countries that fare the worst are those that depend on natural resource extraction for their wealth. Many critics fear globalization gives too much power to multinational corporations and that political decisions are influenced by these major financial players.
### Section Quiz
### Short Answer
### Further Research
The World Social Forum (WSF) was created in response to the creation of the World Economic Forum (WEF). The WSF is a coalition of organizations dedicated to the idea of a worldwide civil society and presents itself as an alternative to WEF, which it says is too focused on capitalism. Learn more about the WSF here rights.
### References
Abedian, Araj. 2002. “Economic Globalization: Some Pros and Cons.” Papers from the Sixth Conference of the International Environment Forum, World Summit on Sustainable Development. Johannesburg, South Africa. Retrieved January 24, 2012 (http://iefworld.org/dabed02.htm).
Bakan, Joel. 2004. The Corporation: The Pathological Pursuit of Profit and Power. New York: Free Press.
Bhagwati, Jagdish. 2004. In Defense of Globalization. New York: Oxford University Press.
Boswell, Terry and Dimitris Stevis. 1997. “Globalization and International Labor Organization.” Work and Occupations 24:288–308.
Central Intelligence Agency (CIA). 2014. "The World Factbook: Country Comparison: GDP Per Capita (PPP)." Retrieved December 15, 2014. (https://www.cia.gov/library/publications/the-world-factbook/rankorder/2004rank.html).
Koroma, Suffyan. 2007. “Globalization, Agriculture, and the Least Developed Countries.” United Nations Ministerial Conference on the Least Developed Countries. Istanbul, Turkey.
Plahe, Jagjit. 2005. “The Global Commodity Chain Approach (GCC) Approach and the Organizational Transformation of Agriculture.” Monash University. Retrieved February 6, 2012 (http://www.buseco.monash.edu.au/mgt/research/working-papers/2005/wp63-05.pdf).
Parks, James. 2011. “Report: NAFTA Has Cost 683,000 Jobs and Counting,” AFL-CIO Blog, May 3. Retrieved February 6, 2012 (http://blog.aflcio.org/2011/05/03/report-nafta-has-cost-683000-jobs-and-counting).
Sassen, Saskia. 2001. The Global City: New York, London, Tokyo. Princeton, NJ: Princeton University Press.
Speth, James G., ed. 2003. Worlds Apart: Globalization and the Environment. Washington, DC: Island Press.
The United Nations: Department of Economic and Social Affairs. 1973. “Multinational Corporations in World Development.” New York: United Nations Publication.
Wallerstein, Immanuel. 1974. The Modern World System. New York: Academic Press. |
# Work and the Economy
## Work in the United States
The American Dream has always been based on opportunity. There is a great deal of mythologizing about the energetic upstart who can climb to success based on hard work alone. Common wisdom states that if you study hard, develop good work habits, and graduate high school or, even better, college, then you'll have the opportunity to land a good job. That has long been seen as the key to a successful life. And although the reality has always been more complex than suggested by the myth, the worldwide recession that began in 2008 took its toll on the American Dream. During the recession, more than 8 million U.S. workers lost their jobs, and unemployment rates surpassed 10 percent on a national level. Today, while the recovery is still incomplete, many sectors of the economy are hiring, and unemployment rates have receded.
### Polarization in the Workforce
The mix of jobs available in the United States began changing many years before the recession struck, and, as mentioned above, the American Dream has not always been easy to achieve. Geography, race, gender, and other factors have always played a role in the reality of success. More recently, the increased outsourcing—or contracting a job or set of jobs to an outside source—of manufacturing jobs to developing nations has greatly diminished the number of high-paying, often unionized, blue-collar positions available. A similar problem has arisen in the white-collar sector, with many low-level clerical and support positions also being outsourced, as evidenced by the international technical-support call centers in Mumbai, India, and Newfoundland, Canada. The number of supervisory and managerial positions has been reduced as companies streamline their command structures and industries continue to consolidate through mergers. Even highly educated skilled workers such as computer programmers have seen their jobs vanish overseas.
The automation of the workplace, which replaces workers with technology, is another cause of the changes in the job market. Computers can be programmed to do many routine tasks faster and less expensively than people who used to do such tasks. Jobs like bookkeeping, clerical work, and repetitive tasks on production assembly lines all lend themselves to automation. Envision your local supermarket’s self-scan checkout aisles. The automated cashiers affixed to the units take the place of paid employees. Now one cashier can oversee transactions at six or more self-scan aisles, which was a job that used to require one cashier per aisle.
Despite the ongoing economic recovery, the job market is actually growing in some areas, but in a very polarized fashion. Polarization means that a gap has developed in the job market, with most employment opportunities at the lowest and highest levels and few jobs for those with mid-level skills and education. At one end, there has been strong demand for low-skilled, low-paying jobs in industries like food service and retail. On the other end, some research shows that in certain fields there has been a steadily increasing demand for highly skilled and educated professionals, technologists, and managers. These high-skilled positions also tend to be highly paid (Autor 2010).
The fact that some positions are highly paid while others are not is an example of the class system, an economic hierarchy in which movement (both upward and downward) between various rungs of the socioeconomic ladder is possible. Theoretically, at least, the class system as it is organized in the United States is an example of a meritocracy, an economic system that rewards merit––typically in the form of skill and hard work––with upward mobility. A theorist working in the functionalist perspective might point out that this system is designed to reward hard work, which encourages people to strive for excellence in pursuit of reward. A theorist working in the conflict perspective might counter with the thought that hard work does not guarantee success even in a meritocracy, because social capital––the accumulation of a network of social relationships and knowledge that will provide a platform from which to achieve financial success––in the form of connections or higher education are often required to access the high-paying jobs. Increasingly, we are realizing intelligence and hard work aren’t enough. If you lack knowledge of how to leverage the right names, connections, and players, you are unlikely to experience upward mobility.
With so many jobs being outsourced or eliminated by automation, what kind of jobs are there a demand for in the United States? While fishing and forestry jobs are in decline, in several markets jobs are increasing. These include community and social service, personal care and service, finance, computer and information services, and healthcare. The chart below, from the U.S. Bureau of Labor Statistics, illustrates areas of projected growth.
Professions that typically require significant education and training and tend to be lucrative career choices. In particular, jobs that require some type of license or formal certification – be it healthcare, technology, or a trade – usually have a higher salary than those that do not. Service jobs, according to the Bureau of Labor Statistics, can include everything from jobs with the fire department to jobs scooping ice cream (Bureau of Labor Statistics 2019). There is a wide variety of training needed, and therefore an equally large wage potential discrepancy. One of the largest areas of growth by industry, rather than by occupational group (as seen above), is in the health field. This growth is across occupations, from associate-level nurse’s aides to management-level assisted-living staff. As baby boomers age, they are living longer than any generation before, and the growth of this population segment requires an increase in capacity throughout our country’s elder care system, from home healthcare nursing to geriatric nutrition.
Notably, jobs in farming are in decline. This is an area where those with less education traditionally could be assured of finding steady, if low-wage, work. With these jobs disappearing, more and more workers will find themselves untrained for the types of employment that are available.
Another projected trend in employment relates to the level of education and training required to gain and keep a job. As the chart below shows us, growth rates are higher for those with more education. Those with a professional degree or a master’s degree may expect job growth of 20 and 22 percent respectively, and jobs that require a bachelor’s degree are projected to grow 17 percent. At the other end of the spectrum, jobs that require a high school diploma or equivalent are projected to grow at only 12 percent, while jobs that require less than a high school diploma will grow 14 percent. Quite simply, without a degree, it will be more difficult to find a job. It is worth noting that these projections are based on overall growth across all occupation categories, so obviously there will be variations within different occupational areas. However, once again, those who are the least educated will be the ones least able to fulfill the American Dream.
In the past, rising education levels in the United States had been able to keep pace with the rise in the number of education-dependent jobs. However, since the late 1970s, men have been enrolling in college at a lower rate than women, and graduating at a rate of almost 10 percent less. The lack of male candidates reaching the education levels needed for skilled positions has opened opportunities for women, minorities, and immigrants (Wang 2011).
### Women in the Workforce
As discussed in the chapter introduction, women have been entering the workforce in ever-increasing numbers for several decades. They have also been finishing college and going on to earn higher degrees at higher rate than men do. This has resulted in many women being better positioned to obtain high-paying, high-skill jobs (Autor 2010).
While women are getting more and better jobs and their wages are rising more quickly than men's wages are, U.S. Census statistics show that they are still earning only 81 percent of what men are for the same positions (U.S. Census Bureau 2020).
### Immigration and the Workforce
Simply put, people will move from where there are few or no jobs to places where there are jobs, unless something prevents them from doing so. The process of moving to a country is called immigration. Due to its reputation as the land of opportunity, the United States has long been the destination of all skill levels of workers. While the rate decreased somewhat during the economic slowdown of 2008, immigrants, both documented and undocumented, continue to be a major part of the U.S. workforce.
In 2005, before the recession arrived, immigrants made up a historic high of 14.7 percent of the workforce (Lowell et al. 2006). During the 1970s through 2000s, the United States experienced both an increase in college-educated immigrants and in immigrants who lacked a high school diploma. With this range across the spectrum, immigrants are well positioned for both the higher-paid jobs and the low-wage low-skill jobs that are predicted to grow in the next decade (Lowell et al. 2006). In the early 2000s, it certainly seemed that the United States was continuing to live up to its reputation of opportunity. But what about during the recession of 2008, when so many jobs were lost and unemployment hovered close to 10 percent? How did immigrant workers fare then?
The answer is that as of June 2009, when the National Bureau of Economic Research (NEBR) declared the recession officially over, “foreign-born workers gained 656,000 jobs while native-born workers lost 1.2 million jobs” (Kochhar 2010). As these numbers suggest, the unemployment rate that year decreased for immigrant workers and increased for native workers. The reasons for this trend are not entirely clear. Some Pew research suggests immigrants tend to have greater flexibility to move from job to job and that the immigrant population may have been early victims of the recession, and thus were quicker to rebound (Kochhar 2010). Regardless of the reasons, the 2009 job gains are far from enough to keep them inured from the country’s economic woes. Immigrant earnings are in decline, even as the number of jobs increases, and some theorize that increase in employment may come from a willingness to accept significantly lower wages and benefits.
While the political debate is often fueled by conversations about low-wage-earning immigrants, there are actually as many highly skilled––and high-earning––immigrant workers as well. Many immigrants are sponsored by their employers who claim they possess talents, education, and training that are in short supply in the U.S. These sponsored immigrants account for 15 percent of all legal immigrants (Batalova and Terrazas 2010). Interestingly, the U.S. population generally supports these high-level workers, believing they will help lead to economic growth and not be a drain on government services (Hainmueller and Hiscox 2010). On the other hand, undocumented immigrants tend to be trapped in extremely low-paying jobs in agriculture, service, and construction with few ways to improve their situation without risking exposure and deportation.
### Poverty in the United States
When people lose their jobs during a recession or in a changing job market, it takes longer to find a new one, if they can find one at all. If they do, it is often at a much lower wage or not full time. This can force people into poverty. In the United States, we tend to have what is called relative poverty, defined as being unable to live the lifestyle of the average person in your country. This must be contrasted with the absolute poverty that is frequently found in underdeveloped countries and defined as the inability, or near-inability, to afford basic necessities such as food (Byrns 2011).
We cannot even rely on unemployment statistics to provide a clear picture of total unemployment in the United States. First, unemployment statistics do not take into account underemployment, a state in which a person accepts a lower paying, lower status job than their education and experience qualifies them to perform. Second, unemployment statistics only count those:
1. who are actively looking for work
2. who have not earned income from a job in the past four weeks
3. who are ready, willing, and able to work
The unemployment statistics provided by the U.S. government are rarely accurate, because many of the unemployed become discouraged and stop looking for work. Not only that, but these statistics undercount the youngest and oldest workers, the chronically unemployed (e.g., homeless), and seasonal and migrant workers.
A certain amount of unemployment is a direct result of the relative inflexibility of the labor market, considered structural unemployment, which describes when there is a societal level of disjuncture between people seeking jobs and the available jobs. This mismatch can be geographic (they are hiring in one area, but most unemployed live somewhere else), technological (workers are replaced by machines, as in the auto industry), educational (a lack of specific knowledge or skills among the workforce) or can result from any sudden change in the types of jobs people are seeking versus the types of companies that are hiring.
Because of the high standard of living in the United States, many people are working at full-time jobs but are still poor by the standards of relative poverty. They are the working poor. The United States has a higher percentage of working poor than many other developed countries (Brady, Fullerton and Cross 2010). In terms of employment, the Bureau of Labor Statistics defines the working poor as those who have spent at least 27 weeks working or looking for work, and yet remain below the poverty line. Many of the facts about the working poor are as expected: Those who work only part time are more likely to be classified as working poor than those with full-time employment; higher levels of education lead to less likelihood of being among the working poor; and those with children under 18 are four times more likely than those without children to fall into this category. In 2009, the working poor included 10.4 million Americans, up almost 17 percent from 2008 (U.S. Bureau of Labor Statistics 2011).
Most developed countries protect their citizens from absolute poverty by providing different levels of social services such as unemployment insurance, welfare, food assistance, and so on. They may also provide job training and retraining so that people can reenter the job market. In the past, the elderly were particularly vulnerable to falling into poverty after they stopped working; however, pensions, retirement plans, and Social Security were designed to help prevent this. A major concern in the United States is the rising number of young people growing up in poverty. Growing up poor can cut off access to the education and services people need to move out of poverty and into stable employment. As we saw, more education was often a key to stability, and those raised in poverty are the ones least able to find well-paying work, perpetuating a cycle.
Another notion important to sociologists and citizens is the expense of being poor. In a practical sense, people with more money on hand, better credit, a more stable income, and reliable insurance can purchase items or services in different ways than people who lack those things. For example, someone with a higher income can pay bills more reliably, as well as have more credit extended to them through credit cards or loans. When it comes time for those people to purchase a car, for example, they can likely negotiate a lower monthly payment or less money down. In an even more simplistic situation, people with more spending money can buy groceries in bulk, spending far less per unit than those who must purchase smaller portions. The single greatest expense for most adults is housing; beyond its significant portion of a family's expenses, housing drives many other costs, such as transportation (how close does someone live to the places they need to go), childcare, and other areas. And people in poverty pay significantly more for their housing than others – sometimes 70-80 percent of their total income. Those with fewer resources are also more likely to rent rather than own, so they do not build credit in the same way, nor do they have the opportunity to sell the property later and utilize their equity (Nobles 2019).
The ways that governments, organizations, individuals, and society as a whole help the poor are matters of significant debate, informed by extensive study. Sociologists and other professionals contribute to these conversations and provide evidence of the impacts of these circumstances and interventions to change them. The decisions made on these issues have a profound effect on working in the United States.
### Summary
The job market in the United States is meant to be a meritocracy that creates social stratifications based on individual achievement. Economic forces, such as outsourcing and automation, are polarizing the workforce, with most job opportunities being either low-level, low-paying manual jobs or high-level, high-paying jobs based on abstract skills. Women's role in the workforce has increased, although women have not yet achieved full equality. Immigrants play an important role in the U.S. labor market. The changing economy has forced more people into poverty even if they are working. Welfare, Social Security, and other social programs exist to protect people from the worst effects of poverty.
### Section Quiz
### Short Answer
### Further Research
The role of women in the workplace is constantly changing. To learn more, check out this page on the U.S. Department of Labor's web site.
To see some jobs and employment trends for the next decade, check out the Employment Projections Program of the U.S. Bureau of Labor Statistics.
### References
Autor, David. 2010. “The Polarization of Job Opportunities in the U.S. Labor Market Implications for Employment and Earnings.” MIT Department of Economics and National Bureau of Economic Research, April. Retrieved February 15, 2012 (http://econ-www.mit.edu/files/5554).
Batalova, Jeanne, and Aaron Terrazas. 2010. “Frequently Requested Statistics on Immigrants and Immigration in the United States.” Migration Policy Institute. Retrieved February 6, 2012 (http://www.migrationinformation.org/USfocus/display.cfm?id=818).
Brady, David, Andrew Fullerton, and Jennifer Moren Cross. 2010. “More Than Just Nickels and Dimes: A Cross-National Analysis of Working Poverty in Affluent Democracies.” Social Problems 57:559–585. Retrieved February 15, 2012 (http://www.soc.duke.edu/~brady/web/Bradyetal2010.pdf).
DeNavas-Walt, Carmen, and Bernadette D. Proctor. 2013. "Income and Poverty in the United States: 2013." U.S. Census Bureau. Retrieved December 15, 2014. (http://www.census.gov/content/dam/Census/library/publications/2014/demo/p60-249.pdf).
Hainmueller, Jens, and Michael J. Hiscox. 2010. “Attitudes Toward Highly Skilled and Low-Skilled Immigration: Evidence from a Survey Experiment.” American Political Science Review 104:61–84.
Holland, Laurence H.M. and David M. Ewalt. 2006. “Making Real Money in Virtual Worlds,” Forbes, August 7. Retrieved January 30, 2012 (http://www.forbes.com/2006/08/07/virtual-world-jobs_cx_de_0807virtualjobs.html).
Kochhar, Rokesh. 2010. “After the Great Recession: Foreign Born Gain Jobs; Native Born Lose Jobs.” Pew Hispanic Center, October 29. Retrieved January 29, 2012 (http://pewresearch.org/pubs/1784/great-recession-foreign-born-gain-jobs-native-born-lose-jobs).
Lowell, Lindsay B., Julia Gelatt, and Jeanne Batalova. 2006. “Immigrants and Labor Force Trends: the Future, Past, and Present.” Migration Policy Institute Insight No. 17. Retrieved February 6, 2012 (http://www.migrationpolicy.org/ITFIAF/TF17_Lowell.pdf).
Nobles, Allison. 2019. "Poverty is Expensive." The Society Pages. November 27 2019. (https://thesocietypages.org/trot/2019/11/27/poverty-is-expensive/)
U.S. Bureau of Labor Statistics. 2010. Occupational Outlook Handbook, 2006–2007 ed. Retrieved from February 15, 2012 (www.bls.gov/oco).
U.S. Bureau of Labor Statistics. 2010. “Overview of the 2008-2018 Projections.” Occupational Outlook Handbook, 2010–2011 ed. Retrieved February 15, 2012 (http://www.bls.gov/oco/oco2003.htm#industry).
U.S. Bureau of Labor Statistics. 2011. “A Profile of the Working Poor, 2009.” Retrieved January 25, 2012 (www.bls.gov/cps/cpswp2009.pdf).
U.S Bureau of Labor Statistics. 2012. "Employment Projections–2010–20." U.S. Department of Labor. Retrieved December 15, 2014. (http://www.bls.gov/news.release/archives/ecopro_02012012.pdf).
U.S. Bureau of Labor Statistics. 2013. "Occupational Employment Projections to 2022." Department of Labor. Retrieved December 15, 2014. (http://www.bls.gov/opub/mlr/2013/article/pdf/occupational-employment-projections-to-2022.pdf).
U.S. Bureau of Labor Statistics. 2013. "Table 7: Employment by Summary Education and Training Assignment, 2012 and Projected 2022." United States Department of Labor. Retrieved December 15, 2014. (http://www.bls.gov/news.release/ecopro.t07.html).
U.S. Census Bureau. 2010. “Income, Poverty, and Health Insurance Coverage in the United States.” Retrieved February 15, 2012 (http://www.census.gov/prod/2011pubs/p60-239.pdf).
Wang, Wendy and Kim Parker. 2011. “Women See Value and Benefit of College; Men Lag Behind on Both Fronts.” Pew Social and Demographic Trends, August 17. Retrieved January 30, 2012 (http://www.pewsocialtrends.org/2011/08/17/women-see-value-and-benefits-of-college-men-lag-on-both-fronts-survey-finds/5/#iv-by-the-numbers-gender-race-and-education).
Wheaton, Sarah. 2011. “Perry Repeats Socialist Charge Against Obama Policies.” New York Times, September 15. Retrieved January 30, 2012 (http://thecaucus.blogs.nytimes.com/2011/09/15/perry-repeats-socialist-charge-against-obama-policies). |
# Health and Medicine
## Introduction
On March 19, 2014 a "mystery" hemorrhagic fever outbreak occurred in Liberia and Sierra Leone. This outbreak was later confirmed to be Ebola, a disease first discovered in what is now the Democratic Republic of Congo. The 2014-2016 outbreak sickened more than 28,000 people and left more than 11,000 dead (CDC 2020).
For the people in West Africa, the outbreak was personally tragic and terrifying. In much of the rest of the world, the outbreak increased tensions, but did not change anyone's behavior. Infection of U.S. medical staff (both in West Africa and at home) led to fear and distrust, and restrictions on flights from West Africa was one proposed way to stop the spread of the disease. Ebola first entered the United States via U.S. missionary medical staff who were infected in West Africa and then transported home for treatment. Several other Ebola outbreaks occurred in West Africa in subsequent years, killing thousands of people.
Six years after the massive 2014 epidemic, the people of West Africa faced another disease, but this time they were not alone. The Coronavirus pandemic swept across the globe in a matter of months. While some countries managed the disease far better than others, it affected everyone. Highly industrialized countries, such as China, Italy, and the United States, were early centers of the outbreak. Brazil and India had later increases, as did the U.K. and Russia. Most countries took measures that were considered extreme—closing their borders, forcing schools and businesses to close, transforming their people's lives. Other nations went further, completely shutting down at the discovery of just a few cases. And some countries had mixed responses, typically resulting in high rates of infection and overwhelming losses of life. In Brazil and the United States, for example, political leaders and large swaths of the populations rejected measures to contain the virus. By the time vaccines became widely available, those two countries had the highest numbers of coronavirus death worldwide.
Did the world learn from the Ebola virus epidemics? Or did only parts of it learn? Prior to the United States facing the worst COVID-19 outbreak in the world, the government shut down travel, as did many countries in Europe. This was certainly an important step, but other measures fell short; conflicting messages about mask wearing and social distancing became political weapons amid the country's Presidential election, and localized outbreaks and spikes of deaths were continually traced to gatherings that occurred against scientific guidance. Brazil's president actively disputed medical opinions, rejected any travel or business restrictions, and was in conflict with many people in his own government (even his political allies); with Brazil's slower pace of vaccination compared to the U.S., it saw a steep increase in cases and deaths just as the United States' numbers started to decline.
Both those opposed to heavy restrictions and those who used them to fight the disease acknowledge that the impacts went far beyond physical health. Families shattered by the loss of a loved one had to go through the pain without relatives to support them at funerals or other gatherings. Many who recovered from the virus had serious health issues to contend with, while other people who delayed important treatments had larger problems than they normally would have. Fear, isolation, and strained familial relationships led to emotional problems. Many families lost income. Learning was certainly impacted as education practices went through sudden shifts. The true outcomes will likely not be fully understood for years after the pandemic is under control.
So now, after the height of the coronavirus pandemic, what does “health” mean to you? Does your opinion of it differ from your pre-COVID attitudes? Many people who became severely ill or died from COVID had other health issues (known as comorbidities) such as hypertension and obesity. Do you know people whose attitudes about their general health changed? Do you know people who are more or less suspicious of the government, more or less likely to listen to doctors or scientists? What do you think will be the best way to prevent illness and death should another pandemic strike?
Medical sociology is the systematic study of how humans manage issues of health and illness, disease and disorders, and healthcare for both the sick and the healthy. Medical sociologists study the physical, mental, and social components of health and illness. Major topics for medical sociologists include the doctor/patient relationship, the structure and socioeconomics of healthcare, and how culture impacts attitudes toward disease and wellness.
### References
ABC News Health News. "Ebola in America, Timeline of a Deadly Virus." Retrieved Oct. 23rd, 2014 (http://abcnews.go.com/Health/ebola-america-timeline/story?id=26159719).
Centers for Disease Control. 2011b. “Pertussis.” The Centers for Disease Control and Prevention. Retrieved December 15, 2011 (http://www.cdc.gov/pertussis/outbreaks.html).
Centers for Disease Control. 2020. "What Is Ebola Virus Disease." (https://www.cdc.gov/vhf/ebola/about.html)
Conrad, Peter, and Kristin Barker. 2010. “The Social Construction of Illness: Key Insights and Policy Implications.” Journal of Health and Social Behavior 51:67–79.
CNN. 2011. “Retracted Autism Study an 'Elaborate Fraud,' British Journal Finds.” CNN, January 5. Retrieved December 16, 2011 (http://www.cnn.com/2011/HEALTH/01/05/autism.vaccines/index.html).
Devlin, Kate. 2008. “Measles worry MMR as vaccination rates stall.” The Telegraph, September 24. Retrieved January 19, 2012 (http://www.telegraph.co.uk/news/uknews/3074023/Measles-worries-as-MMR-vaccination-rates-stall.html).
Sugerman, David E., Albert E. Barskey, Maryann G. Delea, Ismael R. Ortega-Sanchez, Daoling Bi, Kimberly J. Ralston, Paul A. Rota, Karen Waters-Montijo, and Charles W. LeBaron. 2010. “Measles Outbreak in a Highly Vaccinated Population, San Diego, 2008: Role of the Intentionally Undervaccinated.” Pediatrics 125(4):747–755. Retrieved December 16, 2011 (http://www.pediatricsdigest.mobi/content/125/4/747.full).
World Health Organization. 2014. "Global Alert and Response." Retrieved Oct. 23rd 2014 (http://www.who.int/csr/disease/ebola/en/).
Zacharyczuk, Colleen. 2011. “Myriad causes contributed to California pertussis outbreak.” Thorofar, NJ: Pediatric Supersite. Retrieved December 16, 2011 (http://www.pediatricsupersite.com/view.aspx?rid=90516). |
# Health and Medicine
## The Social Construction of Health
The social construction of health is a major research topic within medical sociology. At first glance, the concept of a social construction of health does not seem to make sense. After all, if disease is a measurable, physiological problem, then there can be no question of socially constructing disease, right? Well, it’s not that simple. The idea of the social construction of health emphasizes the socio-cultural aspects of the discipline’s approach to physical, objectively definable phenomena.
Sociologists Conrad and Barker (2010) offer a comprehensive framework for understanding the major findings of the last fifty years of development in this concept. Their summary categorizes the findings in the field under three subheadings: the cultural meaning of illness, the social construction of the illness experience, and the social construction of medical knowledge.
### The Cultural Meaning of Illness
Many medical sociologists contend that illnesses have both a biological and an experiential component and that these components exist independently of each other. Our culture, not our biology, dictates which illnesses are stigmatized and which are not, which are considered disabilities and which are not, and which are deemed contestable (meaning some medical professionals may find the existence of this ailment questionable) as opposed to definitive (illnesses that are unquestionably recognized in the medical profession) (Conrad and Barker 2010).
For instance, sociologist Erving Goffman (1963) described how social stigmas hinder individuals from fully integrating into society. In essence, Goffman (1963) suggests we might view illness as a stigma that can push others to view the ill in an undesirable manner. The stigmatization of illness often has the greatest effect on the patient and the kind of care they receive. Many contend that our society and even our healthcare institutions discriminate against certain diseases—like mental disorders, AIDS, sexually transmitted diseases, and skin disorders (Sartorius 2007). Facilities for these diseases may be sub-par; they may be segregated from other healthcare areas or relegated to a poorer environment. The stigma may keep people from seeking help for their illness, making it worse than it needs to be.
Contested illnesses are those that are questioned or questionable by some medical professionals. Disorders like fibromyalgia or chronic fatigue syndrome may be either true illnesses or only in the patients’ heads, depending on the opinion of the medical professional. This dynamic can affect how a patient seeks treatment and what kind of treatment they receive.
### The Social Construction of the Illness Experience
The idea of the social construction of the illness experience is based on the concept of reality as a social construction. In other words, there is no objective reality; there are only our own perceptions of it. The social construction of the illness experience deals with such issues as the way some patients control the manner in which they reveal their diseases and the lifestyle adaptations patients develop to cope with their illnesses.
In terms of constructing the illness experience, culture and individual personality both play a significant role. For some people, a long-term illness can have the effect of making their world smaller, more defined by the illness than anything else. For others, illness can be a chance for discovery, for re-imaging a new self (Conrad and Barker 2007). Culture plays a huge role in how an individual experiences illness. Widespread diseases like AIDS or breast cancer have specific cultural markers that have changed over the years and that govern how individuals—and society—view them.
Today, many institutions of wellness acknowledge the degree to which individual perceptions shape the nature of health and illness. Regarding physical activity, for instance, the Centers for Disease Control (CDC) recommends that individuals use a standard level of exertion to assess their physical activity. This Rating of Perceived Exertion (RPE) gives a more complete view of an individual’s actual exertion level, since heartrate or pulse measurements may be affected by medication or other issues (Centers for Disease Control 2011a). Similarly, many medical professionals use a comparable scale for perceived pain to help determine pain management strategies.
### The Social Construction of Medical Knowledge
Conrad and Barker show how medical knowledge is socially constructed; that is, it can both reflect and reproduce inequalities in gender, class, race, and ethnicity. Conrad and Barker (2011) use the example of the social construction of women’s health and how medical knowledge has changed significantly in the course of a few generations. For instance, in the early nineteenth century, pregnant women were discouraged from driving or dancing for fear of harming the unborn child, much as they are discouraged, with more valid reason, from smoking or drinking alcohol today.
### Summary
Medical sociology is the systematic study of how humans manage issues of health and illness, disease and disorders, and healthcare for both the sick and the healthy. The social construction of health explains how society shapes and is shaped by medical ideas.
### Section Quiz
### Short Answer
### Further Research
Read this article, which discusses the measures nations and people may take to prevent or manage future pandemics. It contains many links to international efforts and studies. What do you think about our commitment to these steps?
### References
Begos, Kevin. 2011. “Pinkwashing For Breast Cancer Awareness Questioned.” Retrieved December 16, 2011 (http://www.huffingtonpost.com/2011/10/11/breast-cancer-pink-pinkwashing_n_1005906.html).
Centers for Disease Control. 2011a. “Perceived Exertion (Borg Rating of Perceived Exertion Scale).” Centers for Disease Control and Prevention. Retrieved December 12, 2011 (http://www.cdc.gov/physicalactivity/everyone/measuring/exertion.html).
Conrad, Peter, and Kristin Barker. 2010. “The Social Construction of Illness: Key Insights and Policy Implications.” Journal of Health and Social Behavior 51:67–79.
Goffman, Erving. 1963. Stigma: Notes on the Management of Spoiled Identity. London: Penguin.
Hutchison, Courtney. 2010. “Fried Chicken for the Cure?” ABC News Medical Unit. Retrieved December 16, 2011 (http://abcnews.go.com/Health/Wellness/kfc-fights-breast-cancer-fried-chicken/story?id=10458830#.Tutz63ryT4s).
Sartorius, Norman. 2007. “Stigmatized Illness and Health Care.” The Croatian Medical Journal 48(3):396–397. Retrieved December 12, 2011 (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2080544/).
Think Before You Pink. 2012. “Before You Buy Pink.” Retrieved December 16, 2011 (http://thinkbeforeyoupink.org/?page_id=13).
“Vaccines and Immunizations.” 2011. The Centers for Disease Control and Prevention. Retrieved December 16, 2011 (http://www.cdc.gov/vaccines/default.htm).
World Health Organization. .n.d. “Definition of Health.” Retrieved December 12, 2011 (http://www.who.int/about/definition/en/print.html).
World Health Organization: “Health Promotion Glossary Update.” Retrieved December 12, 2011 (http://www.who.int/healthpromotion/about/HPR%20Glossary_New%20Terms.pdf). |
# Health and Medicine
## Global Health
Social epidemiology is the study of the causes and distribution of diseases. Social epidemiology can reveal how social problems are connected to the health of different populations. These epidemiological studies show that the health problems of high-income nations differ from those of low-income nations, but also that diseases and their diagnosis are changing. Cardiovascular disease, for example, is now the both most prevalent disease and the disease most likely to be fatal in lower-income countries. And globally, 70 percent of cardiovascular disease cases and deaths are due to modifiable risks (Dagenais 2019).
Some theorists differentiate among three types of countries: core nations, semi-peripheral nations, and peripheral nations. Core nations are those that we think of as highly developed or industrialized, semi-peripheral nations are those that are often called developing or newly industrialized, and peripheral nations are those that are relatively undeveloped. While the most pervasive issue in the U.S. healthcare system is affordable access to healthcare, other core countries have different issues, and semi-peripheral and peripheral nations are faced with a host of additional concerns. Reviewing the status of global health offers insight into the various ways that politics and wealth shape access to healthcare, and it shows which populations are most affected by health disparities.
### Health in High-Income Nations
Obesity, which is on the rise in high-income nations, has been linked to many diseases, including cardiovascular problems, musculoskeletal problems, diabetes, and respiratory issues. According to the Organization for Economic Cooperation and Development (2011), obesity rates are rising in all countries, with the greatest gains being made in the highest-income countries. The United States has the highest obesity rate at 42 percent; some of these people are considered severely obese, which occurs in 9 percent of U.S. adults (Hales 2020).
Wallace Huffman and his fellow researchers (2006) contend that several factors are contributing to the rise in obesity in developed countries:
1. Improvements in technology and reduced family size have led to a reduction of work to be done in household production.
2. Unhealthy market goods, including processed foods, sweetened drinks, and sweet and salty snacks are replacing home-produced goods.
3. Leisure activities are growing more sedentary, for example, computer games, web surfing, and television viewing.
4. More workers are shifting from active work (agriculture and manufacturing) to service industries.
5. Increased access to passive transportation has led to more driving and less walking.
Obesity and weight issues have significant societal costs, including lower life expectancies and higher shared healthcare costs.
While ischemic heart disease is the single most prevalent cause of death in higher-income countries, cancers of all types combine to be a higher overall cause of death. Cancer accounts for twice as many deaths as cardiovascular disease in higher-income countries (Mahase 2019).
### Health in Low-Income Nations
In peripheral nations with low per capita income, it is not the cost of healthcare that is the most pressing concern. Rather, low-income countries must manage such problems as infectious disease, high infant mortality rates, scarce medical personnel, and inadequate water and sewer systems. Due to such health concerns, low-income nations have higher rates of infant mortality and lower average life spans.
One of the biggest contributors to medical issues in low-income countries is the lack of access to clean water and basic sanitation resources. According to a 2014 UNICEF report, almost half of the developing world’s population lacks improved sanitation facilities. The World Health Organization (WHO) tracks health-related data for 193 countries, and organizes them by region. In their 2011 World Health Statistics report, they document the following statistics:
1. Globally in 2019, the rate of mortality for children under five was 38 per 1,000 live births, which is a dramatic change from previous decades. (In 1990, the rate was 93 deaths per 1,000 births (World Health Organization 2020.)) In low-income countries, however, that rate is much higher. The child mortality rate in low-income nations was 11 times higher than that of high-income countries—76 deaths per 1,000 births compared to 7 deaths per 1,000 births (Keck 2020). To consider it regionally, the highest under-five mortality rate remains in the WHO African Region (74 per 1000 live births), around 9 times higher than that in the WHO European Region (8 per 1000 live births) (World Health Organization 2021).
2. The most frequent causes of death in children under five years old are pneumonia, diarrhea, congenital anomalies, preterm birth complications, birth asphyxia/trauma, and malaria, all of which can be prevented or treated with affordable interventions including immunization, adequate nutrition, safe water and food and quality care by a trained health provider when needed.
The availability of doctors and nurses in low-income countries is one-tenth that of nations with a high income. Challenges in access to medical education and access to patients exacerbate this issue for would-be medical professionals in low-income countries (World Health Organization 2011).
### Summary
Social epidemiology is the study of the causes and distribution of diseases. From a global perspective, the health issues of high-income nations tend toward diseases like cancer as well as those that are linked to obesity, like heart disease, diabetes, and musculoskeletal disorders. Low-income nations are more likely to contend with cardiovascular disease, infectious disease, high infant mortality rates, scarce medical personnel, and inadequate water and sanitation systems.
### Section Quiz
### Short Answer
### Further Research
Study this map on global life expectancies. What trends do you notice?
### References
Bromet et al. 2011. “Cross-National Epidemiology of DSM-IV Major Depressive Episode.” BMC Medicine 9:90. Retrieved December 12, 2011 (http://www.biomedcentral.com/1741-7015/9/90).
Dagenais, Gilles and Darryl P Leong, PhD and Sumathy Rangarajan, MSc and Fernando Lanas, PhD and Prof Patricio Lopez-Jaramillo, PhD and Prof Rajeev Gupta, PhD. 2019. "Variations in common diseases, hospital admissions, and deaths in middle-aged adults in 21 countries from five continents (PURE): a prospective cohort study." September 8 2019. (https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(19)32007-0/fulltext#articleInformation)
Hales CM, Carroll MD, Fryar CD, Ogden CL. Prevalence of obesity and severe obesity among adults: United States, 2017–2018. NCHS Data Brief, no 360. Hyattsville, MD: National Center for Health Statistics. 2020
Huffman, Wallace E., Sonya Kostova Huffman, AbebayehuTegene, and KyrreRickertsen. 2006. “The Economics of Obesity-Related Mortality among High Income Countries” International Association of Agricultural Economists. Retrieved December 12, 2011 (http://purl.umn.edu/25567).
Mahase, Elisabeth. 2019. "Cancer overtakes CVD to become leading cause of death in high income countries" The BMJ. September 3 2019. (https://www.bmj.com/content/366/bmj.l5368)
Organization for Economic Cooperation and Development. 2011. Health at a Glance 2011: OECD Indicators. OECD Publishing. Retrieved December 12, 2011 (http://dx.doi.org/10.1787/health_glance-2011-en).
UNICEF. 2011. “Water, Sanitation and Hygiene.” Retrieved December 12, 2011 (http://www.unicef.org/wash).
World Health Organization. 2011. “World Health Statistics 2011.” Retrieved December 12, 2011 (http://www.who.int/gho/publications/world_health_statistics/EN_WHS2011_Part1.pdf). |
# Health and Medicine
## Health in the United States
Health in the United States is a complex and often contradictory issue. On the one hand, as one of the wealthiest nations, the United States fares well in health comparisons with the rest of the world. However, the United States also lags behind almost every industrialized country in terms of providing care to all its citizens. The following sections look at different aspects of health in the United States.
### Health by Race and Ethnicity
When looking at the social epidemiology of the United States, it is hard to miss the disparities among races. The discrepancy between Black and White Americans shows the gap clearly; in 2018, the average life expectancy for White males was approximately five years longer than for Black males: 78.8 compared to 74.7 (Wamsley 2021). (Note that in 2020 life expectancies of all races declined further, though the unprecedented COVID-19 pandemic was a significant cause.) Other indicates show a similar disparity. The 2018 infant mortality rates for different races and ethnicities are as follows:
1. Non-Hispanic Black people: 10.8
2. Native Hawaiian people or other Pacific Islanders: 9.4
3. Native American/Alaska Native people: 8.2
4. Hispanic people: 4.9
5. Non-Hispanic White people: 4.6
6. Asian and Asian American people: 3.6 (Centers for Disease Control 2021)
According to a report from the Henry J. Kaiser Foundation (2007), African Americans also have higher incidence of several diseases and causes of mortality, from cancer to heart disease to diabetes. In a similar vein, it is important to note that ethnic minorities, including Mexican Americans and Native Americans, also have higher rates of these diseases and causes of mortality than White people.
Lisa Berkman (2009) notes that this gap started to narrow during the Civil Rights movement in the 1960s, but it began widening again in the early 1980s. What accounts for these perpetual disparities in health among different ethnic groups? Much of the answer lies in the level of healthcare that these groups receive. The National Healthcare Disparities Report shows that even after adjusting for insurance differences, racial and ethnic minority groups receive poorer quality of care and less access to care than dominant groups. The Report identified these racial inequalities in care:
1. Black people, Native Americans, and Alaska Native people received worse care than Whites for about 40 percent of quality measures.
2. Hispanic people, Native Hawaiian people, and Pacific Islanders received worse care than White people for more than 30 percent of quality measures.
3. Asian people received worse care than White people for nearly 30 percent of quality measures but better care for nearly 30 percent of quality measures (Agency for Healthcare Research and Quality 2020).
### Health by Socioeconomic Status
Discussions of health by race and ethnicity often overlap with discussions of health by socioeconomic status, since the two concepts are intertwined in the United States. As the Agency for Health Research and Quality (2010) notes, “racial and ethnic minorities are more likely than non-Hispanic whites to be poor or near poor,” so much of the data pertaining to subordinate groups is also likely to be pertinent to low socioeconomic groups. Marilyn Winkleby and her research associates (1992) state that “one of the strongest and most consistent predictors of a person's morbidity and mortality experience is that person's socioeconomic status (SES). This finding persists across all diseases with few exceptions, continues throughout the entire lifespan, and extends across numerous risk factors for disease.” Morbidity is the incidence of disease.
It is important to remember that economics are only part of the SES picture; research suggests that education also plays an important role. Phelan and Link (2003) note that many behavior-influenced diseases like lung cancer (from smoking), coronary artery disease (from poor eating and exercise habits), and AIDS initially were widespread across SES groups. However, once information linking habits to disease was disseminated, these diseases decreased in high SES groups and increased in low SES groups. This illustrates the important role of education initiatives regarding a given disease, as well as possible inequalities in how those initiatives effectively reach different SES groups.
### Health by Gender
Women are affected adversely both by unequal access to and institutionalized sexism in the healthcare industry. According to a recent report from the Kaiser Family Foundation, women experienced a decline in their ability to see needed specialists between 2001 and 2008. In 2008, one quarter of women questioned the quality of their healthcare (Ranji and Salganico 2011). Quality is partially indicated by access and cost. In 2018, roughly one in four (26%) women—compared to one in five (19%) men—reported delaying healthcare or letting conditions go untreated due to cost. Because of costs, approximately one in five women postponed preventive care, skipped a recommended test or treatment, or reduced their use of medication due to cost (Kaiser Family Foundation 2018).
We can see an example of institutionalized sexism in the way that women are more likely than men to be diagnosed with certain kinds of mental disorders. Psychologist Dana Becker notes that 75 percent of all diagnoses of Borderline Personality Disorder (BPD) are for women according to the Diagnostic Statistical Manual of Mental Disorders. This diagnosis is characterized by instability of identity, of mood, and of behavior, and Becker argues that it has been used as a catch-all diagnosis for too many women. She further decries the pejorative connotation of the diagnosis, saying that it predisposes many people, both within and outside of the profession of psychotherapy, against women who have been so diagnosed (Becker).
Many critics also point to the medicalization of women’s issues as an example of institutionalized sexism. Medicalization refers to the process by which previously normal aspects of life are redefined as deviant and needing medical attention to remedy. Historically and contemporaneously, many aspects of women’s lives have been medicalized, including menstruation, premenstrual syndrome, pregnancy, childbirth, and menopause. The medicalization of pregnancy and childbirth has been particularly contentious in recent decades, with many women opting against the medical process and choosing a more natural childbirth. Fox and Worts (1999) find that all women experience pain and anxiety during the birth process, but that social support relieves both as effectively as medical support. In other words, medical interventions are no more effective than social ones at helping with the difficulties of pain and childbirth. Fox and Worts further found that women with supportive partners ended up with less medical intervention and fewer cases of postpartum depression. Of course, access to quality birth care outside the standard medical models may not be readily available to women of all social classes.
### Mental Health and Disability
The treatment received by those defined as mentally ill or disabled varies greatly from country to country. In the post-millennial United States, those of us who have never experienced such a disadvantage take for granted the rights our society guarantees for each citizen. We do not think about the relatively recent nature of the protections, unless, of course, we know someone constantly inconvenienced by the lack of accommodations or misfortune of suddenly experiencing a temporary disability.
### Mental Health
People with mental disorders (a condition that makes it more difficult to cope with everyday life) and people with mental illness (a severe, lasting mental disorder that requires long-term treatment) experience a wide range of effects. According to the National Institute of Mental Health (NIMH), the United States has over 50 million adults with mental illness or mental disorder, or 20 percent of the total adult population. Of these, 13 million have what is considered serious mental illness or mental disorder (5 percent of the adult population); serious mental illness is that which causes impairment or disability (National Institute of Mental Health 2021). Finally, 16.5 percent of children aged 6-17 experienced mental illness or disorder (National Alliance on Mental Illness 2021).
The most common mental disorders in the United States are anxiety disorders. Almost 18 percent of U.S. adults are likely to be affected in a single year, and 28 percent are likely to be affected over the course of a lifetime (Anxiety and Depression Institute of America 2021). It is important to distinguish between occasional feelings of anxiety and a true anxiety disorder. Anxiety is a normal reaction to stress that we all feel at some point, but anxiety disorders are feelings of worry and fearfulness that last for months at a time. Anxiety disorders include obsessive compulsive disorder (OCD), panic disorders, posttraumatic stress disorder (PTSD), and both social and specific phobias.
The second most common mental disorders in the United States are mood disorders; roughly 10 percent of U.S. adults are likely to be affected yearly, while 21 percent are likely to be affected over the course of a lifetime (National Institute of Mental Health 2005). Mood disorders are the most common causes of illness-related hospitalization in the U.S. (Agency for Healthcare Research and Quality 2021). Major mood disorders are depression and dysthymic disorder. Like anxiety, depression might seem like something that everyone experiences at some point, and it is true that most people feel sad or “blue” at times in their lives. A true depressive episode, however, is more than just feeling sad for a short period. It is a long-term, debilitating illness that usually needs treatment to cure. Bipolar disorder is characterized by dramatic shifts in energy and mood, often affecting the individual’s ability to carry out day-to-day tasks. Bipolar disorder used to be called manic depression because of the way people would swing between manic and depressive episodes.
Depending on what definition is used, there is some overlap between mood disorders and personality disorders, which affect 9 percent of people in the United States yearly. A personality disorder is an enduring and inflexible pattern of long duration leading to significant distress or impairment, that is not due to use of substances or another medical condition. In other words, personality disorders cause people to behave in ways that are seen as abnormal to society but seem normal to them.
The diagnosis and classification regarding personality disorders has been evolving and is somewhat controversial. To guide diagnosis and potential treatments of mental disorders, the American Psychological Association publishes the Diagnostic and Statistical Manual on Mental Disorders (DSM). Experts working on the latest version initially proposed changing the categories of personality disorders. However, the final publication retains the original ten categories, but contains an alternate/emerging approach for classifying them. This evolution demonstrates the challenges and the wide array of treating conditions, and also represents areas of difference between theorists, practitioners, governing bodies, and other stakeholders. As discussed in the Sociological Research chapter, study and investigation is a diligent and multi-dimensional process. As the diagnostic application evolves, we will see how their definitions help scholars across disciplines understand the intersection of health issues and how they are defined by social institutions and cultural norms.
Another commonly diagnosed mental disorder is Attention-Deficit/Hyperactivity Disorder (ADHD), which affects 9 percent of U.S. children and 4 percent of adults on a lifetime basis (Danielson 2018). Since ADHD is one of the most common childhood disorders, it is often incorrectly considered only a disease found in children. But ADHD can be a serious issue for adults who either had been diagnosed as children or who are diagnosed as adults. ADHD is marked by difficulty paying attention, difficulty controlling behavior, and hyperactivity. As a result, it can lead to educational and behavioral issues in children, success issues in college, and challenges in workplace and family life. However, there is some social debate over whether such drugs are being overprescribed (American Psychological Association). A significant difficulty in diagnosis, treatment, and societal understanding of ADHD is that it changes in expression based on a wide range of factors, including age (CHADD 2020).
Autism Spectrum Disorders (ASD) encompass a group of developmental brain disorders that are characterized by "deficits in social interaction, verbal and nonverbal communication, and engagement in repetitive behaviors or interests” (National Institute of Mental Health). As of 2021, the CDC estimates that 1 in 54 children has an autism spectrum disorder. Beyond the very high incidence, the rate of diagnosis has been increasing steadily as awareness became more widespread. In 2005, the rate was 1 in 166 children; in 2012 it was 1 in 88 children. The rate of increase and awareness has assisted diagnosis and treatment, but autism is a cause of significant fear among parents and families. Because of its impact on relationships and especially verbal communication, children with autism (and their parents) can be shunned, grossly misunderstood, and mistreated. For example, people with an autism spectrum disorder who cannot verbalize are often assumed to be unintelligent, or are sometimes left out of conversations or activities because others feel they cannot participate. Parents may be reluctant to let their children play with or associate with children with ASD. Adults with ASD go through many of the same misconceptions and mistreatments, such as being denied opportunities or being made to feel unwelcome (Applied Behavior Analysis).
### Disability
Disability refers to a reduction in one’s ability to perform everyday tasks. The World Health Organization makes a distinction between the various terms used to describe disabilities. They use the term impairment to describe the physical limitations, while reserving the term disability to refer to the social limitation.
Before the passage of the Americans with Disabilities Act (ADA) in 1990, people in the United States with disabilities were often excluded from opportunities and social institutions many of us take for granted. This occurred not only through employment and other kinds of discrimination but also through casual acceptance by most people in the United States of a world designed for the convenience of the able-bodied. Imagine being in a wheelchair and trying to use a sidewalk without the benefit of wheelchair-accessible curbs. Imagine as a blind person trying to access information without the widespread availability of Braille. Imagine having limited motor control and being faced with a difficult-to-grasp round door handle. Issues like these are what the ADA tries to address. Ramps on sidewalks, Braille instructions, and more accessible door levers are all accommodations to help people with disabilities.
People with disabilities can be stigmatized by their illnesses. Stigmatization means their identity is spoiled; they are labeled as different, discriminated against, and sometimes even shunned. They are labeled (as an interactionist might point out) and ascribed a master status (as a functionalist might note), becoming “the blind girl” or “the boy in the wheelchair” instead of someone afforded a full identity by society. This can be especially true for people who are disabled due to mental illness or disorders.
As discussed in the section on mental health, many mental health disorders can be debilitating and can affect a person’s ability to cope with everyday life. This can affect social status, housing, and especially employment. According to the Bureau of Labor Statistics (2011), people with a disability had a higher rate of unemployment than people without a disability in 2010: 14.8 percent to 9.4 percent. This unemployment rate refers only to people actively looking for a job. In fact, eight out of ten people with a disability are considered “out of the labor force;” that is, they do not have jobs and are not looking for them. The combination of this population and the high unemployment rate leads to an employment-population ratio of 18.6 percent among those with disabilities. The employment-population ratio for people without disabilities was much higher, at 63.5 percent (U.S. Bureau of Labor Statistics 2011).
### Summary
Although people in the United States are generally in good health compared to less developed countries, the United States is still facing challenging issues such as a prevalence of obesity and diabetes. Moreover, people in the United States of historically disadvantaged racial groups, ethnicities, socioeconomic status, and gender experience lower levels of healthcare. Mental health and disability are health issues that are significantly impacted by social norms.
### Section Quiz
### Short Answer
### Further Research
People with disabilities, disorders, and neurodiversity are often mistreated even by others who do not know the best way to act around them. Children with autism experience this continually. Evaluate this guide from parents of children with autism to learn more about how to treat and think about people with autism.
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Anxiety and Depression Institute of America. 2021. "Facts and Statistics." Retrieved April 1 2021. (https://adaa.org/understanding-anxiety/facts-statistics)
Applied Behavior Analysis. "30 Things Parents of Children on the Autism Spectrum Want You to Know" (https://www.appliedbehavioranalysisprograms.com/things-parents-of-children-on-the-autism-spectrum-want-you-to-know/)
Becker, Dana. n.d. “Borderline Personality Disorder: The Disparagement of Women through Diagnosis.” Retrieved December 13, 2011 (http://www.awpsych.org/index.php?option=com_content&view=article&id=109&catid=74&Itemid=126).
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# Health and Medicine
## Comparative Health and Medicine
There are broad, structural differences among the healthcare systems of different countries. In core nations, those differences might arise in the administration of healthcare, while the care itself is similar. In peripheral and semi-peripheral countries, a lack of basic healthcare administration can be the defining feature of the system. Most countries rely on some combination of modern and traditional medicine. In core countries with large investments in technology, research, and equipment, the focus is usually on modern medicine, with traditional (also called alternative or complementary) medicine playing a secondary role. In the United States, for instance, the American Medical Association (AMA) resolved to support the incorporation of complementary and alternative medicine in medical education. In developing countries, even quickly modernizing ones like China, traditional medicine (often understood as “complementary” by the western world) may still play a larger role.
### U.S. Healthcare
U.S. healthcare coverage can broadly be divided into two main categories: public healthcare (government-funded) and private healthcare (privately funded).
The two main publicly funded healthcare programs are Medicare, which provides health services to people over sixty-five years old as well as people who meet other standards for disability, and Medicaid, which provides services to people with very low incomes who meet other eligibility requirements. Other government-funded programs include service agencies focused on Native Americans (the Indian Health Service), Veterans (the Veterans Health Administration), and children (the Children’s Health Insurance Program).
Private insurance is typically categorized as either employment-based insurance or direct-purchase insurance. Employment-based insurance is health plan coverage that is provided in whole or in part by an employer or union; it can cover just the employee, or the employee and their family. Direct purchase insurance is coverage that an individual buys directly from a private company.
Even with all these options, a sizable portion of the U.S. population remains uninsured. In 2019, about 26 million people, or 8 percent of U.S. residents, had no health insurance. 2020 saw that number go up to 31 million (Keith 2020). Several more million had health insurance for part of the year (Keisler-Starkey 2020). Uninsured people are at risk of both severe illness and also chronic illnesses that develop over time. Fewer uninsured people engage in regular check-ups or preventative medicine, and rely on urgent care for a range of acute health issues.
The number of uninsured people is far lower than in previous decades. In 2013 and in many of the years preceding it, the number of uninsured people was in the 40 million range, or roughly 18 percent of the population. The Affordable Care Act, which came into full force in 2014, allowed more people to get affordable insurance. The uninsured number reached its lowest point in 2016, before beginning to climb again (Garfield 2019).
People having some insurance may mask the fact that they could be underinsured; that is, people who pay at least 10 percent of their income on healthcare costs not covered by insurance or, for low-income adults, those whose medical expenses or deductibles are at least 5 percent of their income (Schoen, Doty, Robertson, and Collins 2011).
Why are so many people uninsured or underinsured? Skyrocketing healthcare costs are part of the issue. While most people get their insurance through their employer, not all employers offer it, especially retail companies or small businesses in which many of the workers may be part time. Finally, for many years insurers could deny coverage to people with pre-existing conditions--previous illnesses or chronic diseases.
The Patient Protection and Affordable Care Act (often abbreviated ACA or nicknamed Obamacare) was a landmark change in U.S. healthcare. Passed in 2010 and fully implemented in 2014, it increased eligibility to programs like Medicaid, helped guarantee insurance coverage for people with pre-existing conditions, and established regulations to make sure that the premium funds collected by insurers and care providers go directly to medical care. It also included an individual mandate, which requires everyone to have insurance coverage by 2014 or pay a penalty. A series of provisions, including significant subsidies, are intended to address the discrepancies in income that are currently contributing to high rates of uninsurance and underinsurance. In 2012 the U.S. Supreme Court upheld the constitutionality of the ACA's individual mandate. 29 million people in the United States have gained health insurance under ACA (Economic Policy Institute 2021).
The ACA remains contentious. The Supreme Court ruled in the case of National Federation of Independent Businesses v. Sebelius in 2012, that states cannot be forced to participate in the PPACA's Medicaid expansion. This ruling opened the door to further challenges to the ACA in Congress and the Federal courts, some state governments, conservative groups and independent businesses. The ACA has been a driving factor in elections and public opinion. In 2010 and 2014, many Republican gains in Congressional seats were related to fierce concern about Obamacare. However, once millions of people were covered by the law and the economy continued to improve, public sentiment and elections swung the other way. Healthcare was the top issue for voters, and desire to preserve the law was credited for many of the Democratic gains in the election, which carried over to 2020.
### Healthcare Elsewhere
Clearly, healthcare in the United States has some areas for improvement. But how does it compare to healthcare in other countries? Many people in the United States are fond of saying that this country has the best healthcare in the world, and while it is true that the United States has a higher quality of care available than many peripheral or semi-peripheral nations, it is not necessarily the “best in the world.” In a report on how U.S. healthcare compares to that of other countries, researchers found that the United States does “relatively well in some areas—such as cancer care—and less well in others—such as mortality from conditions amenable to prevention and treatment” (Docteur and Berenson 2009).
One critique of the Patient Protection and Affordable Care Act is that it will create a system of socialized medicine, a term that for many people in the United States has negative connotations lingering from the Cold War era and earlier. Under a socialized medicine system, the government owns and runs the system. It employs the doctors, nurses, and other staff, and it owns and runs the hospitals (Klein 2009). The best example of socialized medicine is in Great Britain, where the National Health System (NHS) gives free healthcare to all its residents. And despite some U.S. citizens’ knee-jerk reaction to any healthcare changes that hint of socialism, the United States has one socialized system with the Veterans Health Administration.
It is important to distinguish between socialized medicine, in which the government owns the healthcare system, and universal healthcare, which is simply a system that guarantees healthcare coverage for everyone. Germany, Singapore, and Canada all have universal healthcare. People often look to Canada’s universal healthcare system, Medicare, as a model for the system. In Canada, healthcare is publicly funded and is administered by the separate provincial and territorial governments. However, the care itself comes from private providers. This is the main difference between universal healthcare and socialized medicine. The Canada Health Act of 1970 required that all health insurance plans must be “available to all eligible Canadian residents, comprehensive in coverage, accessible, portable among provinces, and publicly administered” (International Health Systems Canada 2010).
Heated discussions about socialization of medicine and managed-care options seem frivolous when compared with the issues of healthcare systems in developing or underdeveloped countries. In many countries, per capita income is so low, and governments are so fractured, that healthcare as we know it is virtually non-existent. Care that people in developed countries take for granted—like hospitals, healthcare workers, immunizations, antibiotics and other medications, and even sanitary water for drinking and washing—are unavailable to much of the population. Organizations like Doctors Without Borders, UNICEF, and the World Health Organization have played an important role in helping these countries get their most basic health needs met.
WHO, which is the health arm of the United Nations, set eight Millennium Development Goals (MDGs) in 2000 with the aim of reaching these goals by 2015. Some of the goals deal more broadly with the socioeconomic factors that influence health, but MDGs 4, 5, and 6 all relate specifically to large-scale health concerns, the likes of which most people in the United States will never contemplate. MDG 4 is to reduce child mortality, MDG 5 aims to improve maternal health, and MDG 6 strives to combat HIV/AIDS, malaria, and other diseases. The goals may not seem particularly dramatic, but the numbers behind them show how serious they are.
For MDG 4, the WHO reports that 2009 infant mortality rates in “children under 5 years old in the WHO African Region (127 per 1000 live births) and in low-income countries (117 per 1000 live births) [had dropped], but they were still higher than the 1990 global level of 89 per 1000 live births” (World Health Organization 2011). The fact that these deaths could have been avoided through appropriate medicine and clean drinking water shows the importance of healthcare.
Much progress has been made on MDG 5, with maternal deaths decreasing by 34 percent. However, almost all maternal deaths occurred in developing countries, with the African region still experiencing high numbers (World Health Organization 2011).
On MDG 6, the WHO is seeing some decreases in per capita incidence rates of malaria, tuberculosis, HIV/AIDS, and other diseases. However, the decreases are often offset by population increases (World Health Organization 2011). Again, the lowest-income countries, especially in the African region, experience the worst problems with disease. An important component of disease prevention and control is epidemiology, or the study of the incidence, distribution, and possible control of diseases. Fear of Ebola contamination, primarily in Western Africa but also to a smaller degree in the United States, became national news in the summer and fall of 2014.
### Summary
There are broad, structural differences among the healthcare systems of different countries. In core nations, those differences include publicly funded healthcare, privately funded healthcare, and combinations of both. In peripheral and semi-peripheral countries, a lack of basic healthcare administration can be the defining feature of the system.
### Section Quiz
### Short Answer Quiz
### Further Research
Project Mosquito Net says that mosquito nets sprayed with insecticide can reduce childhood malaria deaths by half.
### References
Anders, George. 1996. Health Against Wealth: HMOs and the Breakdown of Medical Trust. Boston: Houghton Mifflin.
Centers for Disease Control and Prevention. 2014 "Attention Deficit/Hyperactivity Disorder (ADHD) Data and Statistics." Retrieved October 13, 2014 (http://www.cdc.gov/ncbddd/adhd/data.html)
Docteur, Elizabeth, and Robert A. Berenson. 2009. “How Does the Quality of U.S. Health Care Compare Internationally?” Timely Analysis of Immediate Health Policy Issues 9:1–14.
Economic Policy Institute. 2021. "How would repealing the ACA affect healthcare and jobs in your state?" (https://www.epi.org/aca-obamacare-repeal-impact/)
Garfield, Rachel and Orgera, Kendal and Damico, Anthony. 2019. "The Uninsured and the ACA: A Primer - Key Facts about Health Insurance and the Uninsured amidst Changes to the Affordable Care Act" Faiser Family Foundation. (https://www.kff.org/report-section/the-uninsured-and-the-aca-a-primer-key-facts-about-health-insurance-and-the-uninsured-amidst-changes-to-the-affordable-care-act-how-many-people-are-uninsured/)
Kaiser Family Foundation. 2011. “Health Coverage of Children: The Role of Medicaid and CHIP.” Retrieved December 13, 2011 (http://www.kff.org/uninsured/upload/7698-05.pdf).
Kaiser Family Foundation. 2010. “International Health Systems: Canada.” Retrieved December 14, 2011 (http://www.kaiseredu.org/Issue-Modules/International-Health-Systems/Canada.aspx).
Keisler-Starkey, Katherine and Bunch, Lisa. 2020. "Health Insurance Coverage In the United States 2019." United States Census Bureau. (https://www.census.gov/library/publications/2020/demo/p60-271.html)
Keith, Katie. 2020. "Tracking the uninsured rate in 2019-20." Health Affairs. October 7 2020. (https://www.healthaffairs.org/do/10.1377/hblog20201007.502559/full/)
Klein, Ezra. 2009. “Health Reform for Beginners: The Difference between Socialized Medicine, Single-Payer Health Care, and What We'll Be Getting.” The Washington Post, December 14. Retrieved December 15, 2011 (http://www.bloomberg.com/news/2011-12-15/don-t-let-death-panels-kill-a-better-way-to-die-commentary-by-ezra-klein.html).
Kogan, Richard. 2011. “Program Cuts Under a Balanced Budget Amendment: How Severe Might They Be?” Center on Budget and Policy Priorities. Retrieved December 15, 2011 (http://www.cbpp.org/cms/?fa=view&id=3619).
Pear, Robert. 2011. “In Cuts to Health Programs, Experts See Difficult Task in Protecting Patients.” The New York Times, September 20. Retrieved December 13, 2011 (http://www.nytimes.com/2011/09/21/us/politics/wielding-the-ax-on-medicaid-and-medicare-without-wounding-the-patient.html).
Rooney, Kate and Moyer, Liz. 2018. "Health care topped the economy as the biggest issue for voters now, here’s why." CNBC. November 8, 2018. (https://www.cnbc.com/2018/11/07/healthcare-topped-the-economy-as-the-biggest-issue-for-voters-now-heres-why.html)
Schoen, C., M.M. Doty, R.H. Robertson, and S.R. Collins. 2011. "Affordable Care Act Reforms Could Reduce the Number of Underinsured U.S. Adults by 70 Percent." Health Affairs 30(9):1762–71. Retrieved December 13, 2011 (http://www.commonwealthfund.org/Publications/In-the-Literature/2011/Sep/Reduce-Uninsured.aspx).
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World Health Organization. 2014. "Ebola Virus Disease Fact Sheet, Updated September 2014." Retrieved October 19, 2014 (http://www.who.int/mediacentre/factsheets/fs103/en/). |
# Health and Medicine
## Theoretical Perspectives on Health and Medicine
Each of the three major theoretical perspectives approaches the topics of health, illness, and medicine differently. You may prefer just one of the theories that follow, or you may find that combining theories and perspectives provides a fuller picture of how we experience health and wellness.
### Functionalism
According to the functionalist perspective, health is vital to the stability of the society, and therefore sickness is a sanctioned form of deviance. Talcott Parsons (1951) was the first to discuss this in terms of the sick role: patterns of expectations that define appropriate behavior for the sick and for those who take care of them.
According to Parsons, the sick person has a specific role with both rights and responsibilities. To start with, the sick person has not chosen to be sick and should not be treated as responsible for her condition. The sick person also has the right of being exempt from normal social roles; they are not required to fulfill the obligation of a well person and can avoid her normal responsibilities without censure. However, this exemption is temporary and relative to the severity of the illness. The exemption also requires legitimation by a physician; that is, a physician must certify that the illness is genuine.
The responsibility of the sick person is twofold: to try to get well and to seek technically competent help from a physician. If the sick person stays ill longer than is appropriate (malingers), they may be stigmatized.
Parsons argues that since the sick are unable to fulfill their normal societal roles, their sickness weakens the society. Therefore, it is sometimes necessary for various forms of social control to bring the behavior of a sick person back in line with normal expectations. In this model of health, doctors serve as gatekeepers, deciding who is healthy and who is sick—a relationship in which the doctor has all the power. But is it appropriate to allow doctors so much power over deciding who is sick? And what about people who are sick, but are unwilling to leave their positions for any number of reasons (personal/social obligations, financial need, or lack of insurance, for instance).
### Conflict Perspective
Theorists using the conflict perspective suggest that issues with the healthcare system, as with most other social problems, are rooted in capitalist society. According to conflict theorists, capitalism and the pursuit of profit lead to the commodification of health: the changing of something not generally thought of as a commodity into something that can be bought and sold in a marketplace. In this view, people with money and power—the dominant group—are the ones who make decisions about how the healthcare system will be run. They therefore ensure that they will have healthcare coverage, while simultaneously ensuring that subordinate groups stay subordinate through lack of access. This creates significant healthcare—and health—disparities between the dominant and subordinate groups.
Alongside the health disparities created by class inequalities, there are a number of health disparities created by racism, sexism, ageism, and heterosexism. When health is a commodity, the poor are more likely to experience illness caused by poor diet, to live and work in unhealthy environments, and are less likely to challenge the system. In the United States, a disproportionate number of racial minorities also have less economic power, so they bear a great deal of the burden of poor health. It is not only the poor who suffer from the conflict between dominant and subordinate groups. For many years now, same-sex couples have been denied spousal benefits, either in the form of health insurance or in terms of medical responsibility. Further adding to the issue, doctors hold a disproportionate amount of power in the doctor/patient relationship, which provides them with extensive social and economic benefits.
While conflict theorists are accurate in pointing out certain inequalities in the healthcare system, they do not give enough credit to medical advances that would not have been made without an economic structure to support and reward researchers: a structure dependent on profitability. Additionally, in their criticism of the power differential between doctor and patient, they are perhaps dismissive of the hard-won medical expertise possessed by doctors and not patients, which renders a truly egalitarian relationship more elusive.
### Symbolic Interactionism
According to theorists working in this perspective, health and illness are both socially constructed. As we discussed in the beginning of the chapter, interactionists focus on the specific meanings and causes people attribute to illness. The term medicalization of deviance refers to the process that changes “bad” behavior into “sick” behavior. A related process is demedicalization, in which “sick” behavior is normalized again. Medicalization and demedicalization affect who responds to the patient, how people respond to the patient, and how people view the personal responsibility of the patient (Conrad and Schneider 1992).
An example of medicalization is illustrated by the history of how our society views alcohol and alcoholism. During the nineteenth century, people who drank too much were considered bad, lazy people. They were called drunks, and it was not uncommon for them to be arrested or run out of a town. Drunks were not treated in a sympathetic way because, at that time, it was thought that it was their own fault that they could not stop drinking. During the latter half of the twentieth century, however, people who drank too much were increasingly defined as alcoholics: people with a disease or a genetic predisposition to addiction who were not responsible for their drinking. With alcoholism defined as a disease and not a personal choice, alcoholics came to be viewed with more compassion and understanding. Thus, “badness” was transformed into “sickness.”
There are numerous examples of demedicalization in history as well. During the Civil War era, enslaved people who escaped from their enslavers were diagnosed with a mental disorder called drapetomania. This has since been reinterpreted as a completely appropriate response to being enslaved. A more recent example is homosexuality, which was labeled a mental disorder or a sexual orientation disturbance by the American Psychological Association until 1973.
While interactionism does acknowledge the subjective nature of diagnosis, it is important to remember who most benefits when a behavior becomes defined as illness. Pharmaceutical companies make billions treating illnesses such as fatigue, insomnia, and hyperactivity that may not actually be illnesses in need of treatment, but opportunities for companies to make more money.
### Summary
While the functionalist perspective looks at how health and illness fit into a fully functioning society, the conflict perspective is concerned with how health and illness fit into the oppositional forces in society. The interactionist perspective is concerned with how social interactions construct ideas of health and illness.
### Section Quiz
### Short Answer Quiz
### Further Research
A massive surge in substance use disorders and overdoses occurred in the United States based on usage of prescription drugs. The causes were widespread and were rooted in pharmaceutical company approaches, medical policies, and social causes. Read more in article about the causes of the U.S. opioid crisis.
### References
Conrad, Peter, and Joseph W. Schneider. 1992. Deviance and Medicalization: From Badness to Sickness. Philadelphia, PA: Temple University Press
Parsons, Talcott. 1951. The Social System. Glencoe, IL: Free Press.
Scheff, Thomas. 1963. “The Role of the Mentally Ill and the Dynamics of Mental Disorder.” Sociometry 26:436–453. |
# Population, Urbanization, and the Environment
## Introduction
Fracking, another word for hydraulic fracturing, is a method used to recover gas and oil from shale by drilling down into the earth and directing a high-pressure mixture of water, sand, and proprietary chemicals into the rock. While energy companies view fracking as a profitable revolution in the industry, there are a number of concerns associated with the practice.
First, fracking requires huge amounts of water. Water transportation comes at a high environmental cost. Once mixed with fracking chemicals, water is unsuitable for human and animal consumption, though it is estimated that between 10 percent and 90 percent of the contaminated water is returned to the water cycle. Second, the chemicals used in a fracking mix are potentially carcinogenic. These chemicals may pollute groundwater near the extraction site (Colborn, Kwiatkowski, Schultz, and Bachran 2011; United States 2011). Industry leaders suggest that such contamination is unlikely, and that when it does occur, it is incidental and related to unavoidable human error rather than an expected risk of the practice, but the U.S. Environmental Protection Agency’s study of fracking is ongoing (Environmental Protection Agency 2014). The third concern is that fracking causes minor earthquakes by undermining the seismic stability of an area, though far more induced earthquakes are caused by traditional oil and gas production (USGS n.d.) Finally, gas is not a renewable source of energy; this is a negative in the eyes of those who oppose continued reliance on fossil fuels.
Fracking is not without its advantages. Its supporters offer statistics that suggest it reduces unemployment and contributes to economic growth (IHS Global Insights 2012). Since it allows energy companies access to previously nonviable and completely untapped oil and gas reserves, fracking boosts domestic oil production and lowers energy costs (IHS Global Insights 2012). Finally, since natural gas is a lower-emission fuel than coal, fracking reduces the airborne environmental impacts of industrial energy.
One complexity of lower-priced natural gas production is that demand for coal has plummeted. Coal is both more expensive to produce and more environmentally damaging than natural gas, and the coal industry is concentrated in a few areas, such as Pennsylvania, West Virginia, and Kentucky. Automation had already depleted the employment opportunities in the industry; decades before fracking became widespread, coal companies began widespread replacement of people with machines (Vavra 2017). Although the U.S. was producing more coal than it had in previous decades, it was doing so with fewer workers than it ever had. At its peak, the coal industry employed nearly a million people, and its thriving towns drove other businesses. By 2015, the industry employs about 50,000 people (Money Illusion 2016). Inexpensive natural gas is just another factor that is contributing to the industry’s continued issues. Coal companies continually shutter, and entire regions are full of newly laid off workers who cannot find employment.
As you read this chapter, consider how an increasing global population can balance environmental concerns with opportunities for industrial and economic growth. Think about how much water pollution can be justified by the need to lower U.S. dependence of foreign energy supplies. Is the economic growth associated with fracking worth some environmental degradation? As we see a related industry – coal – further diminished due to fracking, do we owe its workers some compensation or additional support?
As the discussion of fracking illustrates, there are important societal issues connected to the environment and how and where people live. Sociologists begin to examine these issues through demography, or the study of population and how it relates to urbanization, the study of the social, political, and economic relationships in cities. Environmental sociologists look at the study of how humans interact with their environments. Today, as has been the case many times in history, we are at a point of conflict in a number of these areas. The world’s population reached seven billion between 2011 and 2012. When will it reach eight billion? Can our planet sustain such a population? We generate more trash than ever, from Starbucks cups to obsolete cell phones containing toxic chemicals to food waste that could be composted. You may be unaware of where your trash ends up. And while this problem exists worldwide, trash issues are often more acute in urban areas. Cities and city living create new challenges for both society and the environment that make interactions between people and places of critical importance.
How do sociologists study population and urbanization issues? Functionalist sociologists might focus on the way all aspects of population, urbanization, and the environment serve as vital and cohesive elements, ensuring the continuing stability of society. They might study how the growth of the global population encourages emigration and immigration, and how emigration and immigration serve to strengthen ties between nations. Or they might research the way migration affects environmental issues; for example, how have forced migrations, and the resulting changes in a region’s ability to support a new group, affected both the displaced people and the area of relocation? Another topic a functionalist might research is the way various urban neighborhoods specialize to serve cultural and financial needs.
A conflict theorist, interested in the creation and reproduction of inequality, might ask how peripheral nations’ lack of family planning affects their overall population in comparison to core nations that tend to have lower fertility rates. Or, how do inner cities become ghettos, nearly devoid of jobs, education, and other opportunities? A conflict theorist might also study environmental racism and other forms of environmental inequality. For example, which parts of New Orleans society were the most responsive to the evacuation order during Hurricane Katrina? Which area was most affected by the flooding? And where (and in what conditions) were people from those areas housed, both during and before the evacuation?
A symbolic interactionist interested in the day-to-day interaction of groups and individuals might research topics like the way family-planning information is presented to and understood by different population groups, the way people experience and understand urban life, and the language people use to convince others of the presence (or absence) of global climate change. For example, some politicians wish to present the study of global warming as junk science, and other politicians insist it is a proven fact.
### References
Colborn, Theo, Carol Kwiatkowski, Kim Schultz, and Mary Bachran. 2011. “Natural Gas Operations from a Public Health Perspective.” Human & Ecological Risk Assessment 17 (5): 1039-1056.
Environmental Protection Agency. 2014. “EPA’s Study of Hydraulic Fracturing and Its Potential Impact on Drinking Water Resources.” U.S. EPA, September 14. Retrieved October 29, 2014. (http://www2.epa.gov/hfstudy).
Henry, Terrence. 2012. “How Fracking Disposal Wells Are Causing Earthquakes in Dallas-Fort Worth.” Texas RSS. N.p., August 6. Retrieved October 29, 2014 (http://stateimpact.npr.org/texas/2012/08/06/how-fracking-disposal-wells-are-causing-earthquakes-in-dallas-fort-worth/).
IHS Global Insights. 2012. “The Economic and Employment Contributions of Unconventional Gas Development in State Economies.” Prepared for America’s Natural Gas Alliance, June 2012. Retrieved October 29, 2014 (http://www.anga.us/media/content/F7D4500D-DD3A-1073-DA3480BE3CA41595/files/state_unconv_gas_economic_contribution.pdf).
Money Illusion. 2016. “Coal jobs were lost to automation, not trade.” TheMoneyIllusion.com. December 21 2016. (https://www.themoneyillusion.com/coal-jobs-were-lost-to-automation-not-trade/)
USGS. “Does Fracking Cause Earthquakes.” United States Geological Survey. Retrieved April 1, 2021. (https://www.usgs.gov/faqs/does-fracking-cause-earthquakes)
Vavra, Shannon. 2017. “Mining By Machine: Automation Hits Coal Industry.” June 29 2017. (https://www.axios.com/mining-by-machine-automation-hits-coal-industry-1513303325-ba4cf237-d636-4987-88fc-0b277410fa79.html) |
# Population, Urbanization, and the Environment
## Demography and Population
Between 2011 and 2012, we reached a population milestone of 7 billion humans on the earth’s surface. The rapidity with which this happened demonstrated an exponential increase from the time it took to grow from 5 billion to 6 billion people. In short, the planet is filling up. We'll have 8 billion people in this decade. While the population is increasing overall, there are certain countries and regions where growth is slowing. Relocation and migration also change the makeup and quantity of people in an area. In order to properly understand these dynamics and make decisions regarding them, we turn to demography, or the study of populations. Three critical aspects of demography are fertility, mortality, and migration.
The fertility rate of a society is a measure noting the number of children born. The fertility number is generally lower than the fecundity number, which measures the potential number of children that could be born to women of childbearing age. Sociologists measure fertility using the crude birthrate (the number of live births per 1,000 people per year). Just as fertility measures childbearing, the mortality rate is a measure of the number of people who die. The crude death rate is a number derived from the number of deaths per 1,000 people per year. When analyzed together, fertility and mortality rates help researchers understand the overall growth occurring in a population.
Another key element in studying populations is the movement of people into and out of an area. Migration may take the form of immigration, which describes movement into an area to take up permanent residence, or emigration, which refers to movement out of an area to another place of permanent residence. Migration might be voluntary (as when college students study abroad), involuntary (as when Syrians evacuated war-torn areas), or forced (as when many Native American tribes were removed from the lands they’d lived in for generations).
A functional perspective theorist might focus on the dysfunctions caused by the sudden influx of underage asylum seekers, while a conflict perspective theorist might look at the way social stratification influences how the members of a developed country are treating the lower-status migrants from less-developed countries in Latin America. An interactionist theorist might see significance in the attitude of those protesting the presence of migrant children. Which theoretical perspective makes the most sense to you?
### Population Growth
Changing fertility, mortality, and migration rates make up the total population composition, a snapshot of the demographic profile of a population. This number can be measured for societies, nations, world regions, or other groups. The population composition includes the sex ratio, the number of men for every hundred women, as well as the population pyramid, a picture of population distribution by sex and age ().
Comparing the three countries in reveals that there are more men than women in Afghanistan and Finland, whereas the reverse is true in the United States. Afghanistan also has significantly higher fertility and mortality rates than either of the other two countries. In all three cases, the fertility rates have dropped in recent years, but Afghanistan's drop (from 5.4 children per woman to 4.4) will likely be the most impactful (World Bank 2019). Do these statistics surprise you? How do you think the population makeup affects the political climate and economics of the different countries?
### Demographic Theories
Sociologists have long looked at population issues as central to understanding human interactions. Below we will look at four theories about population that inform sociological thought: Malthusian, zero population growth, cornucopian, and demographic transition theories.
### Malthusian Theory
Thomas Malthus (1766–1834) was an English clergyman who made dire predictions about earth’s ability to sustain its growing population. According to Malthusian theory, three factors would control human population that exceeded the earth’s carrying capacity, or how many people can live in a given area considering the amount of available resources. Malthus identified these factors as war, famine, and disease (Malthus 1798). He termed them “positive checks” because they increase mortality rates, thus keeping the population in check. They are countered by “preventive checks,” which also control the population but by reducing fertility rates; preventive checks include birth control and celibacy. Thinking practically, Malthus saw that people could produce only so much food in a given year, yet the population was increasing at an exponential rate. Eventually, he thought people would run out of food and begin to starve. They would go to war over increasingly scarce resources and reduce the population to a manageable level, and then the cycle would begin anew.
Of course, this has not exactly happened. The human population has continued to grow long past Malthus’s predictions. So what happened? Why didn’t we die off? There are three reasons sociologists believe we are continuing to expand the population of our planet. First, technological increases in food production have increased both the amount and quality of calories we can produce per person. Second, human ingenuity has developed new medicine to curtail death from disease. Finally, the development and widespread use of contraception and other forms of family planning have decreased the speed at which our population increases. But what about the future? Some still believe Malthus was correct and that ample resources to support the earth’s population will soon run out.
### Zero Population Growth
A neo-Malthusian researcher named Paul Ehrlich brought Malthus’s predictions into the twentieth century. However, according to Ehrlich, it is the environment, not specifically the food supply, that will play a crucial role in the continued health of the planet’s population (Ehrlich 1968). Ehrlich's ideas suggest that the human population is moving rapidly toward complete environmental collapse, as privileged people use up or pollute a number of environmental resources such as water and air. He advocated for a goal of zero population growth (ZPG), in which the number of people entering a population through birth or immigration is equal to the number of people leaving it via death or emigration. While support for this concept is mixed, it is still considered a possible solution to global overpopulation.
### Cornucopian Theory
Of course, some theories are less focused on the pessimistic hypothesis that the world’s population will meet a detrimental challenge to sustaining itself. Cornucopian theory scoffs at the idea of humans wiping themselves out; it asserts that human ingenuity can resolve any environmental or social issues that develop. As an example, it points to the issue of food supply. If we need more food, the theory contends, agricultural scientists will figure out how to grow it, as they have already been doing for centuries. After all, in this perspective, human ingenuity has been up to the task for thousands of years and there is no reason for that pattern not to continue (Simon 1981).
### Demographic Transition Theory
Whether you believe that we are headed for environmental disaster and the end of human existence as we know it, or you think people will always adapt to changing circumstances, we can see clear patterns in population growth. Societies develop along a predictable continuum as they evolve from unindustrialized to postindustrial. Demographic transition theory (Caldwell and Caldwell 2006) suggests that future population growth will develop along a predictable four-stage model.
In Stage 1, birth, death, and infant mortality rates are all high, while life expectancy is short. An example of this stage is the 1800s in the United States. As countries begin to industrialize, they enter Stage 2, where birth rates are higher while infant mortality and the death rates drop. Life expectancy also increases. Afghanistan is currently in this stage. Stage 3 occurs once a society is thoroughly industrialized; birth rates decline, while life expectancy continues to increase. Death rates continue to decrease. Mexico’s population is at this stage. In the final phase, Stage 4, we see the postindustrial era of a society. Birth and death rates are low, people are healthier and live longer, and society enters a phase of population stability. Overall population may even decline. For example, Sweden is considered to be in Stage 4.
The United Nations Population Fund (2008) categorizes nations as high fertility, intermediate fertility, or low fertility. The United Nations (UN) anticipates the population growth will triple between 2011 and 2100 in high-fertility countries, which are currently concentrated in sub-Saharan Africa. For countries with intermediate fertility rates (the United States, India, and Mexico all fall into this category), growth is expected to be about 26 percent. And low-fertility countries like China, Australia, and most of Europe will actually see population declines of approximately 20 percent. The graphs below illustrate this trend.
### Changes in U.S. Immigration Patterns and Attitudes
Worldwide patterns of migration have changed, though the United States remains the most popular destination. From 1990 to 2013, the number of migrants living in the United States increased from one in six to one in five (The Pew Research Center 2013). Overall, the United States is home to about 45 million foreign-born people, while only about 3 million U.S. citizens lived abroad. Of foreign-born citizens emigrating to the United States, 55 percent originated in Latin America and the Caribbean. However, over the past few years, more people from Asian countries have entered than from Latin American ones (Budiman 2020).
While there are more foreign-born people residing in the United States legally, as of 2017 about 10.5 million resided here without legal status (Budiman 2020). Most immigrants in the U.S. live in either Texas, Florida, or California.
Even before policy changes and COVID-19 affected refugee admittance, a relatively small number of people formally entered the country as refugees. In 2016, about 85,000 refugees were admitted to the U.S. (of over one million total immigrants), with the largest portion arriving from the Democratic Republic of Congo; in 2020, the number of refugees was reduced to 18,000.
Most citizens agree that our national immigration policies are need adjustment. More than two-thirds (69 percent) of those in a recent national survey believed illegal immigrants should have a path to citizenship provided they meet other requirements, such as paying taxes and passing a background check. Even more people (72 percent) supported passing a DREAM Act, which would allow people who immigrated as children to earn citizenship. In both parts of the survey, majorities of both Republicans and Democrats as well as independents supported the pathway to citizenship (Vox and Data for Progress 2021).
### Summary
Scholars understand demography through various analyses. Malthusian, zero population growth, cornucopian theory, and demographic transition theories all help sociologists study demography. The earth’s human population is growing quickly, especially in peripheral countries. Factors that impact population include birthrates, mortality rates, and migration, including immigration and emigration. There are numerous potential outcomes of the growing population, and sociological perspectives vary on the potential effect of these increased numbers. The growth will pressure the already taxed planet and its natural resources.
### Section Quiz
### Short Answer
### Further Research
To learn more about population concerns, from the new-era ZPG advocates to the United Nations reports, check out the Population Connection web site.
Explore an interactive version of the population pyramid for each country, and to see updates and changes over time: at this website.
### References
Budiman, Abby. 2020. “Key Findings About US Immigrants.” Pew Research Center. August 20, 2020. (https://www.pewresearch.org/fact-tank/2020/08/20/key-findings-about-u-s-immigrants/)
Caldwell, John Charles and Bruce Caldwell. 2006. Demographic Transition Theory. The Netherlands: Springer.
CIA World Factbook. 2014. “Guide to Country Comparisons.” Central Intelligence Agency World Factbook. Retrieved October 31, 2014 (https://www.cia.gov/library/publications/the-world-factbook/rankorder/rankorderguide.html).
Colborn, Theo, Carol Kwiatkowski, Kim Schultz, and Mary Bachran. 2011. “Natural Gas Operations from a Public Health Perspective.” Human & Ecological Risk Assessment. 17 (5): 1039-1056
Connor, Phillip, D'Vera Cohn, and Ana Gonzalez-Barrera. 2013. “Changing Patterns of Global Migration and Remittances.” Pew Research Centers Social Demographic Trends Project RSS. N.p., Retrieved October 31, 2014 (http://www.pewsocialtrends.org/2013/12/17/changing-patterns-of-global-migration-and-remittances/).
Dart, Tom. 2014. "Child Migrants at Texas Border: An Immigration Crisis That's Hardly New." The Guardian [Houston]. www.theguardian.com. Guardian News and Media Limited. Retrieved October 30, 2014 (http://www.theguardian.com/world/2014/jul/09/us-immigration-undocumented-children-texas).
Ehrlich, Paul R. 1968. The Population Bomb. New York: Ballantine.
Environmental Protection Agency. 2014. "EPA's Study of Hydraulic Fracturing and Its Potential Impact on Drinking Water Resources." U.S. EPA, September 14. Retrieved October 29, 2014. (http://www2.epa.gov/hfstudy).
Fox News, and Associated Press. 2014. "Protests Turn Back Buses Carrying Illegal Immigrant Children." Fox News. FOX News Network. Retrieved October 30, 2014 (http://www.foxnews.com/us/2014/07/02/protests-force-buses-carrying-illegal-immigrant-children-to-be-rerouted/).
Gomez, Alan. 2014. "Obama Seeks Change to Law That Protects Immigrant Kids." USA Today. July 2 2014. (https://www.usatoday.com/story/news/nation/2014/07/02/immigration-obama-deportation-children-border/11915723/)
Henry, Terrence. 2012. "How Fracking Disposal Wells Are Causing Earthquakes in Dallas-Fort Worth." Texas RSS. N.p., August 6. Retrieved October 29, 2014 (http://stateimpact.npr.org/texas/2012/08/06/how-fracking-disposal-wells-are-causing-earthquakes-in-dallas-fort-worth/).
IHS Global Insights. 2012. "The Economic and Employment Contributions of Unconventional Gas Development in State Economies." Prepared for America's Natural Gas Alliance, June 2012. Retrieved October 29, 2014. (http://www.anga.us/media/content/F7D4500D-DD3A-1073-DA3480BE3CA41595/files/state_unconv_gas_economic_contribution.pdf).
Kanno-Youngs, Zolan and Maggie Haberman. 2020. “Trump Administration Moves to Solidify Restrictive Immigration Policies.” New York Times, June 12, 2020.
Malthus, Thomas R. 1965 [1798]. An Essay on Population. New York: Augustus Kelley.
Montoya-Galvez, Camilo. 2021. "The Facts About How The US Processes Unaccompanied Migrant Children At The Border." CBS News. February 25 2021. (https://www.cbsnews.com/news/unaccompanied-migrant-children-united-states-processing-housing/)
Passel, Jeffrey, D'Vera Cohn, and Ana Gonzalez-Barrera. 2013. "Population Decline of Unauthorized Immigrants Stalls, May Have Reversed." Pew Research Centers Hispanic Trends Project RSS. N.p., Retrieved October 31, 2014 (http://www.pewhispanic.org/2013/09/23/population-decline-of-unauthorized-immigrants-stalls-may-have-reversed/).
Pew Research Center. 2013. "Immigration: Key Data Points from Pew Research." Pew Research Center RSS. N.p., Retrieved October 31, 2014 (http://www.pewresearch.org/key-data-points/immigration-tip-sheet-on-u-s-public-opinion/).
Popescu, Roxana. 2014. "Frequently Asked Questions about the Migrant Crisis." U-T San Diego. San Diego Union-Tribue, Retrieved October 31, 2014 (http://www.utsandiego.com/news/2014/jul/22/Migrant-crisis-FAQ/).
Reyes, Raul A. 2014. "Murrieta Immigration Protests Were Unfortunate, Unnecessary." The Huffington Post. TheHuffingtonPost.com, Retrieved October 31, 2014 (http://www.huffingtonpost.com/raul-a-reyes/murrieta-immigration-prot_b_5569351.html).
Simon, Julian Lincoln. 1981. The Ultimate Resource. Princeton, NJ: Princeton University Press.
Spagat, Elliot. 2019. "US Sees Limitations on Reuniting Migrant Families." Associated Press. February 2 2019. (https://apnews.com/article/48210bbf243e423ea151ff04e4878ce6)
The United Nations Refugee Agency. 2014. "World Refugee Day: Global Forced Displacement Tops 50 Million for First Time in Post-World War II Era." UNHCR News. N.p., Retrieved October 31, 2014 (http://www.unhcr.org/53a155bc6.html).
U.S. Congress. 2008. The William Wilberforce Trafficking Victims Protection Reauthorization Act of 2008. 7311, 110 Cong., U.S. G.P.O. (enacted). Print.
World Bank. 2019. "Fertility Rate." "Mortality Rate." The World Bank Data. Retrieved April 1, 2021. (https://data.worldbank.org/indicator/SP.DYN.TFRT.IN)
Vox and Data for Progress. 2021. "Biden Immigration Agenda Survey Results." Files for Progress. (https://www.filesforprogress.org/datasets/2021/2/dfp-vox-biden-immigration-agenda.pdf) |
# Population, Urbanization, and the Environment
## Urbanization
Urbanization is the study of the social, political, and economic relationships in cities, and someone specializing in urban sociology studies those relationships. In some ways, cities can be microcosms of universal human behavior, while in others they provide a unique environment that yields its own brand of human behavior. There is no strict dividing line between rural and urban; rather, there is a continuum where one bleeds into the other. However, once a geographically concentrated population has reached approximately 100,000 people, it typically behaves like a city regardless of what its designation might be.
### The Growth of Cities
According to sociologist Gideon Sjoberg (1965), there are three prerequisites for the development of a city: First, good environment with fresh water and a favorable climate; second, advanced technology, which will produce a food surplus to support nonfarmers; and third, strong social organization to ensure social stability and a stable economy. Most scholars agree that the first cities were developed somewhere in ancient Mesopotamia, though there are disagreements about exactly where. Most early cities were small by today’s standards, and the largest was most likely Rome, with about 650,000 inhabitants (Chandler and Fox 1974). The factors limiting the size of ancient cities included lack of adequate sewage control, limited food supply, and immigration restrictions. For example, serfs were tied to the land, and transportation was limited and inefficient. Today, the primary influence on cities’ growth is economic forces. Since the recent economic recession reduced housing prices, researchers have been waiting to see what happens to urban migration patterns in response.
### Urbanization in the United States
Urbanization in the United States proceeded rapidly during the Industrial Era. As more and more opportunities for work appeared in factories, workers left farms (and the rural communities that housed them) to move to the cities. From mill towns in Massachusetts to tenements in New York, the industrial era saw an influx of poor workers into U.S. cities. At various times throughout the country’s history, certain demographic groups, from post-Civil War southern Black people to more recent immigrants, have made their way to urban centers to seek a better life in the city.
### Suburbs and Exurbs
As cities grew more crowded, and often more impoverished and costly, more and more people began to migrate back out of them. But instead of returning to rural small towns (like they’d resided in before moving to the city), these people needed close access to the cities for their jobs. In the 1850s, as the urban population greatly expanded and transportation options improved, suburbs developed. Suburbs are the communities surrounding cities, typically close enough for a daily commute in, but far enough away to allow for more space than city living affords. The bucolic suburban landscape of the early twentieth century has largely disappeared due to sprawl. Suburban sprawl contributes to traffic congestion, which in turn contributes to commuting time. And commuting times and distances have continued to increase as new suburbs developed farther and farther from city centers. Simultaneously, this dynamic contributed to an exponential increase in natural resource use, like petroleum, which sequentially increased pollution in the form of carbon emissions.
As the suburbs became more crowded and lost their charm, those who could afford it turned to the exurbs, communities that exist outside the ring of suburbs and are typically populated by even wealthier families who want more space and have the resources to lengthen their commute. Together, the suburbs, exurbs, and metropolitan areas all combine to form a metropolis. New York was the first U.S. megalopolis, a huge urban corridor encompassing multiple cities and their surrounding suburbs. These metropolises use vast quantities of natural resources and are a growing part of the U.S. landscape.
As the Social Policy & Debate feature illustrates, the suburbs also have their share of socio-economic problems. In the United States, White flight refers to the migration of economically secure White people from racially mixed urban areas and toward the suburbs. This occurred throughout the twentieth century, due to causes as diverse as the legal end of racial segregation established by Brown v. Board of Education to the Mariel boatlift of people fleeing Cuba for Miami. Current trends include middle-class African-American families following White flight patterns out of cities, while affluent White people return to cities that have historically had a majority of Black people. The result is that the issues of race, socio-economics, neighborhoods, and communities remain complicated and challenging.
### Urbanization around the World
During the Industrial Era, there was a growth spurt worldwide. The development of factories brought people from rural to urban areas, and new technology increased the efficiency of transportation, food production, and food preservation. For example, from the mid-1670s to the early 1900s, London's population increased from 550,000 to 7 million (Old Bailey Proceedings Online 2011). Global favorites like New York, London, and Tokyo are all examples of postindustrial cities. As cities evolve from manufacturing-based industrial to service- and information-based postindustrial societies, gentrification becomes more common. Gentrification occurs when members of the middle and upper classes enter and renovate city areas that have been historically less affluent while the poor urban underclass are forced by resulting price pressures to leave those neighborhoods for increasingly decaying portions of the city.
Globally, 55 percent of the world’s people currently reside in urban areas, with the most urbanized region being North America (82 percent), followed by Latin America/the Caribbean (81 percent), with Europe coming in third (74 percent). In comparison, Africa is only 40 percent urbanized, though one of its nations, Nigeria, is projected to significantly urbanize in the coming years. With 37 million people, Tokyo is the world’s largest city by population, and New Delhi is the second largest with 29 million. The world’s most densely populated cities are now largely concentrated in the global south, a marked change from several decades ago when the biggest cities were found in the global north. In the next forty years, the biggest global challenge for urbanized populations, particularly in less developed countries, will be to achieve development that occurs without depleting or damaging the natural environment, also called sustainable development (United Nations 2018).
### Theoretical Perspectives on Urbanization
The issues of urbanization play significant roles in the study of sociology. Race, economics, and human behavior intersect in cities. Let’s look at urbanization through the sociological perspectives of functionalism and conflict theory. Functional perspectives on urbanization generally focus on the ecology of the city, while conflict perspective tends to focus on political economy.
Human ecology is a functionalist field of study that looks at the relationship between people and their built and natural physical environments (Park 1915). Generally speaking, urban land use and urban population distribution occur in a predictable pattern once we understand how people relate to their living environment. For example, in the United States, we have a transportation system geared to accommodate individuals and families in the form of interstate highways built for cars. In contrast, most parts of Europe emphasize public transportation such as high-speed rail and commuter lines, as well as walking and bicycling. The challenge for a human ecologist working in U.S. urban planning is to design landscapes and waterscapes with natural beauty, while also figuring out how to provide for free-flowing transport of innumerable vehicles, not to mention parking!
The concentric zone model (Burgess 1925) is perhaps the most famous example of human ecology. This model views a city as a series of concentric circular areas, expanding outward from the center of the city, with various “zones” invading adjacent zones (as new categories of people and businesses overrun the edges of nearby zones) and succeeding (then after invasion, the new inhabitants repurpose the areas they have invaded and push out the previous inhabitants). In this model, Zone A, in the heart of the city, is the center of the business and cultural district. Zone B, the concentric circle surrounding the city center, is composed of formerly wealthy homes split into cheap apartments for new immigrant populations; this zone also houses small manufacturers, pawn shops, and other marginal businesses. Zone C consists of the homes of the working class and established ethnic enclaves. Zone D holds wealthy homes, white-collar workers, and shopping centers. Zone E contains the estates of the upper class (in the exurbs) and the suburbs.
In contrast to the functionalist approach, theoretical models in the conflict perspective focus on the way urban areas change according to specific decisions made by political and economic leaders. These decisions generally benefit the middle and upper classes while exploiting the working and lower classes.
For example, sociologists Feagin and Parker (1990) suggested three factors by which political and economic leaders control urban growth. First, these leaders work alongside each other to influence urban growth and decline, determining where money flows and how land use is regulated. Second, exchange value and use value of land are balanced to favor the middle and upper classes so that, for example, public land in poor neighborhoods may be rezoned for use as industrial land. Finally, urban development is dependent on both structure (groups such as local government) and agency (individuals including businessmen and activists), and these groups engage in a push-pull dynamic that determines where and how land is actually used. For example, Not In My Back Yard (NIMBY) movements are more likely to emerge in middle and upper-class neighborhoods as engaged citizens protest poor environmental practices they fear will affect them, so these groups have more control over the use of local land.
### Summary
Cities provide numerous opportunities for their residents and offer significant benefits including access to goods to numerous job opportunities. At the same time, high population areas can lead to tensions between demographic groups, as well as environmental strain. While the population of urban dwellers is continuing to rise, sources of social strain are rising along with it. The ultimate challenge for today’s urbanites is finding an equitable way to share the city’s resources while reducing the pollution and energy use that negatively impacts the environment.
### Section Quiz
### Short Answer
### Further Research
Interested in learning more about the latest research in the field of human ecology? Visit the Society for Human Ecology web site to discover what’s emerging in this field.
Getting from place to place in urban areas might be more complicated than you think. Read the latest on pedestrian-traffic concerns at the Streetsblog web site.
### References
BBC. 2005. “Timeline: French Riots—A Chronology of Key Events.” November 14. Retrieved December 9, 2011 (http://news.bbc.co.uk/2/hi/europe/4413964.stm).
Burgess, Ernest. 1925. “The Growth of the City.” Pp. 47–62 in The City, edited by R. Park and E. Burgess. Chicago: University of Chicago Press.
Chandler, Tertius and Gerald Fox. 1974. 3000 Years of Urban History. New York: Academic Press.
Dougherty, Connor. 2008. “The End of White Flight.” Wall Street Journal, July 19. Retrieved December 12, 2011 (http://online.wsj.com/article/SB121642866373567057.html).
Feagin, Joe, and Robert Parker. 1990. Building American Cities: The Urban Real Estate Game. 2nd ed. Englewood Cliffs, NJ: Prentice Hall.
France24. 2010. “Sarkozy Promises War without Mercy for Paris Suburbs.” France 24, April 10. Retrieved December 9, 2011 (http://www.france24.com/en/20100420-sarkozy-war-suburbs-drugs-crime-violence-truancy-tremblay-en-france-saint-denis-france).
LeBlanc, Adrien Nicole. 2003. Random Family: Love, Drugs, Trouble and Coming of Age in the Bronx. New York: Scribner.
Park, Robert. 1934 [1915]. “The City: Suggestions for Investigations of Human Behavior in the City.” American Journal of Sociology 20:577–612.
Park, Robert. 1936. “Human Ecology.” American Journal of Sociology 42:1–15.
Old Bailey Proceedings Online. 2011. “Population History of London.” Retrieved December 11, 2011 (http://www.oldbaileyonline.org/static/Population-history-of-london.jsp).
Sciolino, Elaine, and Ariane Bernand. 2006. “Anger Festering in French Areas Scarred in Riots.” New York Times, October 21. Retrieved December 11, 2011 (http://www.nytimes.com/2006/10/21/world/europe/21france.html?scp=2&sq=paris+suburb&st=nyt).
Sjoberg, Gideon. 1965. The Preindustrial City: Past and Present. New York: Free Press.
Talbot, Margaret. 2003. “Review: Random Family. Love, Drugs, Trouble and Coming of Age in the Bronx.” New York Times, February 9. Retrieved December 12, 2011 (http://www.nytimes.com/2003/02/09/books/in-the-other-country.html?pagewanted=all&src=pm).
United Nations, Department of Economic and Social Affairs, Population Division. 2014. “World Urbanization Prospects: The 2014 Revision, Highlights” (ST/ESA/SER.A/352). Retrieved November 3, 2014 (http://esa.un.org/unpd/wup/Highlights/WUP2014-Highlights.pdf).
United Nations, Department of Economic and Social Affairs, Population Division. 2018. "68% of the world population projected to live in urban areas by 2050, says UN." May 16, 2018. (https://www.un.org/development/desa/en/news/population/2018-revision-of-world-urbanization-prospects.html)
United States Census Bureau. 2014, "2010 Census Urban and Rural Classification and Urban Area Criteria." Retrieved December 16, 2014 (http://www.census.gov/geo/reference/ua/urban-rural-2010.html). |
# Population, Urbanization, and the Environment
## The Environment and Society
The subfield of environmental sociology studies the way humans interact with their environments. This field is closely related to human ecology, which focuses on the relationship between people and their built and natural environment. This is an area that is garnering more attention as extreme weather patterns and policy battles over climate change dominate the news. A key factor of environmental sociology is the concept of carrying capacity, which describes the maximum amount of life that can be sustained within a given area. While this concept can refer to grazing lands or to rivers, we can also apply it to the earth as a whole.
### Climate Change
While you might be more familiar with the phrase “global warming,” climate change is the term now used to refer to long-term shifts in temperatures due to human activity and, in particular, the release of greenhouse gases into the environment. The planet as a whole is warming, but the term climate change acknowledges that the short-term variations in this process can include both higher and lower temperatures, despite the overarching trend toward warmth.
Climate change is a deeply controversial subject, despite decades of scientific research and a high degree of scientific consensus that supports its existence. For example, according to NASA scientists, 2020 essentially tied with 2016 as the warmest year on record, continuing the overall trend of increasing worldwide temperatures (NASA 2021). One effect of climate change is more extreme weather. There are increasingly more record-breaking weather phenomena, from the number of Category 4 hurricanes to the amount of snowfall in a given winter. These extremes, while they make for dramatic television coverage, can cause immeasurable damage to crops, property, and lives.
So why is there a controversy? Until relatively recently, the United States was very divided on the existence of climate change as an immediate threat, as well as whether or not human activity causes or contributes to it. But now it appears that the U.S. has joined the ranks of many countries where citizens are concerned about climate change; the nation is divided on what to do about it.
Research conducted in 2020 and 2021 indicated that at least 60 percent of Americans believe climate change is a real and immediate threat (UNDP 2021 and Global Strategy Group 2021). Citizens are also more supportive of clean energy and taking part in international efforts, such as the Paris Climate Accord, which is intended to engage countries in actions to limit the activity that leads to climate change. What's changed these opinions? It may be that younger people are more represented in these polls, and they tend to support climate change initiatives more consistently. It may be that the continued severity of weather and the costly and widespread impact is more difficult to ignore than it was previously. And part of the changing opinions might be driven by the prevalence of green energy sources, from wind power to solar power to electric cars, which are more evident to people across the country. However, deep divides remain. The addition of clean energy producers, such as offshore wind farms, typically meet stiff local opposition (similar to the "not in my backyard" discussion earlier in the chapter). And any punitive or price-raising methods of controlling emissions are unlikely to be welcome by U.S. citizens. Finally, global agreements like the Paris Accord will have limited impact because they are not strictly enforceable.
World systems analysis suggests that while, historically, core nations (like the United States and Western Europe) were the greatest source of greenhouse gases, they have now evolved into postindustrial societies. Industrialized semi-peripheral and peripheral nations are releasing increasing quantities of greenhouse gases, such as carbon dioxide. The core nations, now post-industrial and less dependent on greenhouse-gas-causing industries, wish to enact strict protocols regarding the causes of global warming, but the semi-peripheral and peripheral nations rightly point out that they only want the same economic chance to evolve their economies. Since they were unduly affected by the progress of core nations, if the core nations now insist on "green" policies, they should pay offsets or subsidies of some kind. There are no easy answers to this conflict. It may well not be "fair" that the core nations benefited from ignorance during their industrial boom.
### Pollution
Pollution describes what happens when contaminants are introduced into an environment (water, air, land) at levels that are damaging. Environments can often sustain a limited amount of contaminants without marked change, and water, air, and soil can “heal” themselves to a certain degree. However, once contaminant levels reach a certain point, the results can be catastrophic.
### Water
Typhoid, cholera, and diarrhea from unsafe water kill hundreds of thousands of children each year, and over 160 million children suffer from malnutrition and growth issues due to water issues. An estimated 3 billion people do not have access to clean water at home for hand-washing (CDC 2016). Consider the impact of that, knowing that many of those without water for hand-washing live in agricultural societies in which they work with animals or live in cities with many other people.
The water crisis is exacerbated by many of the other issues we've discussed. Global pandemics, pollution, and climate change all have more severe impacts when coupled with lack of access to clean water. Finally, the cost of obtaining that clean water can interfere with other important aspects of survival and social mobility. Children serve as water haulers, traveling long distances on foot to collect potable water for their family. Those same children (as well as those who similarly collect firewood) are less able to focus on their education, either missing school or not completing the associated work (Water.org 2021). Regular water hauling–which for some people involves carrying 20 kilograms (40 pounds) for 30 minutes or more–also has negative effects on people's bodies, especially pregnant women who often undertake the task. The situation is only getting more dire as the global population increases. Water is a key resource battleground in the twenty-first century.
As every child learns in school, 70 percent of earth is made of water. Despite that figure, there is a finite amount of water usable by humans and it is constantly used and reused in a sustainable water cycle. The way we use this abundant natural resource, however, renders much of it unsuitable for consumption and unable to sustain life. Oil and natural gas production, discussed at the beginning of the chapter, require so much water that there's no safe place to put the wastewater other than deep underground. But more common activities use far more water than many people understand. The immense amount of water to produce almonds (8 percent of California's water supply, equating to roughly one gallon per individual almond) has made headlines, as have the 37 gallons that it takes to produce a cup of coffee. But all crops and livestock have a "water footprint." Dairy milk is actually known to take more water to produce than does almond milk, for example. And steak may take up to 900 gallons of water to produce (WaterCalculuator.org 2020).
Those water costs are important to consider, particularly if the crops are produced in a part of the world where access to safe water is also an issue. But reducing irrigation water usage for U.S. crops would have very limited effects in sub-Saharan Africa. Most experts focus on improving water quality and sanitation in general, as well as reducing the distance people need to travel in order to obtain safe water.
Water pollution has always been a byproduct of industrialization, increased population, and urbanization. Cleveland's Cuyahoga River caught fire several times due to pollution, and was part of what inspired the United States' turn to cleaner water. Other countries are currently undergoing the same crises. As a consequence of population concentrations, water close to human settlements is frequently polluted with untreated or partially treated human waste (sewage), chemicals, radioactivity, and levels of heat sufficient to create large “dead zones” incapable of supporting aquatic life. The methods of food production used by many core nations rely on liberal doses of nitrogen and pesticides, which end up back in the water supply. In some cases, water pollution affects the quality of the aquatic life consumed by water and land animals. As we move along the food chain, the pollutants travel from prey to predator. Since humans consume at all levels of the food chain, we ultimately consume the carcinogens, such as mercury, accumulated through several branches of the food web.
### Soil
You might have read The Grapes of Wrath in English class at some point in time. Steinbeck’s tale of the Joads, driven out of their home by the Dust Bowl, is still playing out today. In China, as in Depression-era Oklahoma, over-tilling soil in an attempt to expand agriculture has resulted in the disappearance of large patches of topsoil.
Soil erosion and desertification are just two of the many forms of soil pollution. In addition, all the chemicals and pollutants that harm our water supplies can also leach into soil with similar effects. Brown zones where nothing can grow are common results of soil pollution. One demand the population boom makes on the planet is a requirement for more food to be produced. The so-called “Green Revolution” in the 1960s saw chemists and world aid organizations working together to bring modern farming methods, complete with pesticides, to developing countries. The immediate result was positive: food yields went up and burgeoning populations were fed. But as time has gone on, these areas have fallen into even more difficult straits as the damage done by modern methods leave traditional farmers with less than they had to start.
Dredging certain beaches in an attempt to save valuable beachfront property from coastal erosion has resulted in greater storm impact on shorelines, and damage to beach ecosystems (Turneffe Atoll Trust 2008). These dredging projects have damaged reefs, sea grass beds, and shorelines and can kill off large swaths of marine life. Ultimately, this damage threatens local fisheries, tourism, and other parts of the local economy.
### Garbage
Where is your last cell phone? What about the one before that? Or the huge old television set your family had before flat screens became popular? For most of us, the answer is a sheepish shrug. We don’t pay attention to the demise of old items, and since electronics drop in price and increase in innovation at an incredible clip, we have been trained by their manufacturers to upgrade frequently.
Garbage creation and control are major issues for most core and industrializing nations, and it is quickly becoming one of the most critical environmental issues faced in the United States. People in the United States buy products, use them, and then throw them away. Did you dispose of your old electronics according to government safety guidelines? Chances are good you didn’t even know there are guidelines. Multiply your electronics times a few million, take into account the numerous toxic chemicals they contain, and then imagine either burying those chemicals in the ground or lighting them on fire.
Those are the two primary means of waste disposal in the United States: landfill and incineration. When it comes to getting rid of dangerous toxins, neither is a good choice. Styrofoam and plastics that many of us use every day do not dissolve in a natural way. Burn them, and they release carcinogens into the air. Their improper incineration (intentional or not) adds to air pollution and increases smog. Dump them in landfills, and they do not decompose. As landfill sites fill up, we risk an increase in groundwater contamination.
### Air
China’s fast-growing economy and burgeoning industry have translated into notoriously poor air quality. Smog hangs heavily over the major cities, sometimes grounding aircraft that cannot navigate through it. Pedestrians and cyclists wear air-filter masks to protect themselves. In Beijing, citizens are skeptical that the government-issued daily pollution ratings are trustworthy. Increasingly, they are taking their own pollution measurements in the hopes that accurate information will galvanize others to action. Given that some days they can barely see down the street, they hope action comes soon (Papenfuss 2011).
Humanity, with its growing numbers, use of fossil fuels, and increasingly urbanized society, is putting too much stress on the earth’s atmosphere. The amount of air pollution varies from locale to locale, and you may be more personally affected than you realize. How often do you check air quality reports before leaving your house? Depending on where you live, this question can sound utterly strange or like an everyday matter. Along with oxygen, most of the time we are also breathing in soot, hydrocarbons, carbon, nitrogen, and sulfur oxides.
Much of the pollution in the air comes from human activity. How many college students move their cars across campus at least once a day? Who checks the environmental report card on how many pollutants each company throws into the air before purchasing a cell phone? Many of us are guilty of taking our environment for granted without concern for how everyday decisions add up to a long-term global problem. How many minor adjustments can you think of, like walking instead of driving, that would reduce your overall carbon footprint?
Remember the “tragedy of the commons.” Each of us is affected by air pollution. But like the herder who adds one more head of cattle to realize the benefits of owning more cows but who does not have to pay the price of the overgrazed land, we take the benefit of driving or buying the latest cell phones without worrying about the end result. Air pollution accumulates in the body, much like the effects of smoking cigarettes accumulate over time, leading to more chronic illnesses. And in addition to directly affecting human health, air pollution affects crop quality as well as heating and cooling costs. In other words, we all pay a lot more than the price at the pump when we fill up our tank with gas.
### Toxic and Radioactive Waste
Radioactivity is a form of air pollution. While nuclear energy promises a safe and abundant power source, increasingly it is looked upon as a danger to the environment and to those who inhabit it. We accumulate nuclear waste, which we must then keep track of long term and ultimately figure out how to store the toxic waste material without damaging the environment or putting future generations at risk.
The 2011 earthquake in Japan illustrates the dangers of even safe, government-monitored nuclear energy. When disaster occurs, how can we safely evacuate the large numbers of affected people? Indeed, how can we even be sure how far the evacuation radius should extend? Radiation can also enter the food chain, causing damage from the bottom (phytoplankton and microscopic soil organisms) all the way to the top. Once again, the price paid for cheap power is much greater than what we see on the electric bill.
The enormous oil disaster that hit the Louisiana Gulf Coast in 2010 is just one of a high number of environmental crises that have led to toxic residue. They include the pollution of the Love Canal neighborhood of the 1970s to the Exxon Valdez oil tanker crash of 1989, the Chernobyl disaster of 1986, and Japan’s Fukushima nuclear plant incident following the earthquake in 2011. Often, the stories are not newsmakers, but simply an unpleasant part of life for the people who live near toxic sites such as Centralia, Pennsylvania and Hinkley, California. In many cases, people in these neighborhoods can be part of a cancer cluster without realizing the cause.
### Environmental Racism
Environmental racism refers to the way in which minority group neighborhoods (populated primarily by people of color and members of low socioeconomic groups) are burdened with a disproportionate number of hazards, including toxic waste facilities, garbage dumps, and other sources of environmental pollution and foul odors that lower the quality of life. All around the globe, members of minority groups bear a greater burden of the health problems that result from higher exposure to waste and pollution. This can occur due to unsafe or unhealthy work conditions where no regulations exist (or are enforced) for poor workers, or in neighborhoods that are uncomfortably close to toxic materials.
The statistics on environmental racism are shocking. Research shows that it pervades all aspects of African Americans' lives: environmentally unsound housing, schools with asbestos problems, facilities and playgrounds with lead paint. A twenty-year comparative study led by sociologist Robert Bullard determined “race to be more important than socioeconomic status in predicting the location of the nation’s commercial hazardous waste facilities” (Bullard et al. 2007). His research found, for example, that Black children are five times more likely to have lead poisoning (the leading environmental health threat for children) than their White counterparts, and that a disproportionate number of people of color reside in areas with hazardous waste facilities (Bullard et al. 2007). Sociologists with the project are examining how environmental racism is addressed in the long-term cleanup of the environmental disasters caused by Hurricane Katrina.
Why does environmental racism exist? The reason is simple. Those with resources can raise awareness, money, and public attention to ensure that their communities are unsullied. This has led to an inequitable distribution of environmental burdens. Another method of keeping this inequity alive is NIMBY protests. Chemical plants, airports, landfills, and other municipal or corporate projects are often the subject of NIMBY demonstrations. And equally often, the NIMBYists win, and the objectionable project is moved closer to those who have fewer resources to fight it.
### Summary
The area of environmental sociology is growing as extreme weather patterns and concerns over climate change increase. Human activity leads to pollution of soil, water, and air, compromising the health of the entire food chain. While everyone is at risk, poor and disadvantaged neighborhoods and nations bear a greater burden of the planet’s pollution, a dynamic known as environmental racism.
### Section Quiz
### Short Answer
### Further Research
Visit the Cleanups in My Community web site to see where environmental hazards have been identified in your backyard, and what is being done about them.
What is your carbon footprint? Find out using the carbon footprint calculator.
Find out using the water footprint calculator.
### References
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Blanchard, Ben. 2007. “Coke Vows to Reduce Water Used in Drink Production.” Reuters, June 5. Retrieved December 14, 2011 (http://www.reuters.com/article/2007/06/05/environment-coke-water-dc-idUSSP28630420070605).
Bullard, Robert D., Paul Mohai, Robin Saha, and Beverly Wright. 2007. Toxic Wastes and Race at Twenty: 1987–2007. United Church of Christ Commission for Racial Justice. Retrieved January 22, 2012 (http://www.ucc.org/assets/pdfs/toxic20.pdf).
Bureau of Indian Affairs. 2012. “FAQs.” Retrieved January 22, 2012 (http://www.bia.gov/FAQ/index/htm).
Centers for Disease Control. 2016. "Global WASH Fast Facts." Updated 2016. (https://www.cdc.gov/healthywater/global/wash_statistics.html)
DeKok, David. 1986. Unseen Danger: A Tragedy of People, Government, and the Centralia Mine Fire. Philadelphia, PA: University of Pennsylvania Press.
Environmental Justice Case Studies. 2004. University of Michigan. Retrieved January 22, 2012 (http://www.umich.edu/~snre492/cses.html).
Frosch, Dan. 2009. “Uranium Contamination Haunts Navajo Country.” New York Times, July 27. Retrieved January 22, 2012 (http://www.newyorktimes.com/2009/07/27/us/navajo.html).
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Hardin, Garrett. 1968. “The Tragedy of the Commons,” Science 162(3859):1243–1248. Retrieved December 10, 2011 (http://www.sciencemag.org/content/162/3859/1243.full).
Kamps, Kevin. 2001. “Environmental Racism, Tribal Sovereignty and Nuclear Waste.” Nuclear Information and Resource Service. Retrieved January 22, 2012 (http://www.nirs.org/factsheets/pfsejfactsheet.htm).
NASA. 2014. “NASA Finds 2013 Sustained Long-Term Climate Warming Trend.” NASA, January 21. Retrieved October 27, 2014(http://www.giss.nasa.gov/research/news/20140121/).
NASA. 2021. "2020 Tied for Warmest Year on Record, NASA Analysis Shows." January 14 2021. (https://www.nasa.gov/press-release/2020-tied-for-warmest-year-on-record-nasa-analysis-shows)
Ogunseitanl, Oladele, Julie M. Stoning, Jean-Daniel M. Sapphires, and Andrew A. Shapiro. 2009. “The Electronics Revolution: From E-Wonderland to E-Wasteland.” Science 326(5953):670–671. Retrieved December 14, 2011 (http://www.sciencemag.org/content/326/5953/670.summary).
Papenfuss, Mary. 2011. “Cynical Chinese Taking Own Smog Readings.” Newser, December 8. Retrieved January 23, 2012 (http://www.newser.com/story/134966/cynical-chinese-taking-own-smog-readings.html).
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Troilo, Pete. 2012. "Yes, We Can? Obama's Global Climate Change Initiative." International Development. Devex, January 30. Retrieved October 27, 2014 (https://www.devex.com/news/yes-we-can-obama-s-global-climate-change-initiative-77363).
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# Social Movements and Social Change
## Introduction to Social Movements and Social Change
When considering social movements, the images that come to mind are often the most dramatic and dynamic: the Boston Tea Party, Martin Luther King's speech at the 1963 March on Washington, anti-war protesters putting flowers in soldiers' rifles, and Gloria Richardson brushing away a bayonet in Cambridge, Maryland. Or perhaps more violent visuals: burning buildings in Watts, protestors fighting with police, or a lone citizen facing a line of tanks in Tiananmen Square.
But social movement occurs every day, often without any pictures or fanfare, by people of all backgrounds and ages. Organizing an awareness event, volunteering at a shelter, donating to a cause, speaking at a school board meeting, running for office, or writing an article are all ways that people participate in or promote social movements. Some people drive social change by educating themselves through books or trainings. Others find one person to help at a time.
Occupy Wall Street (OWS) was a unique movement that defied some of the theoretical and practical expectations regarding social movements. OWS is set apart by its lack of a single message, its leaderless organization, and its target—financial institutions instead of the government. OWS baffled much of the public, and certainly the media, leading many to ask, "Who are they, and what do they want?"
On July 13, 2011, the organization Adbusters posted on its blog, "Are you ready for a Tahrir moment? On September 17th, flood into lower Manhattan, set up tents, kitchens, peaceful barricades and occupy Wall Street" (Castells 2012).
The "Tahrir moment" was a reference to the 2010 political uprising that began in Tunisia and spread throughout the Middle East and North Africa, including Egypt’s Tahrir Square in Cairo. Although OWS was a reaction to the continuing financial chaos that resulted from the 2008 market meltdown and not a political movement, the Arab Spring was its catalyst.
Manuel Castells (2012) notes that the years leading up to the Occupy movement had witnessed a dizzying increase in the disparity of wealth in the United States, stemming back to the 1980s. The top 1 percent in the nation had secured 58 percent of the economic growth in the period for themselves, while real hourly wages for the average worker had increased by only 2 percent. The wealth of the top 5 percent had increased by 42 percent. The average pay of a CEO was at that time 350 times that of the average worker, compared to less than 50 times in 1983 (AFL-CIO 2014). The country’s leading financial institutions, to many clearly to blame for the crisis and dubbed "too big to fail," were in trouble after many poorly qualified borrowers defaulted on their mortgage loans when the loans’ interest rates rose. The banks were eventually "bailed" out by the government with $700 billion of taxpayer money. According to many reports, that same year top executives and traders received large bonuses.
On September 17, 2011, an anniversary of the signing of the U.S. Constitution, the occupation began. About one thousand protestors descended upon Wall Street, and up to 20,000 people moved into Zuccotti Park, only two blocks away, where they began building a village of tents and organizing a system of communication. The protest soon began spreading throughout the nation, and its members started calling themselves "the 99 percent." More than a thousand cities and towns had Occupy demonstrations.
What did they want? Castells has dubbed OWS "A non-demand movement: The process is the message." Using Facebook, Twitter, Tumblr, and live-stream video, the protesters conveyed a multifold message with a long list of reforms and social change, including the need to address the rising disparity of wealth, the influence of money on election outcomes, the notion of "corporate personhood," a corporatized political system (to be replaced by "direct democracy”), political favoring of the rich, and rising student debt.
What did they accomplish? Despite headlines at the time softly mocking OWS for lack of cohesion and lack of clear messaging, the movement is credited with bringing attention to income inequality and the seemingly preferential treatment of financial institutions accused of wrongdoing. Recall from the chapter on Crime and Deviance that many financial crimes are not prosecuted, and their perpetrators rarely face jail time. It is likely that the general population is more sensitive to those issues than they were before the Occupy and related movements made them more visible.
What is the long-term impact? Has the United States changed the way it manages inequality? Certainly not. As discussed in several chapters, income inequality has generally increased. But is a major shift in our future?
The late James C. Davies suggested in his 1962 paper, "Toward a Theory of Revolution" that major change depends upon the mood of the people, and that it is extremely unlikely those in absolute poverty will be able to overturn a government, simply because the government has infinitely more power.
Instead, a shift is more possible when those with more power become involved. When formerly prosperous people begin to have unmet needs and unmet expectations, they become more disturbed: their mood changes. Eventually an intolerable point is reached, and revolution occurs. Thus, change comes not from the very bottom of the social hierarchy, but from somewhere in the middle (Davies 1962). For example, the Arab Spring was driven by mostly young, educated people whose promise and expectations were thwarted by corrupt autocratic governments. OWS too came not from the bottom but from people in the middle, who exploited the power of social media to enhance communication.
### References
AFL-CIO. 2014. "Executive Paywatch." Retrieved December 17, 2014 (http://www.aflcio.org/Corporate-Watch/Paywatch-2014).
Castells, Manuel. 2012. Networks of Outrage and Hope: Social Movements in the Internet Age. Camgridge, UK: Polity.
Davies, James C. 1962. "Toward a Theory of Revolution." American Sociological Review 27, no. 1. Retrieved December 17, 2014 (http://www.jstor.org/discover/2089714?sid=21104884442891&uid=3739256&uid=3739704&uid=4&uid=2).
Gell, Aaron. 2011. "The Wall Street Protesters: What the Hell Do They Want?" New York Observer. Retrieved December 17, 2014 (http://observer.com/2011/09/the-wall-street-protesters-what-the-hell-do-they-want/).
Le Tellier, Alexandria. 2012. "What Occupy Wall Street Wants." Los Angeles Times. Retrieved December 17, 2014 (http://articles.latimes.com/2012/sep/17/news/la-ol-occupy-wall-street-anniversary-message-20120917).
NAACP. 2011. “100 Years of History.” Retrieved December 21, 2011 (http://www.naacp.org/pages/naacp-history). |
# Social Movements and Social Change
## Collective Behavior
### Forms of Collective Behavior
Flash mobs are examples of collective behavior, noninstitutionalized activity in which several or many people voluntarily engage. Other examples are a group of commuters traveling home from work and a population of teens adopting a favorite singer’s hairstyle. In short, collective behavior is any group behavior that is not mandated or regulated by an institution. There are three primary forms of collective behavior: the crowd, the mass, and the public.
It takes a fairly large number of people in close proximity to form a crowd (Lofland 1993). Examples include a group of people attending an Ani DiFranco concert, tailgating at a Patriots game, or attending a worship service. Turner and Killian (1993) identified four types of crowds. Casual crowds consist of people who are in the same place at the same time but who aren’t really interacting, such as people standing in line at the post office. Conventional crowds are those who come together for a scheduled event that occurs regularly, like a religious service. Expressive crowds are people who join together to express emotion, often at funerals, weddings, or the like. The final type, acting crowds, focuses on a specific goal or action, such as a protest movement or riot.
In addition to the different types of crowds, collective groups can also be identified in two other ways. A mass is a relatively large number of people with a common interest, though they may not be in close proximity (Lofland 1993), such as players of the popular Facebook game Farmville. A public, on the other hand, is an unorganized, relatively diffused group of people who share ideas, such as the Libertarian political party. While these two types of crowds are similar, they are not the same. To distinguish between them, remember that members of a mass share interests, whereas members of a public share ideas.
### Theoretical Perspectives on Collective Behavior
Early collective behavior theories (LeBon 1895; Blumer 1969) focused on the irrationality of crowds. Eventually, those theorists who viewed crowds as uncontrolled groups of irrational people were supplanted by theorists who viewed the behavior some crowds engaged in as the rational behavior of logical beings.
### Emergent-Norm Perspective
Sociologists Ralph Turner and Lewis Killian (1993) built on earlier sociological ideas and developed what is known as emergent norm theory. They believe that the norms experienced by people in a crowd may be disparate and fluctuating. They emphasize the importance of these norms in shaping crowd behavior, especially those norms that shift quickly in response to changing external factors. Emergent norm theory asserts that, in this circumstance, people perceive and respond to the crowd situation with their particular (individual) set of norms, which may change as the crowd experience evolves. This focus on the individual component of interaction reflects a symbolic interactionist perspective.
For Turner and Killian, the process begins when individuals suddenly find themselves in a new situation, or when an existing situation suddenly becomes strange or unfamiliar. For example, think about human behavior during Hurricane Katrina. New Orleans was decimated and people were trapped without supplies or a way to evacuate. In these extraordinary circumstances, what outsiders saw as “looting” was defined by those involved as seeking needed supplies for survival. Normally, individuals would not wade into a corner gas station and take canned goods without paying, but given that they were suddenly in a greatly changed situation, they established a norm that they felt was reasonable.
Once individuals find themselves in a situation ungoverned by previously established norms, they interact in small groups to develop new guidelines on how to behave. According to the emergent-norm perspective, crowds are not viewed as irrational, impulsive, uncontrolled groups. Instead, norms develop and are accepted as they fit the situation. While this theory offers insight into why norms develop, it leaves undefined the nature of norms, how they come to be accepted by the crowd, and how they spread through the crowd.
### Value-Added Theory
Neil Smelser’s (1962) meticulous categorization of crowd behavior, called value-added theory, is a perspective within the functionalist tradition based on the idea that several conditions must be in place for collective behavior to occur. Each condition adds to the likelihood that collective behavior will occur. The first condition is structural conduciveness, which occurs when people are aware of the problem and have the opportunity to gather, ideally in an open area. Structural strain, the second condition, refers to people’s expectations about the situation at hand being unmet, causing tension and strain. The next condition is the growth and spread of a generalized belief, wherein a problem is clearly identified and attributed to a person or group.
Fourth, precipitating factors spur collective behavior; this is the emergence of a dramatic event. The fifth condition is mobilization for action, when leaders emerge to direct a crowd to action. The final condition relates to action by the agents. Called social control, it is the only way to end the collective behavior episode (Smelser 1962).
A real-life example of these conditions occurred after the fatal police shooting of teenager Michael Brown, an unarmed eighteen-year-old African American, in Ferguson, MO on August 9, 2014. The shooting drew national attention almost immediately. A large group of mostly Black, local residents assembled in protest—a classic example of structural conduciveness. When the community perceived that the police were not acting in the people's interest and were withholding the name of the officer, structural strain became evident. A growing generalized belief evolved as the crowd of protesters were met with heavily armed police in military-style protective uniforms accompanied by an armored vehicle. The precipitating factor of the arrival of the police spurred greater collective behavior as the residents mobilized by assembling a parade down the street. Ultimately they were met with tear gas, pepper spray, and rubber bullets used by the police acting as agents of social control. The element of social control escalated over the following days until August 18, when the governor called in the National Guard.
### Assembling Perspective
Interactionist sociologist Clark McPhail (1991) developed assembling perspective, another system for understanding collective behavior that credited individuals in crowds as rational beings. Unlike previous theories, this theory refocuses attention from collective behavior to collective action. Remember that collective behavior is a noninstitutionalized gathering, whereas collective action is based on a shared interest. McPhail’s theory focused primarily on the processes associated with crowd behavior, plus the lifecycle of gatherings. He identified several instances of convergent or collective behavior, as shown on the chart below.
As useful as this is for understanding the components of how crowds come together, many sociologists criticize its lack of attention on the large cultural context of the described behaviors, instead focusing on individual actions.
### Summary
Collective behavior is noninstitutionalized activity in which several people voluntarily engage. There are three different forms of collective behavior: crowd, mass, and public. There are three main theories on collective behavior. The first, the emergent-norm perspective, emphasizes the importance of social norms in crowd behavior. The next, the value-added theory, is a functionalist perspective that states that several preconditions must be in place for collective behavior to occur. Finally the assembling perspective focuses on collective action rather than collective behavior, addressing the processes associated with crowd behavior and the lifecycle and various categories of gatherings.
### Section Quiz
### Short Answer
### References
Blumer, Herbert. 1969. “Collective Behavior.” Pp. 67–121 in Principles of Sociology, edited by A.M. Lee. New York: Barnes and Noble.
LeBon, Gustave. 1960 [1895]. The Crowd: A Study of the Popular Mind. New York: Viking Press.
Lofland, John. 1993. “Collective Behavior: The Elementary Forms.” Pp. 70–75 in Collective Behavior and Social Movements, edited by Russel Curtis and Benigno Aguirre. Boston: Allyn and Bacon.
McPhail, Clark. 1991. The Myth of the Madding Crowd. New York: Aldine de Gruyter.
Smelser, Neil J. 1963. Theory of Collective Behavior. New York: Free Press.
Turner, Ralph, and Lewis M. Killian. 1993. Collective Behavior. 4th ed. Englewood Cliffs, N. J., Prentice Hall. |
# Social Movements and Social Change
## Social Movements
Social movements are purposeful, organized groups that strive to work toward a common social goal. While most of us learned about social movements in history classes, we tend to take for granted the fundamental changes they caused —and we may be completely unfamiliar with the trend toward global social movements. But from the antitobacco movement that has worked to outlaw smoking in public buildings and raise the cost of cigarettes, to political uprisings throughout the Arab world, movements are creating social change on a global scale.
### Levels of Social Movements
Movements happen in our towns, in our nation, and around the world. Let’s take a look at examples of social movements, from local to global. No doubt you can think of others on all of these levels, especially since modern technology has allowed us a near-constant stream of information about the quest for social change around the world.
### Local
Local social movements typically refer to those in cities or towns, but they can also affect smaller constituencies, such as college campuses. Sometimes colleges are smaller hubs of a national movement, as seen during the Vietnam War protests or the Black Lives Matter protests. Other times, colleges are managing a more local issue. In 2012, The Cooper Union in New York City announced that, due to financial mismanagement and unforeseen downturns from the Great Recession, the college had a massive shortfall; it would be forced to charge tuition for the first time. To students at most other colleges, tuition would not seem out of line, but Cooper Union was founded (and initially funded) under the principle that it would not charge tuition. When the school formally announced the plan to charge tuition, students occupied a building and, later, the college president's office. Student action eventually contributed to the president's resignation and a financial recovery plan in partnership with the state attorney general.
Another example occurred in Wisconsin. After announcing a significant budget shortfall, Governor Scott Walker put forth a financial repair bill that would reduce the collective bargaining abilities of unions and other organizations in the state. (Collective bargaining was used to attain workplace protections, benefits, healthcare, and fair pay.) Faculty at the state's college system were not in unions, but teaching assistants, researchers, and other staff had regularly collectively bargained. Faced with the prospect of reduced job protections, pay, and benefits, the staff members began one of the earliest protests against Walker's action, by protesting on campus and sending an ironic message of love to the governor on Valentine's Day. Over time, these efforts would spread to other organizations in the state.
### State
The most impactful state-level protest would be to cease being a state, and organizations in several states are working toward that goal. Texas secession has been a relatively consistent movement since about 1990. The past decade has seen an increase in rhetoric and campaigns to drive interest and support for a public referendum (a direct vote on the matter by the people). The Texas Nationalist Movement, Texas Secede!, and other groups have provided formal proposals and programs designed to make the idea seem more feasible. Texit has become a widely used nickname and hashtag for the movement. And in February 2021, a bill was introduced to hold a referendum that would begin formal discussions on creating an independent nation—though the bill's sponsor indicated that it was mainly intended to begin conversation and evaluations rather than directly lead to secession (De Alba 2021).
States also get involved before and after national decisions. The legalization of same-sex marriage throughout the United States led some people to feel their religious beliefs were under attack. Following swiftly upon the heels of the Supreme Court Obergefell ruling, the Indiana legislature passed a Religious Freedom Restoration Act (RFRA, pronounced "rifra"). Originally crafted decades ago with the purpose of preserving the rights of minority religious people, more recent RFRA laws allow individuals, businesses, and other organizations to decide whom they will serve based on religious beliefs. For example, Arkansas's 2021 law allowed doctors to refuse to treat patients based on the doctor's religious beliefs (Associated Press 2021). In this way, state-level organizations and social movements are responding to a national decision.
### Global
Social organizations worldwide take stands on such general areas of concern as poverty, sex trafficking, and the use of genetically modified organisms (GMOs) in food. Nongovernmental organizations (NGOs) are sometimes formed to support such movements, such as the International Federation of Organic Agriculture Movement (FOAM). Global efforts to reduce poverty are represented by the Oxford Committee for Famine Relief (OXFAM), among others. The Fair Trade movement exists to protect and support food producers in developing countries. Occupy Wall Street, although initially a local movement, also went global throughout Europe and, as the chapter’s introductory photo shows, the Middle East.
### Types of Social Movements
We know that social movements can occur on the local, national, or even global stage. Are there other patterns or classifications that can help us understand them? Sociologist David Aberle (1966) addresses this question by developing categories that distinguish among social movements based on what they want to change and how much change they want. Reform movements seek to change something specific about the social structure. Examples include antinuclear groups, Mothers Against Drunk Driving (MADD), the Dreamers movement for immigration reform, and the Human Rights Campaign’s advocacy for Marriage Equality. Revolutionary movements seek to completely change every aspect of society. These include the 1960s counterculture movement, including the revolutionary group The Weather Underground, as well as anarchist collectives. Texas Secede! is a revolutionary movement. Religious/Redemptive movements are “meaning seeking,” and their goal is to provoke inner change or spiritual growth in individuals. Organizations pushing these movements include Heaven’s Gate or the Branch Davidians. The latter is still in existence despite government involvement that led to the deaths of numerous Branch Davidian members in 1993. Alternative movements are focused on self-improvement and limited, specific changes to individual beliefs and behavior. These include trends like transcendental meditation or a macrobiotic diet. Resistance movements seek to prevent or undo change to the social structure. The Ku Klux Klan, the Minutemen, and pro-life movements fall into this category.
### Stages of Social Movements
Later sociologists studied the lifecycle of social movements—how they emerge, grow, and in some cases, die out. Blumer (1969) and Tilly (1978) outline a four-stage process. In the preliminary stage, people become aware of an issue, and leaders emerge. This is followed by the coalescence stage when people join together and organize in order to publicize the issue and raise awareness. In the institutionalization stage, the movement no longer requires grassroots volunteerism: it is an established organization, typically with a paid staff. When people fall away and adopt a new movement, the movement successfully brings about the change it sought, or when people no longer take the issue seriously, the movement falls into the decline stage. Each social movement discussed earlier belongs in one of these four stages. Where would you put them on the list?
### Social Media and Social Movements
As we have mentioned throughout this text, and likely as you have experienced in your life, social media is a widely used mechanism in social movements. In the Groups and Organizations chapter, we discussed Tarana Burke first using "Me Too" in 2006 on a major social media venue of the time (MySpace). The phrase later grew into a massive movement when people began using it on Twitter to drive empathy and support regarding experiences of sexual harassment or sexual assault. In a similar way, Black Lives Matter began as a social media message after George Zimmerman was acquitted in the shooting death of 17-year-old Trayvon Martin, and the phrase burgeoned into a formalized (though decentralized) movement in subsequent years.
Social media has the potential to dramatically transform how people get involved in movements ranging from local school district decisions to presidential campaigns. As discussed above, movements go through several stages, and social media adds a dynamic to each of them. In the the preliminary stage, people become aware of an issue, and leaders emerge. Compared to movements of 20 or 30 years ago, social media can accelerate this stage substantially. Issue awareness can spread at the speed of a click, with thousands of people across the globe becoming informed at the same time. In a similar vein, those who are savvy and engaged with social media may emerge as leaders, even if, for example, they are not great public speakers.
At the next stage, the coalescence stage, social media is also transformative. Coalescence is the point when people join together to publicize the issue and get organized. President Obama’s 2008 campaign was a case study in organizing through social media. Using Twitter and other online tools, the campaign engaged volunteers who had typically not bothered with politics. Combined with comprehensive data tracking and the ability to micro-target, the campaign became a blueprint for others to build on. The 2020 elections featured a level of data analysis and rapid response capabilities that, while echoing the Obama campaign's early work, made the 2008 campaign look quaint. The campaigns and political analysts could measure the level of social media interaction following any campaign stop, debate, statement by the candidate, news mention, or any other event, and measure whether the tone or "sentiment" was positive or negative. Political polls are still important, but social media provides instant feedback and opportunities for campaigns to act, react, or—on a daily basis—ask for donations based on something that had occurred just hours earlier (Knowledge at Wharton 2020).
Interestingly, social media can have interesting outcomes once a movement reaches the institutionalization stage. In some cases, a formal organization might exist alongside the hashtag or general sentiment, as is the case with Black Lives Matter. At any one time, BLM is essentially three things: a structured organization, an idea with deep and personal meaning for people, and a widely used phrase or hashtag. It's possible that users of the hashtag are not referring to the formal organization. It's even possible that people who hold a strong belief that Black lives matter do not agree with all of the organization's principles or its leadership. And in other cases, people may be very aligned with all three contexts of the phrase. Social media is still crucial to the social movement, but its interplay is both complex and evolving.
In a similar way, MeToo activists, including Tarana Burke herself, have sought to clarify the interweaving of different aspects of the movement. She told the Harvard Gazette in 2020:
Sociologists have identified high-risk activism, such as the civil rights movement, as a “strong-tie” phenomenon, meaning that people are far more likely to stay engaged and not run home to safety if they have close friends who are also engaged. The people who dropped out of the movement—who went home after the danger became too great—did not display any less ideological commitment. But they lacked the strong-tie connection to other people who were staying. Social media had been considered “weak-tie” (McAdam 1993 and Brown 2011). People follow or friend people they have never met. Weak ties are important for our social structure, but they seemed to limit the level of risk we’ll take on their behalf. For some people, social media remains that way, but for others it can relate to or build stronger ties. For example, if people, who had for years known each other only through an online group, meet in person at an event, they may feel far more connected at that event and afterward than people who had never interacted before. And as we discussed in the Groups chapter, social media itself, even if people never meet, can bring people into primary group status, forming stronger ties.
Another way to consider the impact of social media on activism is through something that may or may not be emotional, has little implications regarding tie strength, and may be fleeting rather than permanent, but still be one of the largest considerations of any formal social movement: money. Returning to politics, think of the massive amounts of campaign money raised in each election cycle through social media. In the 2020 Presidential election and its aftermath, hundreds of millions of dollars were raised through social media. Likewise, 55 percent of people who engage with nonprofits through social media take some sort of action; and for 60 percent of them (or 33 percent of the total) that action is to give money to support the cause (Nonprofit Source 2020).
### Theoretical Perspectives on Social Movements
Most theories of social movements are called collective action theories, indicating the purposeful nature of this form of collective behavior. The following three theories are but a few of the many classic and modern theories developed by social scientists.
### Resource Mobilization
McCarthy and Zald (1977) conceptualize resource mobilization theory as a way to explain movement success in terms of the ability to acquire resources and mobilize individuals. Resources are primarily time and money, and the more of both, the greater the power of organized movements. Numbers of social movement organizations (SMOs), which are single social movement groups, with the same goals constitute a social movement industry (SMI). Together they create what McCarthy and Zald (1977) refer to as "the sum of all social movements in a society."
### Resource Mobilization and the Civil Rights Movement
An example of resource mobilization theory is activity of the civil rights movement in the decade between the mid 1950s and the mid 1960s. Social movements had existed before, notably the Women's Suffrage Movement and a long line of labor movements, thus constituting an existing social movement sector, which is the multiple social movement industries in a society, even if they have widely varying constituents and goals. The civil rights movement had also existed well before Rosa Parks refused to give up her bus seat to a white man. Less known is that Parks was a member of the NAACP and trained in leadership (A&E Television Networks, LLC. 2014). But her action that day was spontaneous and unplanned (Schmitz 2014). Her arrest triggered a public outcry that led to the famous Montgomery bus boycott, turning the movement into what we now think of as the "civil rights movement" (Schmitz 2014).
Mobilization had to begin immediately. Boycotting the bus made other means of transportation necessary, which was provided through car pools. Churches and their ministers joined the struggle, and the protest organization In Friendship was formed as well as The Friendly Club and the Club From Nowhere. A social movement industry, which is the collection of the social movement organizations that are striving toward similar goals, was growing.
Martin Luther King Jr. emerged during these events to become the charismatic leader of the movement, gained respect from elites in the federal government, and aided by even more emerging SMOs such as the Student Non-Violent Coordinating Committee (SNCC), the Congress of Racial Equality (CORE), the National Association for the Advancement of Colored People (NAACP), and the Southern Christian Leadership Conference (SCLC), among others. Several still exist today. Although the movement in that period was an overall success, and laws were changed (even if not attitudes), the "movement" continues. So do struggles to keep the gains that were made, even as the U.S. Supreme Court has recently weakened the Voter Rights Act of 1965, once again making it more difficult for Black Americans and other minorities to vote.
### Framing/Frame Analysis
Over the past several decades, sociologists have developed the concept of frames to explain how individuals identify and understand social events and which norms they should follow in any given situation (Goffman 1974; Snow et al. 1986; Benford and Snow 2000). Imagine entering a restaurant. Your “frame” immediately provides you with a behavior template. It probably does not occur to you to wear pajamas to a fine-dining establishment, throw food at other patrons, or spit your drink onto the table. However, eating food at a sleepover pizza party provides you with an entirely different behavior template. It might be perfectly acceptable to eat in your pajamas and maybe even throw popcorn at others or guzzle drinks from cans.
Successful social movements use three kinds of frames (Snow and Benford 1988) to further their goals. The first type, diagnostic framing, states the problem in a clear, easily understood way. When applying diagnostic frames, there are no shades of gray: instead, there is the belief that what “they” do is wrong and this is how “we” will fix it. The anti-gay marriage movement is an example of diagnostic framing with its uncompromising insistence that marriage is only between a man and a woman. Prognostic framing, the second type, offers a solution and states how it will be implemented. Some examples of this frame, when looking at the issue of marriage equality as framed by the anti-gay marriage movement, include the plan to restrict marriage to “one man/one woman” or to allow only “civil unions” instead of marriages. As you can see, there may be many competing prognostic frames even within social movements adhering to similar diagnostic frames. Finally, motivational framing is the call to action: what should you do once you agree with the diagnostic frame and believe in the prognostic frame? These frames are action-oriented. In the gay marriage movement, a call to action might encourage you to vote “no” on Proposition 8 in California (a move to limit marriage to male-female couples), or conversely, to contact your local congressperson to express your viewpoint that marriage should be restricted to male-female couples.
With so many similar diagnostic frames, some groups find it best to join together to maximize their impact. When social movements link their goals to the goals of other social movements and merge into a single group, a frame alignment process (Snow et al. 1986) occurs—an ongoing and intentional means of recruiting participants to the movement.
This frame alignment process has four aspects: bridging, amplification, extension, and transformation. Bridging describes a “bridge” that connects uninvolved individuals and unorganized or ineffective groups with social movements that, though structurally unconnected, nonetheless share similar interests or goals. These organizations join together to create a new, stronger social movement organization. Can you think of examples of different organizations with a similar goal that have banded together?
In the amplification model, organizations seek to expand their core ideas to gain a wider, more universal appeal. By expanding their ideas to include a broader range, they can mobilize more people for their cause. For example, the Slow Food movement extends its arguments in support of local food to encompass reduced energy consumption, pollution, obesity from eating more healthfully, and more.
In extension, social movements agree to mutually promote each other, even when the two social movement organization’s goals don’t necessarily relate to each other’s immediate goals. This often occurs when organizations are sympathetic to each others’ causes, even if they are not directly aligned, such as women’s equal rights and the civil rights movement.
Transformation means a complete revision of goals. Once a movement has succeeded, it risks losing relevance. If it wants to remain active, the movement has to change with the transformation or risk becoming obsolete. For instance, when the women’s suffrage movement gained women the right to vote, members turned their attention to advocating equal rights and campaigning to elect women to office. In short, transformation is an evolution in the existing diagnostic or prognostic frames that generally achieves a total conversion of the movement.
### New Social Movement Theory
New social movement theory, a development of European social scientists in the 1950s and 1960s, attempts to explain the proliferation of postindustrial and postmodern movements that are difficult to analyze using traditional social movement theories. Rather than being one specific theory, it is more of a perspective that revolves around understanding movements as they relate to politics, identity, culture, and social change. Some of these more complex interrelated movements include ecofeminism, which focuses on the patriarchal society as the source of environmental problems, and the transgender rights movement. Sociologist Steven Buechler (2000) suggests that we should be looking at the bigger picture in which these movements arise—shifting to a macro-level, global analysis of social movements.
### Summary
Social movements are purposeful, organized groups, either with the goal of pushing toward change, giving political voice to those without it, or gathering for some other common purpose. Social movements intersect with environmental changes, technological innovations, and other external factors to create social change. There are a myriad of catalysts that create social movements, and the reasons that people join are as varied as the participants themselves. Sociologists look at both the macro- and microanalytical reasons that social movements occur, take root, and ultimately succeed or fail.
### Section Quiz
### Short Answer
### References
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# Social Movements and Social Change
## Social Change
Collective behavior and social movements are just two of the forces driving social change, which is the change in society created through social movements as well as external factors. Essentially, any disruptive shift in the status quo, be it intentional or random, human-caused or natural, can lead to social change.
### Causes of Social Change
Throughout this text, we have discussed various causes and effects of social change. Below is a recap of some major drivers, including technology, social institutions, population, and the environment. Alone or in combination, these agents can disturb, improve, disrupt, or otherwise influence society.
### Technology
Some would say that improving technology has made our lives easier. Imagine what your day would be like without the Internet, the automobile, or electricity. In The World Is Flat, Thomas Friedman (2005) argues that technology is a driving force behind globalization, while the other forces of social change (social institutions, population, environment) play comparatively minor roles. He suggests that we can view globalization as occurring in three distinct periods. First, globalization was driven by military expansion, powered by horsepower and wind power. The countries best able to take advantage of these power sources expanded the most, and exert control over the politics of the globe from the late fifteenth century to around the year 1800. The second shorter period from approximately 1800 C.E. to 2000 C.E. consisted of a globalizing economy. Steam and rail power were the guiding forces of social change and globalization in this period. Finally, Friedman brings us to the post-millennial era. In this period of globalization, change is driven by technology, particularly the Internet (Friedman 2005).
Technology can change other societal forces. For example, advances in medical technology allow people to live longer, have more children, and survive some natural disasters or problems. Advances in agricultural technology have allowed us to alter food products, which impacts our health as well as the environment. A given technology can create beneficiaries, but that same technology—especially if it is disruptive—can lead others to lose their jobs, suffer from pollution, or be monitored or victimized.
The digital divide—the increasing gap between the technological haves and have-nots—exists both locally and globally. Added security issues include theft of personal information, cyber aggression, and loss of privacy. The constant change in technology leads to an almost inevitable lack of preparation for new risks on both personal and societal scales.
### The Darker Side of Technology: Electronic Aggression in the Information Age
The U.S. Center for Disease Control (CDC) uses the term "electronic aggression" to describe "any type of harassment or bullying that occurs through e-mail, a chat room, instant messaging, a website (including blogs), or text messaging" (CDC, n.d.) We generally think of this as cyberbullying. A 2011 study by the U.S. Department of Education found that 27.8 percent of students aged twelve through eighteen reported experiencing bullying. From the same sample 9 percent specifically reported having been a victim of cyberbullying (Robers et al. 2013).
Cyberbullying represents a powerful change in modern society. William F. Ogburn (1922) might have been describing it nearly a century ago when he defined "cultural lag," which occurs when material culture precedes nonmaterial culture. That is, society may not fully comprehend all the consequences of a new technology and so may initially reject it (such as stem cell research) or embrace it, sometimes with unintended negative consequences (such as pollution).
Cyberbullying is a special feature of the Internet. Unique to electronic aggression is that it can happen twenty-four hours a day, every day; it can reach a child (or an adult) even though she or he might otherwise feel safe in a locked house. The messages and images may be posted anonymously and to a very wide audience, and they might even be impossible to trace. Finally, once posted, the texts and images are very hard to delete. Its effects range from the use of alcohol and drugs to lower self-esteem, health problems, and even suicide (CDC, n.d.).
### Social Institutions
Each change in a single social institution leads to changes in all social institutions. For example, the industrialization of society meant that there was no longer a need for large families to produce enough manual labor to run a farm. Further, new job opportunities were in close proximity to urban centers where living space was at a premium. The result is that the average family size shrunk significantly.
This same shift toward industrial corporate entities also changed the way we view government involvement in the private sector, created the global economy, provided new political platforms, and even spurred new religions and new forms of religious worship like Scientology. It has also informed the way we educate our children: originally schools were set up to accommodate an agricultural calendar so children could be home to work the fields in the summer, and even today, teaching models are largely based on preparing students for industrial jobs, despite that being an outdated need. A shift in one area, such as industrialization, means an interconnected impact across social institutions.
### Population
Population composition is changing at every level of society. Births increase in one nation and decrease in another. Some families delay childbirth while others start bringing children into their folds early. Population changes can be due to random external forces, like an epidemic, or shifts in other social institutions, as described above. But regardless of why and how it happens, population trends have a tremendous interrelated impact on all other aspects of society.
In the United States, we are experiencing an increase in our senior population as Baby Boomers retire, which will in turn change the way many of our social institutions are organized. For example, there is an increased demand for housing in warmer climates, a massive shift in the need for elder care and assisted living facilities, and growing incidence of elder abuse. Retiring Boomers may also lead to labor or expertise shortages, and (as discussed extensively in the chapter on Aging and the Elderly) healthcare costs will increase to become a larger and larger portion of our economy.
Globally, often the countries with the highest fertility rates are least able to absorb and attend to the needs of a growing population. Family planning is a large step in ensuring that families are not burdened with more children than they can care for. On a macro level, the increased population, particularly in the poorest parts of the globe, also leads to increased stress on the planet’s resources.
### The Environment
As discussed extensively in the chapter on Population, Urbanization, and the Environment, changes in the environment and our interaction with it can have promising or devastating effects. Access to safe water is a primary determinant of health and prosperity. And as human populations expand in more vulnerable areas while natural disasters occur with more frequency, we see an increase in the number of people affected by those disasters.
Overall health and wellbeing are deeply affected by the environment even in urbanized areas. Many types of cancers, which are collectively the leading cause of death in higher-income countries, have environmental influences (Mahase 2019).
### Modernization
Modernization describes the processes that increase the amount of specialization and differentiation of structure in societies resulting in the move from an undeveloped society to a developed, technologically driven society (Irwin 1975). By this definition, the level of modernity within a society is judged by the sophistication of its technology, particularly as it relates to infrastructure, industry, and the like. However, it is important to note the inherent ethnocentric bias of such assessment. Why do we assume that those living in semi-peripheral and peripheral nations would find it so wonderful to become more like the core nations? Is modernization always positive?
One contradiction of all kinds of technology is that they often promise time-saving benefits, but somehow fail to deliver. How many times have you ground your teeth in frustration at an Internet site that refused to load or at a dropped call on your cell phone? Despite time-saving devices such as dishwashers, washing machines, and, now, remote control vacuum cleaners, the average amount of time spent on housework is the same today as it was fifty years ago. And the dubious benefits of 24/7 e-mail and immediate information have simply increased the amount of time employees are expected to be responsive and available. While once businesses had to travel at the speed of the U.S. postal system, sending something off and waiting until it was received before the next stage, today the immediacy of information transfer means there are no such breaks.
Further, the Internet bought us information, but at a cost. The morass of information means that there is as much poor information available as trustworthy sources. There is a delicate line to walk when core nations seek to bring the assumed benefits of modernization to more traditional cultures. For one, there are obvious procapitalist biases that go into such attempts, and it is short-sighted for western governments and social scientists to assume all other countries aspire to follow in their footsteps. Additionally, there can be a kind of neo-liberal defense of rural cultures, ignoring the often crushing poverty and diseases that exist in peripheral nations and focusing only on a nostalgic mythology of the happy peasant. It takes a very careful hand to understand both the need for cultural identity and preservation as well as the hopes for future growth.
### Summary
There are numerous and varied causes of social change. Four common causes, as recognized by social scientists, are technology, social institutions, population, and the environment. All four of these areas can impact when and how society changes. And they are all interrelated: a change in one area can lead to changes throughout. Modernization is a typical result of social change. Modernization refers to the process of increased differentiation and specialization within a society, particularly around its industry and infrastructure. While this assumes that more modern societies are better, there has been significant pushback on this western-centric view that all peripheral and semi-peripheral countries should aspire to be like North America and Western Europe.
### Section Quiz
### Short Answer
### References
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Robers, Simone, Jana Kemp, Jennifer, Truman, and Thomas D. Snyder. 2013. Indicators of School Crime and Safety: 2012. National Center for Education Statistics, U.S. Department of Education, and Bureau of Justice Statistics, Office of Justice Programs, U.S. Department of Justice: Washington, DC. Retrieved December 17, 2014 (http://nces.ed.gov/pubs2013/2013036.pdf).
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# Funciones
## Introducción
Hacia el final del siglo XX, el valor de las acciones de las empresas de Internet y tecnología aumentó de forma espectacular. En consecuencia, el promedio bursátil de Standard and Poor's también subió. El gráfico anterior muestra el valor de esa inversión inicial de algo menos de 100 dólares a lo largo de 40 años. Muestra que una inversión que valía menos de 500 dólares hasta aproximadamente 1995 se disparó hasta unos 1.100 dólares a principios de 2000. Ese periodo de cinco años se conoció como la "burbuja de las puntocom" porque se formaron muchas empresas de Internet. Sin embargo, como suelen hacer las burbujas, la burbuja de las puntocom acabó por explotar. Muchas empresas crecieron demasiado deprisa y de repente quebraron. El resultado provocó el fuerte descenso representado en el gráfico a partir de finales de 2000.
Observe que, al considerar este ejemplo, existe una relación definida entre el año y la media bursátil. Para cualquier año que elijamos, podemos determinar el valor correspondiente de la media bursátil. En este capítulo, exploraremos estos tipos de relaciones y sus propiedades. |
# Funciones
## Funciones y notación de funciones
Un avión de pasajeros cambia de altitud a medida que aumenta su distancia desde el punto de partida de un vuelo. El peso de un niño en crecimiento aumenta con el tiempo. En cada caso, una cantidad depende de otra. Existe una relación entre ambas cantidades que podemos describir, analizar y utilizar para hacer predicciones. En esta sección, analizaremos estas relaciones.
### Determinar si una relación representa una función
La relación es un conjunto de pares ordenados. El conjunto de las primeras componentes de cada par ordenado se llama dominio y el conjunto de las segundas componentes de cada par ordenado se llama rango. Considere el siguiente conjunto de pares ordenados. Los primeros números de cada par son los cinco primeros números naturales. El segundo número de cada par es el doble del primero.
El dominio es
El rango es
Observe que cada valor en el dominio también se conoce como un valor de entrada, o variable independiente, y se suele marcar con la letra minúscula
Cada valor del rango se conoce también como valor de salida, o variable dependiente, y se suele marcar con letra minúscula
Una función
es una relación que asigna un único valor del rango a cada valor del dominio. Es decir, no se repiten los valores x. Para nuestro ejemplo que relaciona los cinco primeros números naturales con los números del doble de sus valores, esta relación es una función porque cada elemento del dominio,
está emparejado con exactamente un elemento del rango,
Consideremos ahora el conjunto de pares ordenados que relaciona los términos "par" e "impar" con los cinco primeros números naturales. Aparecerían como
Observe que cada elemento en el dominio,
no está emparejado con exactamente un elemento en el rango,
Por ejemplo, el término "impar" corresponde a tres valores del rango,
y el término "par" corresponde a dos valores del rango,
Esto viola la definición de una función, por lo que esta relación no es una función.
La compara las relaciones que son funciones y las que no lo son.
### Uso de la notación de función
Una vez que determinamos que una relación es una función, necesitamos mostrar y definir las relaciones funcionales para poder entenderlas y utilizarlas, y a veces también para poder programarlas en las computadoras. Hay varias formas de representar las funciones. La notación de función estándar es una representación que facilita el trabajo con las funciones.
Para representar "la altura es una función de la edad", empezamos por identificar las variables descriptivas
para la altura y
para la edad. Las letras
y
se utilizan a menudo para representar funciones al igual que utilizamos
y
para representar números y
y
para representar conjuntos.
Recuerde que podemos utilizar cualquier letra para designar la función; la notación
nos muestra que
depende de
El valor
debe introducirse en la función
para obtener un resultado. Los paréntesis indican que la edad es la entrada en la función; no indican la multiplicación.
También podemos dar una expresión algebraica como entrada a una función. Por ejemplo
significa “primero se suman a y b, y el resultado es la entrada para la función f”. Las operaciones deben realizarse en este orden para obtener el resultado correcto.
### Representación de funciones mediante tablas
Un método habitual para representar las funciones es en forma de tabla. Las filas o columnas de la tabla muestran los valores de entrada y salida correspondientes. En algunos casos, estos valores representan todo lo que sabemos sobre la relación; otras veces, la tabla ofrece algunos ejemplos seleccionados de una relación más completa.
La indica el número de entrada de cada mes (enero = 1, febrero = 2, y así sucesivamente) y el valor de salida del número de días de ese mes. Esta información representa todo lo que sabemos sobre los meses y días de un año determinado (que no es bisiesto). Observe que, en esta tabla, definimos una función de días al mes
donde
identifica los meses por un número entero en lugar de por su nombre.
La define una función
Recuerde que esta notación nos dice que
es el nombre de la función que toma la entrada
y da como salida
La muestra la edad de los niños en años y sus correspondientes alturas. Esta tabla muestra solo algunos de los datos disponibles sobre la altura y la edad de los niños. Observamos enseguida que esta tabla no representa una función porque el mismo valor de entrada, 5 años, tiene dos valores de salida diferentes, 40 in y 42 in.
### Hallar los valores de entrada y salida de una función
Cuando conocemos un valor de entrada y queremos determinar el correspondiente valor de salida de una función, evaluamos la función. La evaluación siempre producirá un resultado porque cada valor de entrada de una función corresponde exactamente a un valor de salida.
Cuando conocemos un valor de salida y queremos determinar los valores de entrada que producirían ese valor de salida, establecemos la salida igual a la fórmula de la función y resolvemos la entrada. La resolución puede producir más de una solución porque diferentes valores de entrada pueden producir el mismo valor de salida.
### Evaluación de funciones en formas algebraicas
Cuando tenemos una función en forma de fórmula, suele ser sencillo evaluar la función. Por ejemplo, la función
se puede evaluar elevando al cuadrado el valor de entrada, multiplicando por 3 y restando el producto de 5.
### Evaluación de funciones expresadas en fórmulas
Algunas funciones se definen mediante reglas o procedimientos matemáticos expresados en forma de ecuación. Si es posible expresar la salida de la función con una fórmula que implique la cantidad de entrada, entonces podemos definir una función en forma algebraica. Por ejemplo, la ecuación
expresa una relación funcional entre
y
Podemos reescribirlo para decidir si
es una función de
### Evaluación de una función dada en forma de tabla
Como hemos visto anteriormente, podemos representar funciones en tablas. A la inversa, podemos utilizar la información de las tablas para escribir funciones, y podemos evaluar funciones utilizando las tablas. Por ejemplo, ¿qué tan bien recuerdan nuestras mascotas los buenos recuerdos que compartimos con ellas? Hay una leyenda urbana que dice que un pez dorado tiene una memoria de 3 segundos, pero esto es solo un mito. El pez dorado puede recordar hasta 3 meses, mientras que el pez betta tiene una memoria de hasta 5 meses. Y mientras que la capacidad de memoria de un cachorro no supera los 30 segundos, el perro adulto puede recordar durante 5 minutos. Esto es escaso comparado con un gato, cuya memoria dura 16 horas.
La función que relaciona el tipo de mascota con la duración de su memoria se visualiza más fácilmente con el uso de una tabla. Vea la .http://www.kgbanswers.com/how-long-is-a-dogs-memory-span/4221590. Consultado el 24 mar 2014.
A veces, evaluar una función en forma de tabla puede ser más útil que utilizar ecuaciones. Llamemos aquí a la función
El dominio de la función es el tipo de mascota y el rango es un número real que representa el número de horas que dura la memoria de la mascota. Evaluamos la función
en el valor de entrada de “pez dorado”. Escribiríamos
Observe que, para evaluar la función en forma de tabla, identificamos el valor de entrada y el correspondiente valor de salida de la fila pertinente de la tabla. La forma de tabla de la función
parece ideal para esta función, más que escribirla en forma de párrafo o función.
### Hallar los valores de una función a partir de un gráfico
Evaluar una función mediante un gráfico también requiere encontrar el valor de salida correspondiente para un valor de entrada dado, solo que en este caso, encontramos el valor de salida mirando el gráfico. La resolución de una ecuación de función mediante un gráfico requiere encontrar todos los casos del valor de salida dados en el gráfico y observar el valor o valores de entrada correspondientes.
### Cómo determinar si una función es biunívoca
Algunas funciones tienen un valor de salida determinado que corresponde a dos o más valores de entrada. Por ejemplo, en el gráfico de acciones que se muestra en la figura al principio de este capítulo, el precio de las acciones era de 1.000 dólares en cinco fechas diferentes, lo que significa que había cinco valores de entrada diferentes que daban como resultado el mismo valor de salida de 1.000 dólares.
Sin embargo, algunas funciones solo tienen un valor de entrada para cada valor de salida, así como solo tienen una salida para cada entrada. A estas funciones las llamamos funciones biunívocas. A modo de ejemplo, considere una escuela que solo utiliza calificaciones con letras y equivalentes decimales, como se indica en la .
Este sistema de calificación representa una función biunívoca, ya que cada letra de entrada produce un promedio de calificación particular como salida y cada promedio de calificación corresponde a una letra de entrada.
Para visualizar este concepto, veamos de nuevo las dos funciones simples esbozadas en la (a) y la (b). La función de la parte (a) muestra una relación que no es una función biunívoca porque las entradas
y
producen una salida
La función de la parte (b) muestra una relación que es una función biunívoca porque cada entrada está asociada a una única salida.
### Uso de la prueba de la línea vertical
Como hemos visto en algunos ejemplos anteriores, podemos representar una función mediante un gráfico. Los gráficos muestran un gran número de pares de entrada-salida en un espacio reducido. La información visual que proporcionan suele facilitar la comprensión de las relaciones. Por convención, los gráficos se construyen normalmente con los valores de entrada en el eje horizontal y los valores de salida en el eje vertical.
Los gráficos más comunes nombran el valor de entrada
y el valor de salida
y decimos
es una función de
o
cuando la función se llama
El gráfico de la función es el conjunto de todos los puntos
en el plano que satisface la ecuación
Si la función está definida solo para unos pocos valores de entrada, entonces el gráfico de la función son solo unos pocos puntos, donde la coordenada x de cada punto es un valor de entrada y la coordenada y de cada punto es el valor de salida correspondiente. Por ejemplo, los puntos negros del gráfico de la nos indican que
y
Sin embargo, el conjunto de todos los puntos
lo que cumple con
es una curva. La curva mostrada incluye
y
porque la curva pasa por esos puntos.
La prueba de la línea vertical puede utilizarse para determinar si un gráfico representa una función. Si podemos dibujar cualquier línea vertical que cruce un gráfico más de una vez, entonces el gráfico no define una función, porque una función solo tiene un valor de salida para cada valor de entrada. Vea la .
### Utilizar la prueba de la línea horizontal
Una vez que hemos determinado que un gráfico define una función, una forma fácil de determinar si es una función biunívoca es utilizar la prueba de la línea horizontal. Dibuje líneas horizontales a través del gráfico. Si alguna línea horizontal lo cruza más de una vez, entonces el gráfico no representa una función biunívoca.
### Identificar las funciones básicas de la caja de herramientas
En este texto, exploraremos las funciones: las formas de sus gráficos, sus características únicas, sus fórmulas algebraicas y cómo resolver problemas con ellas. Cuando aprendemos a leer, empezamos por el alfabeto. Cuando aprendemos a hacer aritmética, empezamos con los números. Cuando trabajamos con funciones, es igualmente útil tener un conjunto base de elementos de construcción. Los llamamos "funciones de la caja de herramientas", que forman un conjunto de funciones básicas que conocemos con los nombres de gráfico, fórmula y propiedades especiales. Algunas de estas funciones están programadas en botones individuales de muchas calculadoras. Para estas definiciones utilizaremos
como variable de entrada y
como variable de salida.
A lo largo de este libro veremos con frecuencia estas funciones de la caja de herramientas, sus combinaciones de funciones, sus gráficos y sus transformaciones. Será muy útil si podemos reconocer rápidamente estas funciones de la caja de herramientas y sus características por su nombre, fórmula, gráfico y propiedades básicas de la tabla. Los gráficos y los valores de la tabla de muestra se incluyen con cada función mostrada en la .
### Ecuaciones clave
### Conceptos clave
1. Una relación es un conjunto de pares ordenados. Una función es un tipo específico de relación en la que cada valor de dominio, o entrada, conduce exactamente a un valor de rango, o salida. Vea el y el .
2. La notación de función es un método abreviado para relacionar la entrada con la salida de la forma
Vea el y el .
3. En forma de tabla, una función puede representarse mediante filas o columnas que se refieren a los valores de entrada y salida. Vea el .
4. Para evaluar una función, determinamos un valor de salida para un valor de entrada correspondiente. Las formas algebraicas de una función se pueden evaluar sustituyendo la variable de entrada por un valor determinado. Vea el y el .
5. Para resolver el valor de una función específica, determinamos los valores de entrada que producen el valor de salida específico. Vea el .
6. La forma algebraica de una función puede escribirse a partir de una ecuación. Vea el y el .
7. Los valores de entrada y salida de una función pueden identificarse a partir de una tabla. Vea el .
8. Relacionar los valores de entrada con los de salida en un gráfico es otra forma de evaluar una función. Vea el .
9. Una función es biunívoca si cada valor de salida corresponde a un solo valor de entrada. Vea el .
10. Un gráfico representa una función si cualquier línea vertical dibujada en él lo interseca en no más de un punto. Vea el .
11. El gráfico de una función biunívoca pasa la prueba de la línea horizontal. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, determine si la relación representa una función.
En los siguientes ejercicios, determine si la relación representa a
en función de
En los siguientes ejercicios, evalúe
a los valores indicados
### Gráficos
En los siguientes ejercicios, utilice la prueba de la línea vertical para determinar qué gráficos muestran relaciones que son funciones.
En los siguientes ejercicios, determine si el gráfico dado es una función biunívoca.
### Numéricos
En los siguientes ejercicios, determine si la relación representa una función.
En los siguientes ejercicios, determine si la relación representada en forma de tabla representa
en función de
En los siguientes ejercicios, utilice la función
representada en la .
En los siguientes ejercicios, evalúe la función
en los valores
y
En los siguientes ejercicios, evalúe las expresiones, dadas las funciones
y
1.
2.
3.
### En tecnología
En los siguientes ejercicios, grafique
en el dominio dado. Determine el rango correspondiente. Muestre cada gráfico.
En los siguientes ejercicios, grafique
en el dominio dado. Determine el rango correspondiente. Muestre cada gráfico.
En los siguientes ejercicios, grafique
en el dominio dado. Determine el rango correspondiente. Muestre cada gráfico.
En los siguientes ejercicios, grafique
en el dominio dado. Determine el rango correspondiente. Muestre cada gráfico.
### Aplicaciones en el mundo real
|
# Funciones
## Dominio y rango
Las películas de terror y de suspenso son populares y, muy a menudo, muy rentables. Cuando se incluyen actores de gran presupuesto, lugares de rodaje y efectos especiales, los estudios cuentan con una audiencia aún mayor para tener éxito. Consideremos cinco grandes obras de suspenso/terror de principios del siglo XXI: Soy Leyenda, Hannibal, El Aro, La Maldición y El Conjuro. La muestra la cantidad en dólares que recaudó cada una de esas películas cuando se estrenaron, así como la venta de entradas para las películas de terror en general por año. Observe que podemos utilizar los datos para crear una función de la cantidad que ganó cada película o el total de ventas de entradas de todas las películas de terror por año. Al crear varias funciones utilizando los datos, podemos identificar diferentes variables dependientes e independientes, y podemos analizar los datos y las funciones para determinar el dominio y el rango. En esta sección, investigaremos métodos para determinar el dominio y el rango de funciones como estas.
### Hallar el dominio de una función definida por una ecuación
En Funciones y notación de funciones, se introdujeron los conceptos de dominio y rango. En esta sección, practicaremos la determinación de dominios y rangos para funciones específicas. Tenga en cuenta que, al determinar los dominios y los rangos, tenemos que considerar lo que es físicamente posible o significativo en los ejemplos del mundo real, como la venta de entradas y el año en el ejemplo anterior de las películas de terror. También hay que tener en cuenta lo que está matemáticamente permitido. Por ejemplo, no podemos incluir ningún valor de entrada que nos lleve a tomar una raíz par de un número negativo si el dominio y el rango consisten en números reales. O en una función expresada como fórmula, no podemos incluir ningún valor de entrada en el dominio que nos lleve a dividir entre 0.
Podemos visualizar el dominio como una "zona de espera" que contiene "materias primas" para una "máquina funcional" y el rango como otra "zona de espera" para los productos de la máquina. Vea la .
Podemos escribir el dominio y el rango en notación intervalo, que utiliza valores entre paréntesis para describir un conjunto de números. En la notación intervalo, utilizamos un corchete “[“ cuando el conjunto incluye el punto final y un paréntesis “(“ para indicar que el punto final no está incluido o que el intervalo no está acotado. Por ejemplo, si una persona tiene 100 dólares para gastar, tendría que expresar el intervalo que es mayor que 0 y menor o igual que 100 y escribir
Más adelante hablaremos con más detalle de la notación intervalo.
Vamos a centrar nuestra atención en encontrar el dominio de una función de la que se proporciona una ecuación. A menudo, encontrar el dominio de tales funciones implica recordar tres formas diferentes. En primer lugar, si la función no tiene denominador o tiene una raíz impar, considere si el dominio podrían ser todos los números reales. En segundo lugar, si hay un denominador en la ecuación de la función, excluya los valores en el dominio que obligan al denominador a ser cero. En tercer lugar, si hay una raíz par, considere la posibilidad de excluir los valores que harían que el radicando fuera negativo.
Antes de empezar, repasemos las convenciones de la notación intervalo:
1. El término más pequeño del intervalo se escribe primero.
2. El término más grande del intervalo se escribe en segundo lugar, tras una coma.
3. Los paréntesis, “(“ o “)”, se utilizan para indicar que un punto final no está incluido, lo que se denomina exclusivo.
4. Los corchetes, “[“ o “]”, se utilizan para indicar que un punto final está incluido, lo que se denomina inclusivo.
Vea la para conocer un resumen de la notación intervalo.
### Usar notaciones para especificar el dominio y el rango
En los ejemplos anteriores, utilizamos inecuaciones y listas para describir el dominio de las funciones. También podemos utilizar desigualdades, u otros enunciados que puedan definir conjuntos de valores o datos, para describir el comportamiento de la variable en la notación del constructor de conjuntos. Por ejemplo,
describe el comportamiento de
en la notación del constructor de conjuntos. Las llaves
se leen como "el conjunto de", y la barra vertical | se lee como "tal que", por lo que leeríamos
como "el conjunto de valores x tales que 10 es menor o igual que
y
es menos de 30”.
La compara la notación de inecuación, la notación del constructor de conjuntos y la notación intervalos.
Para combinar dos intervalos utilizando la notación de inecuación o la notación del constructor de conjuntos, utilizamos la palabra “o”. Como hemos visto en los ejemplos anteriores, utilizamos el símbolo de unión,
para combinar dos intervalos no conectados. Por ejemplo, la unión de los conjuntos
y
es el conjunto
Es el conjunto de todos los elementos que pertenecen a uno u otro (o a ambos) de los dos conjuntos originales. En el caso de conjuntos con un número finito de elementos como este, no es necesario enumerar los elementos en orden ascendente de valor numérico. Si los dos conjuntos originales tienen algunos elementos en común, esos elementos deben figurar solo una vez en el conjunto de unión. Para conjuntos de números reales en intervalos, otro ejemplo de unión es
### Hallar el dominio y el rango de los gráficos
Otra forma de identificar el dominio y el rango de las funciones es mediante el uso de gráficos. Dado que el dominio se refiere al conjunto de posibles valores de entrada, el dominio de un gráfico consiste en todos los valores de entrada mostrados en el eje x. El rango es el conjunto de posibles valores de salida, que se muestran en el eje y. Tenga en cuenta que si el gráfico continúa más allá de la porción que podemos ver, el dominio y el rango pueden ser mayores que los valores visibles. Vea la .
Podemos observar que el gráfico se extiende horizontalmente desde
a la derecha sin límite, por lo que el dominio es
La extensión vertical del gráfico son todos los valores del rango
y por debajo, por lo que el rango es
Observe que el dominio y el rango se escriben siempre de menor a mayor valor, o de izquierda a derecha, para el dominio, y de la parte inferior del gráfico a la superior para el rango.
### Hallar dominios y rangos de las funciones de la caja de herramientas
Ahora volveremos a nuestro conjunto de funciones de la caja de herramientas para determinar el dominio y el rango de cada una.
### Graficar funciones definidas por partes
A veces, nos encontramos con una función que requiere más de una fórmula para obtener la salida dada. Por ejemplo, en las funciones de la caja de herramientas, introducimos la función de valor absoluto
Con un dominio de todos los números reales y un rango de valores mayor o igual a 0, el valor absoluto puede definirse como la magnitud, o módulo, de un valor de un número real sin importar el signo. Es la distancia desde el 0 en la línea numérica. Todas estas definiciones requieren que la salida sea mayor o igual a 0.
Si introducimos 0, o un valor positivo, la salida es la misma que la entrada.
Si introducimos un valor negativo, la salida es la opuesta a la entrada.
Ya que esto requiere dos procesos o piezas diferentes, la función de valor absoluto es un ejemplo de función definida por partes. Una función definida por partes es una función en la que se utiliza más de una fórmula para definir la salida sobre diferentes partes del dominio.
Utilizamos funciones definidas por partes para describir situaciones en las que una regla o relación cambia cuando el valor de entrada cruza ciertos "límites". Por ejemplo, a menudo nos encontramos con situaciones en las que el costo por pieza de un determinado artículo se descuenta una vez que el número de pedidos supera un determinado valor. Las categorías impositivas son otro ejemplo real de funciones definidas por partes. Por ejemplo, consideremos un sistema fiscal simple en el que los ingresos hasta 10.000 dólares se gravan al 10 %, y cualquier ingreso adicional se grava al 20 %. El impuesto sobre una renta total
sería
si
y
si
### Conceptos clave
1. El dominio de una función incluye todos los valores reales de entrada que no nos harían intentar una operación matemática indefinida, como dividir entre cero o sacar la raíz cuadrada de un número negativo.
2. El dominio de una función puede determinarse enumerando los valores de entrada de un conjunto de pares ordenados. Vea el .
3. El dominio de una función también puede determinarse identificando los valores de entrada de una función escrita como una ecuación. Vea el , el y el .
4. Los valores de los intervalos representados en una recta numérica pueden describirse utilizando la notación de inecuación, la notación del constructor de conjuntos y la notación intervalo. Vea el .
5. Para muchas funciones, el dominio y el rango se pueden determinar a partir de un gráfico. Vea el y el .
6. La comprensión de las funciones de la caja de herramientas puede utilizarse para encontrar el dominio y el rango de las funciones relacionadas. Vea el , el y el .
7. Una función definida por partes se describe con más de una fórmula. Vea el y el .
8. Una función definida por partes se puede graficar utilizando cada fórmula algebraica en su subdominio asignado. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, halle el dominio de cada función utilizando la notación intervalo.
### Gráficos
En los siguientes ejercicios, escriba el dominio y el rango de cada función utilizando la notación intervalo.
En los siguientes ejercicios, dibuje un gráfico de la función definida por partes. Escriba el dominio en notación intervalo.
### Numéricos
En los siguientes ejercicios, dada cada función
evaluar
y
En los siguientes ejercicios, dada cada función
evaluar
y
En los siguientes ejercicios, escriba el dominio de la función definida por partes en notación intervalo.
### En tecnología
### Extensión
### Aplicaciones en el mundo real
|
# Funciones
## Tasas de variación y comportamiento de los gráficos
Los costos de la gasolina han experimentado algunas fluctuaciones salvajes en las últimas décadas. La http://www.eia.gov/totalenergy/data/annual/showtext.cfm?t=ptb0524. Consultado el 5 mar 2014. muestra el costo promedio, en dólares, de un galón de gasolina entre los años 2005 a 2012. El costo de la gasolina puede considerarse en función del año.
Si solo nos interesara la evolución de los precios de la gasolina entre 2005 y 2012, podríamos calcular que el costo por galón ha pasado de 2,31 a 3,68 dólares, lo que supone un aumento de 1,37 dólares. Aunque esto es interesante, podría ser más útil observar cuánto ha cambiado el precio por año. En esta sección, investigaremos cambios como estos.
### Hallar la tasa media de cambio de una función
La variación del precio por año es una tasa de cambio porque describe cómo cambia una cantidad de salida en relación con el cambio de la cantidad de entrada. Observamos que el precio de la gasolina en la no cambió en la misma cantidad cada año, por lo que la tasa de cambio no fue constante. Si utilizamos solo los datos iniciales y finales, estaríamos encontrando la tasa de cambio promedio durante el periodo especificado. Para calcular la intersección en tasa media de cambio, dividimos el cambio en la salida entre el cambio del valor en la entrada.
La letra griega
(delta) significa el cambio en una cantidad; leemos el cociente como “delta y sobre delta x" o "el cambio en
dividido entre el cambio en
De vez en cuando escribimos
en vez de
que sigue representando el cambio en el valor de salida de la función resultante de un cambio en su valor de entrada. No significa que estemos cambiando la función por otra.
En nuestro ejemplo, el precio de la gasolina aumentó 1,37 dólares de 2005 a 2012. A lo largo de 7 años, la tasa de cambio promedio fue
En promedio, el precio de la gasolina aumentó unos 19,6 céntimos cada año.
Otros ejemplos de tasas de cambio son:
1. Una población de ratas que aumenta en 40 ratas por semana
2. Un automóvil que viaja a 68 millas por hora (la distancia recorrida cambia en 68 millas cada hora a medida que pasa el tiempo)
3. Un automóvil que recorre 27 millas por galón (la distancia recorrida cambia en 27 millas por cada galón)
4. La corriente que atraviesa un circuito eléctrico aumenta en 0,125 amperios por cada voltio de aumento de voltaje
5. La cantidad de dinero en una cuenta universitaria disminuye en 4.000 dólares por trimestre
### Usar un gráfico para determinar si una función es creciente, decreciente o constante
Como parte de la exploración de cómo cambian las funciones, podemos identificar los intervalos en los que la función cambia de forma específica. Decimos que una función es creciente en un intervalo si los valores de la función aumentan a medida que los valores de entrada aumentan dentro de ese intervalo. Del mismo modo, una función es decreciente en un intervalo si los valores de la función disminuyen a medida que los valores de entrada aumentan en ese intervalo. La tasa de cambio promedio de una función creciente es positiva, y la tasa de cambio promedio de una función decreciente es negativa. La muestra ejemplos de intervalos crecientes y decrecientes en una función.
Mientras que algunas funciones son crecientes (o decrecientes) en todo su dominio, muchas otras no lo son. Un valor de la entrada en el que una función pasa de ser creciente a decreciente (al ir de izquierda a derecha, es decir, al aumentar la variable de entrada) es la ubicación de un máximo local. El valor de la función en ese punto es el máximo local. Si una función tiene más de uno, decimos que tiene máximos locales. Del mismo modo, un valor de la entrada en el que una función cambia de decreciente a creciente a medida que la variable de entrada aumenta es la ubicación de un mínimo local. El valor de la función en ese punto es el mínimo local. La forma plural es "mínimos locales". En conjunto, los máximos y mínimos locales se denominan extremos locales, o valores extremos locales, de la función (la forma singular es “extremo”). A menudo, el término local se sustituye por el término relativo. En este texto, utilizaremos el término local.
Es evidente que una función no es creciente ni decreciente en un intervalo en el que es constante. Una función tampoco es creciente ni decreciente en los extremos. Observe que tenemos que hablar de extremos locales, porque cualquier extremo local dado, tal como se define aquí, no es necesariamente el máximo más alto o el mínimo más bajo en todo el dominio de la función.
Para la función cuyo gráfico se muestra en la , el máximo local es 16, y se produce en
El mínimo local es
y se produce en
Para ubicar los máximos y mínimos locales de un gráfico, tenemos que observar el gráfico para determinar dónde alcanza sus puntos más altos y más bajos, respectivamente, dentro de un intervalo abierto. Como la cima de una montaña rusa, el gráfico de una función es más alto en un máximo local que en los puntos cercanos de ambos lados. El gráfico también será más bajo en un mínimo local que en los puntos vecinos. La ilustra estas ideas para un máximo local.
Estas observaciones nos llevan a una definición formal de los extremos locales.
### Analizar las funciones de la caja de herramientas para aumentar o disminuir los intervalos
Ahora volveremos a nuestras funciones de la caja de herramientas y discutiremos su comportamiento gráfico en la , la y la .
### Utilizar un gráfico para localizar el máximo absoluto y el mínimo absoluto
Hay una diferencia entre ubicar los puntos más altos y más bajos de un gráfico en una región alrededor de un intervalo abierto (localmente) y ubicar los puntos más altos y más bajos del gráfico para todo el dominio. Las coordenadas
(salida) en los puntos más altos y más bajos se denominan máximo absoluto y mínimo absoluto, respectivamente.
Para localizar los máximos y mínimos absolutos de un gráfico, tenemos que observar el gráfico para determinar dónde alcanza sus puntos más altos y más bajos en el dominio de la función. Vea la .
No todas las funciones tienen un valor máximo o mínimo absoluto. La función de la caja de herramientas
es una de esas funciones.
### Ecuaciones clave
### Conceptos clave
1. La tasa de cambio relaciona el cambio de una cantidad de salida con el de una cantidad de entrada. La tasa de cambio promedio se determina utilizando solo los datos iniciales y finales. Vea el .
2. La identificación de los puntos que marcan el intervalo en un gráfico puede utilizarse para hallar la tasa de cambio promedio. Vea el .
3. La comparación de pares de valores de entrada y salida en una tabla también puede utilizarse para encontrar la tasa de cambio promedio. Vea el .
4. Una tasa de cambio promedio también se puede calcular determinando los valores de la función en los puntos finales de un intervalo descrito por una fórmula. Vea el y el .
5. A veces, la tasa de cambio promedio puede determinarse como una expresión. Vea el .
6. Una función es creciente cuando su tasa de cambio es positiva y decreciente cuando su tasa de cambio es negativa. Vea el .
7. Un máximo local es cuando una función pasa de ser creciente a decreciente y tiene un valor de salida mayor (más positivo o menos negativo) que los valores de salida en los valores de entrada vecinos.
8. Un mínimo local es cuando la función pasa de ser decreciente a creciente (a medida que aumenta la entrada) y tiene un valor de salida menor (más negativo o menos positivo) que los valores de salida en los valores de entrada vecinos.
9. Los mínimos y los máximos también se llaman extremos.
10. Podemos encontrar los extremos locales de un gráfico. Vea el y el .
11. Los puntos más altos y más bajos de un gráfico indican los máximos y los mínimos. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, halle la tasa de cambio promedio de cada función en el intervalo especificado para los números reales
o
### Gráficos
En los siguientes ejercicios, considere el gráfico de
que se muestra en la .
En los siguientes ejercicios, utilice el gráfico de cada función para estimar los intervalos en los que la función es creciente o decreciente.
En los siguientes ejercicios, considere el gráfico mostrado en la .
En los siguientes ejercicios, considere el gráfico en la .
### Numéricos
En los siguientes ejercicios, halle la tasa de cambio promedio de cada función en el intervalo especificado.
### En tecnología
En los siguientes ejercicios, utilice una herramienta gráfica para estimar los extremos locales de cada función y para estimar los intervalos en los que la función es creciente y decreciente.
### Extensión
### Aplicaciones en el mundo real
|
# Funciones
## Composición de las funciones
Supongamos que queremos calcular cuánto cuesta calentar una casa en un día particular del año. El costo de calentar una casa dependerá de la temperatura promedio diaria y, a su vez, la temperatura promedio diaria depende del día particular del año. Observe que acabamos de definir dos relaciones: el costo depende de la temperatura, y la temperatura depende del día.
Utilizando variables descriptivas, podemos anotar estas dos funciones. La función
da el costo
de calentar una casa para una determinada temperatura promedio diaria en
grados Celsius. La función
da la temperatura promedio diaria en el día
del año. Para un día cualquiera,
significa que el costo depende de la temperatura, que a su vez depende del día del año. Así, podemos evaluar la función de costos a la temperatura
Por ejemplo, podríamos evaluar
para determinar la temperatura media diaria del 5.º día del año. Entonces, podríamos evaluar la función de costos a esa temperatura. Escribiríamos
Al combinar estas dos relaciones en una sola función, hemos realizado la composición de las funciones, que es el objetivo de esta sección.
### Combinar funciones mediante operaciones algebraicas
La composición de las funciones es solo una forma de combinar funciones existentes. Otra forma es realizar las operaciones algebraicas habituales sobre las funciones, como la suma, la resta, la multiplicación y la división. Para ello, realizamos las operaciones con las salidas de las funciones, definiendo el resultado como la salida de nuestra nueva función.
Supongamos que tenemos que sumar dos columnas de números que representan los ingresos anuales por separado de una pareja durante un periodo de años, y el resultado es el total de los ingresos de la familia. Queremos hacer esto para cada año, añadiendo solo los ingresos de ese año y recogiendo luego todos los datos en una nueva columna. Si los valores de
es el ingreso de la esposa y
es el ingreso del esposo en el año
y queremos que
represente los ingresos totales, entonces podemos definir una nueva función.
Si esto es cierto para todos los años, entonces podemos centrarnos en la relación entre las funciones sin referencia a un año y escribir
Al igual que para esta suma de dos funciones, podemos definir funciones de diferencia, producto y cociente para cualquier par de funciones que tengan el mismo tipo de entradas (no necesariamente números) y también el mismo tipo de salidas (que sí tienen que ser números para que se les puedan aplicar las operaciones habituales del álgebra, y que además deben tener las mismas unidades o ninguna cuando sumamos y restamos). De este modo, podemos pensar en funciones de suma, resta, multiplicación y división.
Para dos funciones
y
con salidas de números reales, definimos nuevas funciones
y
por las relaciones
### Crear una función por composición de las funciones
Realizar operaciones algebraicas sobre las funciones las combina en una nueva función, pero también podemos crear funciones componiéndolas. Cuando queremos calcular el costo de la calefacción a partir de un día del año, creamos una nueva función que toma un día como entrada y da un costo como salida. El proceso de la combinación de funciones para que la salida de una función se convierta en la entrada de otra se conoce como composición de las funciones. El resultado se conoce como función compuesta. Representamos esta combinación mediante la siguiente notación:
Leemos el lado izquierdo como
compuesto con
a las
y el lado derecho como
de
de
Los dos lados de la ecuación tienen el mismo significado matemático y son iguales. El símbolo del círculo abierto
se denomina operador de composición. Utilizamos este operador principalmente cuando queremos destacar la relación entre las propias funciones sin referirnos a ningún valor de entrada en particular. La composición es una operación binaria que toma dos funciones y forma una nueva función, al igual que la suma o la multiplicación toma dos números y da un nuevo número. Sin embargo, es importante no confundir la composición de las funciones con la multiplicación porque, como hemos aprendido anteriormente, en la mayoría de los casos
También es importante entender el orden de las operaciones al evaluar una función compuesta. Seguimos la convención habitual con los paréntesis, comenzando por los más internos y luego trabajando hacia el exterior. En la ecuación anterior, la función
toma la entrada
primero y da una salida
Entonces la función
toma
como entrada y produce una salida
En general,
y
son funciones diferentes. En otras palabras, en muchos casos
para todo
También veremos que a veces dos funciones solo pueden componerse en un orden concreto.
Por ejemplo, si
y
entonces
pero
Estas expresiones no son iguales para todos los valores de
por lo que las dos funciones no son iguales. Es irrelevante que las expresiones sean iguales para el único valor de entrada
Observe que el rango de la función interior (la primera función a evaluar) tiene que estar dentro del dominio de la función exterior. De manera menos formal, la composición tiene que tener sentido en términos de entradas y salidas.
### Evaluar funciones compuestas
Una vez que componemos una nueva función a partir de dos funciones existentes, tenemos que ser capaces de evaluarla para cualquier entrada en su dominio. Lo haremos con entradas numéricas específicas para funciones expresadas como tablas, gráficos y fórmulas, y con variables como entradas de funciones expresadas como fórmulas. En cada caso, evaluamos la función interna utilizando la entrada inicial y luego utilizamos la salida de la función interna como entrada para la función externa.
### Evaluar funciones compuestas mediante tablas
Cuando se trabaja con funciones dadas como tablas, se leen los valores de entrada y salida de las entradas de la tabla y se trabaja siempre de adentro hacia fuera. Primero evaluamos la función interior y luego utilizamos la salida de la función interior como entrada de la función exterior.
### Evaluar funciones compuestas mediante gráficos
Cuando se nos dan funciones individuales como gráficos, el procedimiento para evaluar las funciones compuestas es similar al proceso que utilizamos para evaluar las tablas. Leemos los valores de entrada y salida, pero esta vez, desde los ejes
y
de los gráficos.
### Evaluar funciones compuestas mediante fórmulas
Cuando se evalúa una función compuesta en la que hemos creado o nos han dado fórmulas, la regla de trabajar de adentro hacia afuera sigue siendo la misma. El valor de entrada a la función externa será la salida de la función interna, que puede ser un valor numérico, un nombre de variable o una expresión más complicada.
Aunque podemos componer las funciones para cada valor de entrada individual, a veces es útil encontrar una única fórmula que calcule el resultado de una composición
Para ello, ampliaremos nuestra idea de evaluación de funciones. Recordemos que, cuando evaluamos una función como
sustituimos el valor dentro de los paréntesis en la fórmula siempre que veamos la variable de entrada.
### Halle el dominio de una función compuesta
Como hemos comentado anteriormente, el dominio de una función compuesta como
depende del dominio de
y el dominio de
Es importante saber cuándo podemos aplicar una función compuesta y cuándo no; es decir, conocer el dominio de una función como
Supongamos que conocemos los dominios de las funciones
y
por separado. Si escribimos la función compuesta para una entrada
cuando
podemos ver de inmediato que
debe ser miembro del dominio de
para que la expresión tenga sentido, porque de lo contrario no podemos completar la evaluación de la función interna. Sin embargo, también vemos que
debe ser miembro del dominio de
de lo contrario la segunda evaluación de la función en
no se puede completar, y la expresión sigue siendo indefinida. Así, el dominio de
se compone únicamente de las entradas en el dominio de
que producen resultados de
pertenecientes al dominio de
Observe que el dominio de
compuesto con
es el conjunto de todas las
tal que
está en el dominio de
y
está en el dominio de
### Descomponer una función compuesta en sus funciones componentes
En algunos casos, es necesario descomponer una función complicada. En otras palabras, la escribimos como una composición de dos funciones más simples. Puede haber más de una forma de descomponer una función compuesta, por lo que podemos elegir la descomposición que nos parezca más conveniente.
### Ecuación clave
### Conceptos clave
1. Podemos realizar operaciones algebraicas con funciones. Vea el .
2. Cuando las funciones se combinan, la salida de la primera función (interna) se convierte en la entrada de la segunda función (externa).
3. La función producida al combinar dos funciones es una función compuesta. Vea el y el .
4. Al interpretar el significado de las funciones compuestas hay que tener en cuenta el orden de composición de las mismas. Vea el .
5. Se puede evaluar una función compuesta evaluando la función interna utilizando el valor de entrada dado y luego evaluando la función externa tomando como entrada la salida de la función interna.
6. Se puede evaluar una función compuesta a partir de una tabla. Vea el .
7. Se puede evaluar una función compuesta a partir de un gráfico. Vea el .
8. Se puede evaluar una función compuesta a partir de una fórmula. Vea el .
9. El dominio de una función compuesta consiste en aquellas entradas en el dominio de la función interna que corresponden a salidas de la función interna que están en el dominio de la función externa. Vea el y el .
10. Al igual que las funciones pueden combinarse para formar una función compuesta, las funciones compuestas pueden descomponerse en funciones más simples.
11. A menudo, las funciones pueden descomponerse de más de una manera. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, utilice cada par de funciones para calcular
y
Simplifique sus respuestas.
En los siguientes ejercicios, utilice cada conjunto de funciones para hallar
Simplifique sus respuestas.
En los siguientes ejercicios, halle las funciones
y
para que la función dada pueda expresarse como
### Gráficos
En los siguientes ejercicios, utilice los gráficos de
que se muestra en la , y
que se muestra en la , para evaluar las expresiones.
En los siguientes ejercicios, utilice los gráficos de
que se muestra en la ,
que se muestra en la , y
que se muestra en la , para evaluar las expresiones.
### Numéricos
En los siguientes ejercicios, utilice los valores de la función para
que se muestra la para evaluar cada expresión.
En los siguientes ejercicios, utilice los valores de la función para
que se muestra en la para evaluar las expresiones.
En los siguientes ejercicios, utilice cada par de funciones para calcular
y
En los siguientes ejercicios, utilice las funciones
y
para evaluar o encontrar la función compuesta como se indica.
### Extensiones
En los siguientes ejercicios, utilice
y
En los siguientes ejercicios, supongamos que
y
En los siguientes ejercicios, halle la composición cuando
para todas las
y
### Aplicaciones en el mundo real
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# Funciones
## Transformación de funciones
Todos sabemos que un espejo plano nos permite ver una imagen exacta de nosotros mismos y de lo que hay detrás. Cuando inclinamos el espejo, las imágenes que vemos pueden desplazarse horizontal o verticalmente. Sin embargo, ¿qué ocurre cuando doblamos un espejo flexible? Como un espejo de feria, nos presenta una imagen distorsionada de nosotros mismos, estirada o comprimida horizontal o verticalmente. Del mismo modo, podemos distorsionar o transformar las funciones matemáticas para adaptarlas mejor a la descripción de objetos o procesos del mundo real. En esta sección, echaremos un vistazo a varios tipos de transformación.
### Graficar funciones con desplazamiento vertical y horizontal.
A menudo, cuando se nos plantea un problema, intentamos modelar el escenario con las matemáticas en forma de palabras, tablas, gráficos y ecuaciones. Un método que podemos emplear es adaptar los gráficos básicos de las funciones del conjunto de herramientas para construir nuevos modelos en un escenario determinado. Hay formas sistemáticas de alterar las funciones para construir modelos adecuados a los problemas que intentamos resolver.
### Identificación del desplazamiento vertical
Un tipo sencillo de transformación consiste en desplazar todo el gráfico de una función hacia arriba, hacia abajo, hacia la derecha o hacia la izquierda. El desplazamiento más sencillo es un desplazamiento vertical, moviendo el gráfico hacia arriba o hacia abajo, porque esta transformación implica añadir una constante positiva o negativa a la función. En otras palabras, sumamos la misma constante al valor de salida de la función, independientemente de la entrada. Para una función
la función
se desplaza verticalmente
unidades. Vea la a modo de ejemplo.
Para ayudarle con el concepto de desplazamiento vertical, considere que
Por lo tanto,
equivale a
Cada unidad de
se sustituye por
por lo que el valor
valor aumenta o disminuye, dependiendo del valor de
El resultado es un desplazamiento hacia arriba o hacia abajo.
### Identificar el desplazamiento horizontal
Acabamos de ver que el desplazamiento vertical es un cambio en la salida, o fuera, de la función. Ahora veremos cómo los cambios en la entrada, en el interior de la función, cambian su gráfico y su significado. Un desplazamiento a la entrada provoca un movimiento del gráfico de la función a la izquierda o a la derecha, en lo que se conoce como desplazamiento horizontal, que se muestra en la .
Por ejemplo, si
entonces
es una nueva función. Cada entrada se reduce en 2 antes de elevar la función al cuadrado. El resultado es que el gráfico se desplaza 2 unidades a la derecha, porque tendríamos que aumentar la entrada anterior en 2 unidades para obtener el mismo valor de salida que se da en
### Combinar el desplazamiento vertical y el desplazamiento horizontal
Ahora que tenemos dos transformaciones, podemos combinarlas. El desplazamiento vertical es un cambio externo que incide en los valores del eje de salida (
) y desplaza la función hacia arriba o hacia abajo. El desplazamiento horizontal es un cambio interno que incide en los valores del eje de entrada (
) y desplaza la función hacia la izquierda o hacia la derecha. La combinación de los dos tipos de desplazamiento hará que el gráfico de una función se desplace hacia arriba o hacia abajo y hacia la derecha o la izquierda.
### Graficar funciones mediante reflexiones alrededor de los ejes
Otra transformación que puede aplicarse a una función es una reflexión alrededor de los ejes x o y. La reflexión vertical refleja un gráfico verticalmente a través del eje x, mientras que la reflexión horizontal refleja un gráfico horizontalmente a través del eje y. Las reflexiones se muestran en la .
Observe que la reflexión vertical produce un nuevo gráfico, que es una imagen especular del gráfico base u original alrededor del eje x. La reflexión horizontal produce un nuevo gráfico, que es una imagen especular del gráfico base u original alrededor del eje y.
### Determinar las funciones pares e impares
Algunas funciones presentan simetría, de modo que las reflexiones dan lugar al gráfico original. Por ejemplo, reflejar horizontalmente las funciones de la caja de herramientas
o
dará lugar al gráfico original. Decimos que este tipo de gráficos es simétrico con respecto al eje y. Las funciones cuyos gráficos son simétricos respecto al eje y se denominan funciones pares.
Si los gráficos de
o
se reflejaran alrededor de ambos ejes, el resultado sería el gráfico original, como se muestra en la .
Decimos que estos gráficos son simétricos respecto al origen. La función cuyo gráfico es simétrico con respecto al origen recibe el nombre de función impar.
Nota: La función no puede ser ni par ni impar si no exhibe alguna simetría. Por ejemplo,
no es ni par ni impar. También, la única función que es tanto par como impar es la función constante
### Graficar funciones mediante estiramiento y compresión
Sumar una constante a las entradas o salidas de una función cambia la posición de un gráfico con respecto a los ejes, pero no afecta la forma de un gráfico. Ahora exploramos los efectos de multiplicar los valores de entrada o de salida por alguna cantidad.
Podemos transformar el interior (valores de entrada) de una función o podemos transformar el exterior (valores de salida) de una función. Cada cambio tiene un efecto específico que puede verse gráficamente.
### Estiramiento y compresión vertical
Cuando multiplicamos una función por una constante positiva, obtenemos una función cuyo gráfico se estira o comprime verticalmente en relación con el gráfico de la función original. Si la constante es mayor a 1, obtenemos un estiramiento vertical; si la constante está entre 0 y 1, obtenemos una compresión vertical. La muestra una función multiplicada por los factores constantes 2 y 0,5 y el estiramiento y la compresión vertical resultantes.
### Estiramiento y compresión horizontal
Ahora, consideramos los cambios en el interior de una función. Cuando multiplicamos la entrada de una función por una constante positiva, obtenemos una función cuyo gráfico se estira o comprime horizontalmente en relación con el gráfico de la función original. Si la constante se ubica entre 0 y 1, obtenemos un estiramiento horizontal; si la constante es mayor que 1, obtenemos una compresión horizontal de la función.
Dada una función
la forma
da como resultado el estiramiento o compresión horizontal. Considere la función
Observe la . El gráfico de
es el estiramiento horizontal del gráfico de la función
por un factor de 2. El gráfico de
es la compresión horizontal del gráfico de la función
por un factor de .
### Realizar una secuencia de transformaciones
Al combinar las transformaciones, es muy importante tener en cuenta el orden de las mismas. Por ejemplo, desplazar verticalmente en 3 y luego estirar verticalmente en 2 no crea el mismo gráfico que estirar verticalmente en 2 y luego desplazar verticalmente en 3, porque cuando desplazamos primero, tanto la función original como el desplazamiento se estiran, mientras que solo se estira la función original cuando estiramos primero.
Cuando vemos una expresión como
¿con cuál transformación deberíamos comenzar primero? La respuesta se desprende del orden de las operaciones. Dado el valor de salida de
multiplicamos primero por 2, lo que causa el estiramiento vertical, y luego sumamos 3, lo que causa el desplazamiento vertical. Es decir, la multiplicación antes que la suma.
Las transformaciones horizontales son un poco más complicadas. Cuando escribimos
por ejemplo, tenemos que pensar de qué manera las entradas a la función
se relacionan con las entradas a la función
Supongamos que sabemos
¿Qué entrada a
produciría este valor de salida? En otras palabras, ¿qué valor de
permitirá
Necesitaríamos
Para resolver
primero restamos 3, lo que causa un desplazamiento horizontal, y luego dividimos entre 2, lo que causa una compresión horizontal.
Este formato acaba siendo muy difícil de trabajar, porque suele ser mucho más fácil estirar horizontalmente un gráfico antes de desplazarlo. Podemos evitarlo al factorizar dentro de la función.
Exploremos un ejemplo.
Podemos sacar un factor común 2.
Ahora podemos observar con mayor claridad un desplazamiento horizontal hacia la izquierda en 2 unidades, así como una compresión horizontal. La factorización de este modo nos permite estirar primero en sentido horizontal y luego desplazar en sentido horizontal.
### Ecuaciones clave
### Conceptos clave
1. Una función puede desplazarse verticalmente al sumar una constante a la salida. Vea el y el .
2. Una función puede desplazarse horizontalmente al sumar una constante a la entrada. Vea el , el y el .
3. Relacionar el desplazamiento con el contexto de un problema permite comparar e interpretar los desplazamientos verticales y horizontales. Vea el .
4. A menudo se combina el desplazamiento vertical con el horizontal. Vea el y el .
5. La reflexión vertical refleja un gráfico con respecto al eje
. Un gráfico puede reflejarse verticalmente al multiplicar la salida por -1.
6. La reflexión horizontal refleja un gráfico con respecto al eje
. Un gráfico puede relejarse horizontalmente al multiplicar la entrada por -1.
7. Un gráfico puede reflejarse tanto vertical como horizontalmente. El orden en que se aplican las reflexiones no afecta el gráfico final. Vea el .
8. Una función presentada en forma tabular también puede reflejarse al multiplicar los valores de las filas o columnas de entrada y salida según corresponda. Vea el .
9. La función presentada en forma de ecuación puede reflejarse al aplicar las transformaciones una a la vez. Vea el .
10. Las funciones pares son simétricas con respecto al eje
, mientras que las funciones impares son simétricas respecto al origen.
11. Las funciones pares satisfacen la condición
12. Las funciones impares cumplen la condición
13. Una función puede ser impar, par o ninguna de las dos. Vea el .
14. Una función puede comprimirse o estirarse verticalmente al multiplicar la salida por una constante. Vea el , el y el .
15. Una función puede comprimirse o estirarse horizontalmente al multiplicar la entrada por una constante. Vea el , el y el .
16. El orden en el que se apliquen las distintas transformaciones no afecta la función final. Las transformaciones verticales y horizontales deberán aplicarse en el orden indicado. Sin embargo, una transformación vertical puede combinarse con una transformación horizontal en cualquier orden. Vea el y el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, describa en qué medida el gráfico de la función es la transformación del gráfico de la función original
En los siguientes ejercicios, determine los intervalos en los que la función es creciente y decreciente.
### Gráficos
En los siguientes ejercicios, utilice el gráfico de
que se muestra en la para dibujar un gráfico de cada transformación de
En los siguientes ejercicios, dibuje un gráfico de la función como transformación del gráfico de una de las funciones de la caja de herramientas.
### Numéricos
En los siguientes ejercicios, escriba una ecuación por cada función graficada mediante el empleo de las transformaciones de los gráficos de una de las funciones de la caja de herramientas.
En los siguientes ejercicios, utilice los gráficos de las transformaciones de la función de raíz cuadrada para hallar una fórmula por cada una de las funciones.
En los siguientes ejercicios, utilice los gráficos de las funciones transformadas de la caja de herramientas para escribir una fórmula por cada una de las funciones resultantes.
En los siguientes ejercicios, determine si la función es par, impar o ninguna de las dos.
En los siguientes ejercicios, describa de qué manera el gráfico de cada función es la transformación del gráfico de la función original
En los siguientes ejercicios, escriba una fórmula para la función
que resulta cuando el gráfico de una determinada función de la caja de herramientas se transforma como se ha descrito.
En los siguientes ejercicios, describa cómo la fórmula es la transformación de una función de la caja de herramientas. Luego dibuje un gráfico de la transformación.
En los siguientes ejercicios, utilice el gráfico en la para dibujar las transformaciones dadas. |
# Funciones
## Funciones de valor absoluto
Hasta la década de 1920, se creía que las llamadas nebulosas espirales eran nubes de polvo y gas en nuestra propia galaxia, a unas decenas de miles de años luz. Luego, el astrónomo Edwin Hubble demostró que estos objetos son galaxias en sí mismas, a distancias de millones de años luz. Hoy en día, los astrónomos pueden detectar galaxias que están a miles de millones de años luz. Las distancias en el universo se pueden medir en todas las direcciones. Por ello, vale la pena considerar la distancia como función de valor absoluto. En esta sección, investigaremos las funciones de valor absoluto.
### Comprensión del valor absoluto
Recordemos que en su forma básica
la función de valor absoluto, es una de las funciones de nuestra caja de herramientas. La función de valor absoluto se considera comúnmente como la que proporciona la distancia del número a cero en una línea numérica. Algebraicamente, para cualquier valor de entrada, la salida es el valor sin importar el signo.
### Graficar una función de valor absoluto
La característica más significativa del gráfico de valor absoluto es el vértice en el que el gráfico cambia de dirección. Este punto se muestra en el origen en la .
La muestra el gráfico de
El gráfico de
se ha desplazado 3 unidades a la derecha, se ha estirado verticalmente por un factor de 2 y se ha desplazado 4 unidades hacia arriba. Esto significa que el vértice se encuentra en
para esta función transformada.
### Resolver una ecuación de valor absoluto
Ahora que podemos graficar una función de valor absoluto, aprenderemos a resolver una ecuación de valor absoluto. Para resolver una ecuación como
observamos que el valor absoluto será igual a 8 si la cantidad dentro del valor absoluto es 8 o -8. Esto nos lleva a dos ecuaciones distintas que podemos resolver independientemente.
Resulta útil saber cómo resolver problemas que impliquen funciones de valor absoluto. Por ejemplo, tendríamos que identificar números o puntos en una línea que están a una distancia determinada de un punto de referencia dado.
La ecuación de valor absoluto es aquella en la que la variable desconocida aparece en barras de valor absoluto. Por ejemplo,
### Resolver una inecuación de valor absoluto
Las ecuaciones de valor absoluto no siempre implican igualdad. En cambio, quizá tengamos que resolver una ecuación dentro de un rango de valores. Utilizaríamos una inecuación de valor absoluto para resolver dicha ecuación. La inecuación de valor absoluto es una ecuación de la forma
donde la expresión
(y posiblemente, pero no usualmente
) depende de una variable
Resolver la inecuación significa hallar el conjunto de todos los valores
que satisfacen la inecuación. Normalmente este conjunto será un intervalo o la unión de dos intervalos.
Hay dos enfoques básicos para resolver inecuaciones de valor absoluto: el gráfico y el algebraico. La ventaja del enfoque gráfico es que podemos leer la solución al interpretar los gráficos de dos funciones. La ventaja del enfoque algebraico es que produce soluciones que serían difíciles de leer en el gráfico.
Por ejemplo, sabemos que todos los números dentro de las 200 unidades de 0 pueden expresarse como
Supongamos que queremos conocer todo el rendimiento posible de una inversión si pudiéramos ganar alguna cantidad de dinero entre 200 y 600 dólares. Podemos resolver algebraicamente el conjunto de valores
tales que la distancia entre
y 600 es menos de 200. Representamos la distancia entre
y 600 como
Esto significa que nuestro rendimiento estaría entre 400 y 800 dólares.
A veces un problema de inecuación de valor absoluto se nos presentará en términos de una función de valor absoluto desplazada, estirada o comprimida, donde debemos determinar para qué valores de la entrada será la salida de la función negativa o positiva.
### Conceptos clave
1. La función de valor absoluto se utiliza habitualmente para medir las distancias entre los puntos. Vea el .
2. Los problemas aplicados, como los rangos de valores posibles, también se resuelven con la función de valor absoluto. Vea el .
3. El gráfico de la función valor absoluto se parece a una letra V. Tiene un vértice en el que el gráfico cambia de dirección. Vea el .
4. En una ecuación de valor absoluto, una incógnita de la variable es la entrada de una función de valor absoluto.
5. Si el valor absoluto de una expresión es igual a un número positivo, espere dos soluciones para la incógnita. Vea el .
6. La ecuación de valor absoluto puede tener una solución, dos soluciones o ninguna solución. Vea el .
7. La inecuación de valor absoluto es similar a una ecuación de valor absoluto, pero tiene la forma
Se resuelve al delimitar el conjunto de soluciones y luego probar cuáles segmentos están en el conjunto. Vea el .
8. Las inecuaciones de valor absoluto se resuelven gráficamente. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, resuelva las ecuaciones que aparecen a continuación y exprese la respuesta con la notación de conjuntos.
En los siguientes ejercicios, halle las intersecciones en x y en y de los gráficos de cada función.
En los siguientes ejercicios, resuelva cada inecuación y escriba la solución en notación de intervalo.
### Gráficos
En los siguientes ejercicios, grafique la función de valor absoluto. Trace al menos cinco puntos a mano para cada gráfico.
En los siguientes ejercicios, grafique a mano las funciones dadas.
### En tecnología
En los siguientes ejercicios, grafique cada función con una herramienta gráfica. Especifique la ventana de visualización.
### Extensiones
En los siguientes ejercicios, resuelva la inecuación.
### Aplicaciones en el mundo real
|
# Funciones
## Funciones inversas
Una bomba de calor reversible es un sistema de climatización que es un acondicionador de aire y un calentador en un solo aparato. Si funciona en una dirección, bombea el calor de una casa para proporcionar refrigeración. Funcionando a la inversa, bombea calor al edificio desde el exterior, incluso en tiempo frío, para proporcionar calefacción. La bomba de calor es varias veces más eficiente que la calefacción por resistencia eléctrica convencional.
Si algunas máquinas físicas pueden funcionar en dos direcciones, podríamos preguntarnos si algunas de las "máquinas" de funciones que hemos estado estudiando también pueden funcionar al revés. La ofrece una representación visual de esta cuestión. En esta sección, consideraremos la naturaleza inversa de las funciones.
### Comprobar que dos funciones son inversas
Betty viaja a Milán para un desfile de modas y quiere saber cuál será la temperatura. No conoce la escala Celsius. Para hacerse una idea de cómo se relacionan las medidas de temperatura, Betty quiere convertir 75 grados Fahrenheit a grados Celsius, mediante la fórmula
y sustituye 75 por
para calcular
Sabiendo que una temperatura agradable de 75 grados Fahrenheit equivale a unos 24 grados Celsius, Betty obtiene la previsión meteorológica de la semana a partir de la para Milán, y quiere convertir todas las temperaturas a grados Fahrenheit.
Al principio, Betty se plantea utilizar la fórmula que ya ha encontrado para efectuar las conversiones. Después de todo, conoce el álgebra y puede resolver fácilmente la ecuación para
después de sustituir un valor por
Por ejemplo, para convertir 26 grados Celsius, podría escribir
Sin embargo, después de considerar esta opción por un momento, se da cuenta de que resolver la ecuación para cada una de las temperaturas será terriblemente tedioso. Se percata de que, dado que la evaluación es más fácil que la resolución, sería mucho más conveniente tener otra fórmula, que tome la temperatura Celsius y dé como resultado la temperatura Fahrenheit.
La fórmula que busca Betty corresponde a la idea de función inversa, que es aquella para la que la entrada de la función original se convierte en la salida de la función inversa y la salida de la función original se convierte en la entrada de la función inversa.
Dada una función
representamos su inversa como
que se lee como
inversa de
El elevado
forma parte de la notación. No es un exponente; no implica una potencia de
. En otras palabras,
no significa
porque
es el recíproco de
y no la inversa.
La notación "exponencial" proviene de una analogía entre la composición de funciones y la multiplicación: al igual que
(1 es el elemento de identidad para la multiplicación) para cualquier número no nulo
por lo que
es igual a la función de identidad, es decir:
Esto es válido para todos los valores
en el dominio de
Informalmente, esto significa que las funciones inversas se "deshacen" entre sí. Sin embargo, así como el cero no tiene recíproco, algunas funciones no tienen inversa.
Dada una función
podemos verificar si alguna otra función
es la inversa de
al comprobar si
o
es verdadera. Podemos probar cualquier ecuación que sea más conveniente, porque son lógicamente equivalentes (es decir, si una es verdadera, entonces también lo es la otra).
Por ejemplo,
y
son funciones inversas.
y
Algunos pares de coordenadas del gráfico de la función
son (-2, -8), (0, 0) y (2, 8). Algunos pares de coordenadas del gráfico de la función
son (-8, -2), (0, 0) y (8, 2). Si intercambiamos la entrada y la salida de cada par de coordenadas de una función, los pares de coordenadas intercambiados aparecerían en el gráfico de la función inversa.
### Hallar el dominio y el rango de las funciones inversas
Las salidas de la función
son las entradas a
por lo que el rango de
es también el dominio de
Asimismo, dado que las entradas a
son las salidas de
el dominio de
es el rango de
Podemos visualizar la situación como en la .
Cuando una función no tenga inversa, es posible crear una función en un dominio limitado donde sí la tenga. Por ejemplo, la inversa de
es
porque un cuadrado "deshace" una raíz cuadrada; pero el cuadrado es apenas la inversa de la raíz cuadrada en el dominio
ya que ese es el rango de
Podemos ver este problema desde el otro lado, comenzando con la función cuadrada (cuadrática de la caja de herramientas)
Si queremos construir la inversa de esta función, nos encontramos con un problema, porque para cada salida dada de la función cuadrática, hay dos entradas correspondientes (excepto cuando la entrada es 0). Por ejemplo, la salida 9 de la función cuadrática corresponde a las entradas 3 y -3. Sin embargo, la salida de una función es la entrada para su inversa; si esta entrada inversa corresponde a más de una salida inversa (entrada de la función original), ¡entonces la "inversa" no es una función en absoluto! Por decirlo de otra manera, la función cuadrática no es una función biunívoca; no pasa la prueba de la línea horizontal, por lo que no tiene ninguna función inversa. Para que tenga una inversa, deberá ser una función biunívoca.
En muchos casos, si la función no es biunívoca, podemos restringirla a una parte de su dominio en la que lo sea. Por ejemplo, podemos hacer una versión restringida de la función cuadrada
con su dominio limitado a
que es una función biunívoca (pasa la prueba de la línea horizontal) y que tiene una inversa (la función de raíz cuadrada).
Si los valores de
en
entonces la función inversa es
1. El dominio de
= rango de
=
2. El dominio de
= rango de
=
### Hallar y evaluar funciones inversas
Una vez que tenemos una función biunívoca, podemos evaluar su inversa en entradas específicas de la función inversa o construir una representación completa de la función inversa en muchos casos.
### Invertir funciones tabulares
Supongamos que queremos hallar la inversa de una función representada en forma tabular. Recuerde que el dominio de la función es el rango de la inversa y el rango de la función es el dominio de la inversa. Así que tenemos que intercambiar el dominio y el rango.
Cada fila (o columna) de entradas se convierte en la fila (o columna) de salidas de la función inversa. Del mismo modo, cada fila (o columna) de salidas se convierte en la fila (o columna) de entradas para la función inversa.
### Evaluación de la inversa de una función, dado el gráfico de la función original
Vimos en Funciones y notación de funciones que el dominio de una función puede leerse a partir de la extensión horizontal de su gráfico. Hallamos el dominio de la función inversa observando la extensión vertical del gráfico de la función original, ya que esta corresponde a la extensión horizontal de la función inversa. Del mismo modo, hallamos el rango de la función inversa a partir de la extensión horizontal del gráfico de la función original, ya que es la extensión vertical de la función inversa. Si queremos evaluar una función inversa, hallamos su entrada dentro de su dominio, que es todo o parte del eje vertical del gráfico de la función original.
### Hallar las inversas de las funciones representadas por fórmulas
A veces necesitaremos conocer una función inversa para todos los elementos de su dominio, no solo para algunos. Si la función original viene dada como una fórmula —por ejemplo,
en función de
a menudo podemos hallar la función inversa al resolver para obtener
en función de
### Hallar funciones inversas y sus gráficos
Ahora que podemos hallar la inversa de una función, exploraremos los gráficos de las funciones y sus inversas. Volvamos a la función cuadrática
restringida al dominio
en el que esta función es biunívoca, y grafíquela como en la .
Restringir el dominio a
hace que la función sea biunívoca (obviamente pasará la prueba de la línea horizontal), por lo que tiene una inversa en este dominio restringido.
Ya sabemos que la inversa de la función cuadrática de la caja de herramientas es la función de raíz cuadrada, es decir,
¿Qué sucede si graficamos tanto
y
en el mismo conjunto de ejes, donde utilizamos el eje
para la entrada, tanto para
Observamos una clara relación: el gráfico de
es el gráfico de
reflejado sobre la línea diagonal
que llamaremos línea de identidad, y que se indica en la .
Esta relación se observará en todas las funciones biunívocas, porque es el resultado de que la función y su inversa intercambien entradas y salidas. Esto equivale a intercambiar los papeles de los ejes vertical y horizontal.
### Conceptos clave
1. Si los valores de
es la inversa de
entonces
Vea el , el y el .
2. Cada una de las funciones de la caja de herramientas tiene una inversa. Vea el .
3. Para que una función tenga una inversa, deberá ser biunívoca (pasar la prueba de la línea horizontal).
4. Aquella función que no sea biunívoca en todo su dominio puede serlo en parte de su dominio.
5. Para una función tabular, intercambie las filas de entrada y salida para obtener la inversa. Vea el .
6. La inversa de la función puede determinarse en puntos específicos en su gráfico. Vea el .
7. Para hallar la inversa de una fórmula, resuelva la ecuación
para
en función de
A continuación, intercambie las etiquetas
y
Vea el , el y el .
8. El gráfico de una función inversa es la reflexión del gráfico de la función original a través de la línea
Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, calcule
por cada función.
En los siguientes ejercicios, halle un dominio en el que cada función
sea biunívoca y no decreciente. Escriba el dominio en notación de intervalo. Entonces calcule la inversa de
restringida a ese dominio.
En los siguientes ejercicios, utilice la composición de funciones para verificar que
y
son funciones inversas.
### Gráficos
En los siguientes ejercicios, utilice una herramienta gráfica para determinar si cada función es biunívoca.
En los siguientes ejercicios, determine si el gráfico representa una función biunívoca.
En los siguientes ejercicios, utilice el gráfico de
que se muestra en la .
En los siguientes ejercicios, utilice el gráfico de la función biunívoca que se muestra en la .
### Numéricos
En los siguientes ejercicios, evalúe o resuelva, suponiendo que la función
es biunívoca.
En los siguientes ejercicios, utilice los valores que aparecen en la para evaluar o resolver.
### En tecnología
En los siguientes ejercicios, halle la función inversa. A continuación, grafique la función y su inversa.
### Aplicaciones en el mundo real
### Ejercicios de repaso del capítulo
### Funciones y notación de funciones
En los siguientes ejercicios, determine si la relación es una función.
En los siguientes ejercicios, evalúe la función en los valores indicados:
En los siguientes ejercicios, determine si las funciones son biunívocas.
En los siguientes ejercicios, utilice la prueba de la línea vertical para determinar si la relación cuyo gráfico se proporciona es una función.
En los siguientes ejercicios, grafique las funciones.
En los siguientes ejercicios, utilice la para estimar los valores.
En los siguientes ejercicios, utilice la función
para estimar los valores.
### Dominio y rango
En los siguientes ejercicios, halle el dominio de cada función, y exprese las respuestas utilizando la notación intervalo.
### Tasas de variación y comportamiento de los gráficos
En los siguientes ejercicios, calcule la tasa promedio de cambio de las funciones a partir de
En los siguientes ejercicios, utilice los gráficos para determinar los intervalos en los que las funciones son crecientes, decrecientes o constantes.
### Composición de las funciones
En los siguientes ejercicios, calcule
y
por cada par de funciones.
En los siguientes ejercicios, calcule
y el dominio para
por cada par de funciones.
En los siguientes ejercicios, exprese cada función
como una composición de dos funciones
y
donde
### Transformación de funciones
En los siguientes ejercicios, dibuje un gráfico de la función dada.
En los siguientes ejercicios, dibuje el gráfico de la función
si el gráfico de la función
se muestra en la .
En los siguientes ejercicios, anote la ecuación de la función estándar representada por cada uno de los gráficos que aparecen a continuación.
En los siguientes ejercicios, determine si cada función de abajo es par, impar o ninguna de las dos.
En los siguientes ejercicios, analice el gráfico y determine si la función graficada es par, impar o ninguna de las dos.
### Funciones de valor absoluto
En los siguientes ejercicios, escriba una ecuación para la transformación de
En los siguientes ejercicios, grafique la función de valor absoluto.
En los siguientes ejercicios, resuelva la ecuación de valor absoluto.
En los siguientes ejercicios, resuelva la inecuación y exprese la solución con la notación de intervalo.
### Funciones inversas
En los siguientes ejercicios, calcule
por cada función.
En el siguiente ejercicio, halle un dominio en el que la función
sea biunívoca y no decreciente. Escriba el dominio en notación de intervalo. Entonces calcule la inversa de
restringida a ese dominio.
En los siguientes ejercicios, utilice una herramienta gráfica para determinar si cada función es biunívoca.
### Prueba de práctica
En los siguientes ejercicios, determine si cada una de las siguientes relaciones es una función.
En los siguientes ejercicios, evalúe la función
en la entrada dada.
En los siguientes ejercicios, utilice las funciones
para hallar las funciones compuestas.
En los siguientes ejercicios, grafique las funciones al trasladar, estirar o comprimir una función de la caja de herramientas.
En los siguientes ejercicios, determine si las funciones son pares, impares o ninguna de las dos.
En los siguientes ejercicios, halle la inversa de la función.
En los siguientes ejercicios, utilice el gráfico de
que se muestra en la .
En los siguientes ejercicios, utilice el gráfico de la función definida por partes que se muestra en la .
En los siguientes ejercicios, utilice los valores que aparecen en la . |
# Funciones lineales
## Introducción
Imagínese que coloca una planta en el suelo un día y descubre que ha crecido el doble a los pocos días. Aunque parezca increíble, esto ocurre con ciertas especies de bambú. Estos miembros de la familia de las gramíneas son las plantas que más rápido crecen en el mundo. Se ha observado que una especie de bambú crece casi 1,5 pulgadas cada hora.http://www.guinnessworldrecords.com/records-3000/fastest-growing-plant/ En un lapso de veinticuatro horas, esta planta de bambú crece unas 36 pulgadas, es decir, ¡unos increíbles 3 pies! Una tasa de cambio constante, como el ciclo de crecimiento de esta planta de bambú, es una función lineal.
Recordemos de Funciones y notación de funciones que una función es una relación que asigna a cada elemento del dominio exactamente un elemento en el rango. Las funciones lineales son un tipo específico de función que se utiliza para modelar muchas aplicaciones en el mundo real, como el crecimiento de las plantas en el tiempo. En este capítulo, exploraremos las funciones lineales, sus gráficos y cómo relacionarlas con los datos. |
# Funciones lineales
## Funciones lineales
Al igual que el crecimiento de una planta de bambú, hay muchas situaciones que implican un cambio constante con el paso del tiempo. Pensemos, por ejemplo, en el primer tren comercial de levitación magnética del mundo, el Tren MagLev de Shaghai (). Transporta cómodamente a los pasajeros en un viaje de 30 kilómetros desde el aeropuerto hasta la estación de metro en apenas ocho minutos.http://www.chinahighlights.com/shanghai/transportation/maglev-train.htm
Supongamos que un tren de levitación magnética recorre una larga distancia, a una velocidad constante de 83 metros por segundo durante un tiempo una vez que se aleja 250 metros de la estación. ¿Cómo analizaríamos la distancia del tren a la estación en función del tiempo? En esta sección, investigaremos un tipo de función que sirve para este propósito, y la utilizaremos para investigar situaciones del mundo real como la distancia del tren a la estación en un momento dado.
### Representar funciones lineales
La función que describe el movimiento del tren es una función lineal, la cual se define como una función con una tasa de cambio constante, es decir, un polinomio de grado 1. Hay varias formas de representar una función lineal, entre ellas la forma verbal, la notación de funciones, la forma tabular y la forma gráfica. Describiremos el movimiento del tren como una función mediante el empleo de cada método.
### Representar una función lineal en forma verbal
Empecemos por describir la función lineal con palabras. Para el problema del tren que acabamos de considerar, se puede utilizar la siguiente frase para describir la relación de funciones.
1. La distancia entre el tren y la estación es una función del tiempo durante el cual el tren se mueve a una velocidad constante más su distancia original a la estación cuando comenzó a moverse a velocidad constante.
La velocidad es la tasa de cambio. Recordemos que la tasa de cambio es una medida de la rapidez con la que cambia la variable dependiente con respecto a la variable independiente. La tasa de cambio para este ejemplo es constante, lo que significa que es la misma para cada valor de entrada. A medida que el tiempo (entrada) aumenta en 1 segundo, la distancia correspondiente (salida) aumenta en 83 metros. El tren comenzó a moverse a esta velocidad constante a una distancia de 250 metros de la estación.
### Representar una función lineal en notación de funciones
Otro enfoque para representar funciones lineales es utilizar la notación de funciones. Un ejemplo de notación de funciones es una ecuación escrita en lo que se conoce como forma pendiente-intersección de una línea, donde
es el valor de entrada,
es la tasa de cambio y
es el valor inicial de la variable dependiente.
En el ejemplo del tren, podríamos utilizar la notación
en la que la distancia total
es una función del tiempo
La tasa,
es de 83 metros por segundo. El valor inicial de la variable dependiente
es la distancia original de la estación, 250 metros. Podemos escribir una ecuación generalizada para representar el movimiento del tren.
### Representar una función lineal en forma tabular
Un tercer método para representar una función lineal es mediante el uso de una tabla. La relación entre la distancia de la estación y el tiempo se representa en la . En la tabla, podemos ver que la distancia cambia en 83 metros por cada aumento de 1 segundo en el tiempo.
### Representar una función lineal de forma gráfica
Otra forma de representar las funciones lineales es visualmente, mediante un gráfico. Podemos utilizar la relación de funciones de arriba,
para dibujar un gráfico, representado en la . Observe que el gráfico es una línea. Cuando trazamos una función lineal, el gráfico es siempre una recta.
La tasa de cambio, que es constante, determina la inclinación o pendiente de la línea. El punto en el que el valor de entrada es cero es la intersección vertical, o intersección en , de la línea. Podemos ver en el gráfico de la que la intersección en y en el ejemplo del tren que acabamos de ver es
y representa la distancia del tren a la estación cuando comenzó a moverse a velocidad constante.
Observe que el gráfico del ejemplo del tren está restringido, pero no siempre es así. Considere el gráfico de la línea
Pregúntese qué números se pueden introducir en la función, es decir, cuál es el dominio de la función. El dominio está compuesto por todos los números reales porque cualquier número puede duplicarse, y luego sumar uno al producto.
### Determinar si una función lineal es creciente, decreciente o constante
Las funciones lineales que hemos utilizado en los dos ejemplos anteriores aumentan con el tiempo, pero no todas lo hacen. La función lineal puede ser creciente, decreciente o constante. En el caso de una función creciente, como en el ejemplo del tren, los valores de salida aumentan a medida que aumentan los valores de entrada. El gráfico de la función creciente tiene una pendiente positiva. Una línea con pendiente positiva se inclina hacia arriba de izquierda a derecha como en (a). En el caso de una función decreciente, la pendiente es negativa. Los valores de salida disminuyen a medida que aumentan los valores de entrada. Una línea con pendiente negativa se inclina hacia abajo de izquierda a derecha como en la (b). Si la función es constante, los valores de salida son los mismos para todos los valores de entrada, por lo que la pendiente es cero. Una línea con pendiente cero es horizontal como en la (c).
### Calcular e interpretar la pendiente
En los ejemplos que hemos visto hasta ahora, nos han proporcionado la pendiente. Sin embargo, a menudo necesitamos calcular la pendiente dados los valores de entrada y salida. Dados dos valores de entrada,
y
y dos valores correspondientes para la salida,
y
, que puede representarse mediante un conjunto de puntos,
y
, podemos calcular la pendiente
como sigue
donde es el desplazamiento vertical y es el desplazamiento horizontal. Observe en la notación de la función dos valores correspondientes a la salida y para la función
y por lo que podríamos escribir de forma equivalente
la indica cómo se calcula la pendiente de la línea entre los puntos,
y
. Recordemos que la pendiente mide la inclinación. Cuanto mayor sea el valor absoluto de la pendiente, más pronunciada será la línea.
### Escribir la forma punto-pendiente de una ecuación lineal
Hasta ahora, hemos utilizado la forma pendiente-intersección de la ecuación lineal para describir funciones lineales. Aquí aprenderemos otra forma de escribir una función lineal, la forma punto-pendiente.
La forma punto-pendiente se deriva de la fórmula de la pendiente.
Tenga presente que la forma pendiente-intersección y la forma punto-pendiente pueden utilizarse para describir la misma función. Podemos pasar de una forma a otra con el álgebra básica. Por ejemplo, supongamos que nos dan una ecuación en forma de punto-pendiente,
. Podemos convertirla a la forma pendiente-intersección, como se indica.
Por lo tanto, la misma línea puede describirse en forma de pendiente-intersección como
### Escribir la ecuación de una recta mediante un punto y la pendiente
La forma punto-pendiente es especialmente útil si conocemos un punto y la pendiente de una línea. Supongamos, por ejemplo, que nos dicen que una línea tiene una pendiente de 2 y pasa por el punto
Sabemos que
y que
y
Podemos sustituir estos valores en la ecuación general de punto-pendiente.
Si quisiéramos reescribir la ecuación en forma de pendiente-intersección, aplicaríamos técnicas algebraicas.
Ambas ecuaciones,
y
describen la misma línea. Vea la .
### Escribir la ecuación de una línea con dos puntos
La forma punto-pendiente de una ecuación también sirve si conocemos dos puntos cualesquiera por los que pasa una línea. Supongamos, por ejemplo, que sabemos que una línea pasa por los puntos
y
Podemos utilizar las coordenadas de los dos puntos para calcular la pendiente.
Ahora podemos utilizar la pendiente que hemos calculado y las coordenadas de uno de los puntos para hallar la ecuación de la línea. Utilicemos (0, 1) para nuestro punto.
Como antes, podemos utilizar el álgebra para reescribir la ecuación en la forma pendiente-intersección.
Ambas ecuaciones describen la línea mostrada en la .
### Escribir e interpretar una ecuación para una función lineal
Ahora que hemos escrito las ecuaciones de las funciones lineales tanto en la forma pendiente-intersección como en la forma punto-pendiente, podemos elegir qué método utilizar en función de la información que nos brinden. Esa información puede proporcionarse en forma de gráfico, un punto y una pendiente, dos puntos, etc. Mire el gráfico de la función
en la .
No se nos da la pendiente de la línea, pero podemos elegir dos puntos cualesquiera para determinar la pendiente. Elijamos
y
Podemos utilizar estos puntos para calcular la pendiente.
Ahora podemos sustituir la pendiente y las coordenadas de uno de los puntos en la forma punto-pendiente.
Si queremos reescribir la ecuación en la forma pendiente-intersección, hallaríamos
Si quisiéramos determinar la forma pendiente-intersección sin escribir primero la forma punto-pendiente, podríamos haber reconocido que la línea cruza el eje y cuando el valor de salida es 7. Por lo tanto, Ahora tenemos el valor inicial y la pendiente por lo que podemos sustituir y en la forma pendiente-intersección de una línea.
Así que la función es
y la ecuación lineal sería
### Modelar problemas del mundo real con funciones lineales
En el mundo real, los problemas no siempre se plantean explícitamente en términos de una función o se representan con un gráfico. Afortunadamente, podemos analizar el problema al representarlo primero como una función lineal y luego interpretar los componentes de la función. Siempre que conozcamos, o podamos averiguar, el valor inicial y la tasa de cambio de una función lineal, podremos resolver muchos tipos de problemas del mundo real.
### Ecuaciones clave
### Conceptos clave
1. Los pares ordenados y dados por una función lineal representan los puntos en una línea.
2. Las funciones lineales se representan con palabras, en notación de funciones, en forma tabular y en forma gráfica. Vea el .
3. La tasa de cambio de una función lineal también se conoce como la pendiente.
4. Una ecuación en la forma pendiente-intersección de una línea incluye la pendiente y el valor inicial de la función.
5. El valor inicial, o intersección en y, es el valor de salida cuando la entrada de una función lineal es cero. Es el valor de y del punto en el que la línea cruza el eje de y.
6. La función lineal creciente da lugar a un gráfico que se inclina hacia arriba, de izquierda a derecha, y tiene una pendiente positiva.
7. La función lineal decreciente da lugar a un gráfico que se inclina hacia abajo, de izquierda a derecha, y tiene una pendiente negativa.
8. La función lineal constante da lugar a un gráfico que es una línea horizontal.
9. El análisis de la pendiente en el contexto de un problema indica si la función lineal es creciente, decreciente o constante. Vea el .
10. La pendiente de una función lineal puede calcularse al dividir la diferencia entre los valores de y entre la diferencia de los correspondientes valores de x de dos puntos cualesquiera de la línea. Vea el y el .
11. La pendiente y el valor inicial se pueden determinar dado un gráfico o dos puntos cualesquiera en la línea.
12. Un tipo de notación de función es la forma pendiente-intersección de una ecuación.
13. La forma punto-pendiente sirve para determinar una ecuación lineal cuando se da la pendiente de una línea y un punto. Vea el .
14. La forma punto-pendiente también es conveniente para hallar una ecuación lineal cuando se dan dos puntos por los que pasa una línea. Vea el .
15. La ecuación de una función lineal se puede escribir si la pendiente y el valor inicial son conocidas. Vea el , el , y el .
16. La función lineal puede utilizarse para resolver problemas del mundo real. Vea el y el .
17. La función lineal puede escribirse de forma tabular. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, determine si la ecuación de la curva puede escribirse como una función lineal.
En los siguientes ejercicios, determine si cada función es creciente o decreciente.
En los siguientes ejercicios, calcule la pendiente de la línea que pasa por los dos puntos dados.
En los siguientes ejercicios, dado cada conjunto de información, halle una ecuación lineal que satisfaga las condiciones, si es posible.
### Gráficos
En los siguientes ejercicios, halle la pendiente de las líneas graficadas.
En los siguientes ejercicios, escriba una ecuación para las líneas graficadas.
### Numéricos
En los siguientes ejercicios, ¿cuál de las tablas podría representar una función lineal? Para cada uno de los que podrían ser lineales, halle una ecuación lineal que modele los datos.
### En tecnología
### Extensiones
### Aplicaciones en el mundo real
|
# Funciones lineales
## Gráficos de funciones lineales
Dos compañías telefónicas de la competencia ofrecen diferentes planes de pago. Los dos planes cobran la misma tarifa por minuto de larga distancia, pero cobran una tarifa plana mensual diferente. Un consumidor quiere determinar si los dos planes costarán alguna vez la misma cantidad para un número determinado de minutos de larga distancia utilizados. El costo total de cada plan de pago puede representarse mediante una función lineal. Para resolver el problema, tendremos que comparar las funciones. En esta sección, consideraremos los métodos de comparación de funciones mediante gráficos.
### Gráficos de funciones lineales
En Funciones lineales, vimos que el gráfico de una función lineal es una línea recta. También pudimos ver los puntos de la función, así como el valor inicial de un gráfico. Por lo tanto, al graficar dos funciones, podemos comparar más fácilmente sus características.
Existen tres métodos básicos para graficar funciones lineales. El primero es trazar puntos y luego dibujar una línea a través de ellos. El segundo consiste en utilizar la intersección en y, así como la pendiente. El tercero es utilizar transformaciones de la función de identidad
### Graficar una función mediante el trazado de puntos
Para hallar los puntos de una función, podemos elegir los valores de entrada, evaluar la función en estos valores de entrada y calcular los valores de salida. Los valores de entrada y los correspondientes valores de salida forman pares de coordenadas. A continuación, trazamos los pares de coordenadas en una cuadrícula. En general, deberíamos evaluar la función en un mínimo de dos entradas para hallar al menos dos puntos en el gráfico. Por ejemplo, dada la función, podríamos utilizar los valores de entrada 1 y 2. Evaluando la función para un valor de entrada de 1 se obtiene un valor de salida de 2, que se representa con el punto Evaluando la función para un valor de entrada de 2 se obtiene un valor de salida de 4, representado por el punto A menudo se aconseja elegir tres puntos, porque si no caen en la misma línea, sabemos que hemos cometido un error.
### Graficar una función mediante la intersección en y, además de la pendiente
Otra forma de representar gráficamente las funciones lineales es utilizar las características específicas de la función en lugar de trazar puntos. La primera característica es su intersección en y, que es el punto en el que el valor de entrada es cero. Para hallar la intersección en , podemos establecer en la ecuación.
La otra característica de la función lineal es su pendiente que es una medida de su inclinación. Recordemos que la pendiente es la tasa de cambio de la función. La pendiente de una función es igual la relación entre la variación de las salidas y de las entradas. Otra forma de pensar en la pendiente es dividir la diferencia vertical, o subida, entre la diferencia horizontal, o recorrido. Hallamos tanto la intersección en y como la pendiente en Funciones lineales.
Consideremos la función siguiente.
La pendiente es Dado que la pendiente es positiva, sabemos que el gráfico se inclinará hacia arriba y de izquierda a derecha. La intersección en y es el punto del gráfico cuando El gráfico cruza el eje y en Ahora conocemos la pendiente y la intersección en y. Podemos empezar a graficar al trazar el punto Sabemos que la pendiente se eleva sobre el recorrido, De nuestro ejemplo, tenemos lo que significa que la subida es 1 y el recorrido es 2. Por lo tanto, a partir de nuestra intersección en y podemos subir 1 y luego recorrer 2, o recorrer 2 y luego subir 1. Lo repetimos hasta que tengamos unos cuantos puntos, y entonces trazamos una línea a través de los puntos como se muestra en la .
### Graficar una función mediante transformaciones
Otra opción para graficar es utilizar transformaciones de la función de identidad . Una función puede transformarse mediante un desplazamiento hacia arriba, hacia abajo, hacia la izquierda o hacia la derecha. Una función también puede transformarse mediante una reflexión, un estiramiento o una compresión.
### Estiramiento o compresión vertical
En la ecuación el plano actúa como el estiramiento o la compresión vertical de la función de identidad. Cuando es negativo, también hay una reflexión vertical del gráfico. Observe que en la al multiplicar la ecuación de por estira el gráfico de por un factor de unidades si y comprime el gráfico de por un factor de unidades si Esto significa que, cuanto mayor sea el valor absoluto de mayor será la pendiente.
### Desplazamiento vertical
En el plano actúa como el desplazamiento vertical, al mover el gráfico hacia arriba y hacia abajo sin afectar la pendiente de la línea. Observe en la que la adición de un valor de a la ecuación de desplaza el gráfico de un total de unidades hacia arriba si es positivo y unidades hacia abajo si es negativo.
El uso de estiramiento o compresión vertical junto con desplazamiento vertical es otra forma de ver la identificación de diferentes tipos de funciones lineales. Aunque esta no sea la forma más fácil de graficar este tipo de funciones, es importante practicar cada método.
### Escribir la ecuación de una función a partir del gráfico de una recta
Recuerde que en Funciones lineales, escribimos la ecuación de una función lineal a partir de un gráfico. Ahora podemos ampliar lo que sabemos con respecto a la graficación de funciones lineales para analizar los gráficos de manera pormenorizada. Comience por echar un vistazo a la . Podemos ver de inmediato que el gráfico cruza el eje y en el punto así que esta es la intersección y.
Entonces podemos calcular la pendiente al hallar la subida y el recorrido. Podemos elegir dos puntos cualesquiera, pero veamos el punto
Para llegar desde este punto hasta la intersección en y, debemos movernos hacia arriba 4 unidades (subida) y hacia la derecha 2 unidades (recorrido). Por lo que la pendiente deberá ser
Sustituyendo la pendiente y la intersección en y en la forma pendiente-intersección de una línea se obtiene
### Hallar la intersección en x de una línea
Hasta ahora, hemos hallado las intersecciones en y de una función: el punto en el que el gráfico de la función cruza el eje y. Una función también puede tener una intersección en , que es la coordenada de la x del punto donde el gráfico de la función cruza el eje x. En otras palabras, es el valor de entrada cuando el valor de salida es cero.
Para hallar la intersección en x, se establece una función igual a cero y se resuelve para el valor de Por ejemplo, considere la función indicada.
Iguale la función a 0 y resuelva para
El gráfico de la función cruza el eje x en el punto
### Describir líneas horizontales y verticales
Hay dos casos especiales de líneas en un gráfico: horizontales y verticales. La línea horizontal indica una salida constante o valor de y. En la , vemos que la salida tiene un valor de 2 para cada valor de entrada. Por lo tanto, la variación en las salidas entre dos puntos cualesquiera es 0. En la fórmula de la pendiente, el numerador es 0, por lo que la pendiente es 0. Si utilizamos en la ecuación la ecuación se simplifica a En otras palabras, el valor de la función es una constante. Este gráfico representa la función
Una línea vertical indica una entrada constante o valor de x. Podemos ver que el valor de entrada para cada punto de la línea es 2, pero el valor de salida varía. Dado que este valor de entrada se asigna a más de un valor de salida, una línea vertical no representa una función. Observe que entre dos puntos cualesquiera, el cambio en los valores de entrada es cero. En la fórmula de la pendiente, el denominador será cero, por lo que la pendiente de una línea vertical es indefinida.
Observe que una línea vertical, como la que aparece en la , tiene una intersección en x, pero no tiene intersección en y, a menos que sea la línea Este gráfico representa la línea
### Determinar si las líneas son paralelas o perpendiculares
Las dos líneas en la son líneas paralelas: nunca se intersecan. Observe que tienen exactamente la misma inclinación, lo que significa que sus pendientes son idénticas. La única diferencia entre las dos líneas es la intersección en y. Si desplazamos una línea verticalmente hacia la intersección en y de la otra, se convertirían en la misma línea.
Podemos determinar a partir de sus ecuaciones si dos líneas son paralelas al comparar sus pendientes. Si las pendientes son iguales y las intersecciones en y son diferentes, las líneas son paralelas. Si las pendientes son diferentes, las líneas no son paralelas.
A diferencia de las líneas paralelas, las líneas perpendiculares sí se intersecan. Su intersección forma un ángulo recto o de 90 grados. Las dos líneas en la son perpendiculares.
Las líneas perpendiculares no tienen la misma pendiente. Las pendientes de las líneas perpendiculares son diferentes entre sí de una manera específica. La pendiente de una línea es el recíproco negativo de la pendiente de la otra línea. El producto de un número por su recíproco es 1. Por lo tanto, si y son recíprocos negativos entre sí, se pueden multiplicar entre sí para obtener –1.
Para calcular el recíproco de un número, divídalo entre 1. Así, el recíproco de 8 es y el recíproco de es 8. Para hallar el recíproco negativo, primero hay que calcular el recíproco y luego cambiar el signo.
Al igual que con las líneas paralelas, podemos determinar si dos líneas son perpendiculares al comparar sus pendientes, suponiendo que las líneas no sean horizontales ni verticales. La pendiente de cada una de las líneas de abajo es el recíproco negativo de la otra, por lo que son perpendiculares.
El producto de las pendientes es -1.
### Escribir la ecuación de una línea paralela o perpendicular a una línea dada
Si conocemos la ecuación de una línea, podemos utilizar lo que sabemos sobre la pendiente para escribir la ecuación de una línea que sea paralela o perpendicular a la línea dada.
### Escribir ecuaciones de líneas paralelas
Supongamos, por ejemplo, que nos dan la siguiente ecuación.
Sabemos que la pendiente de la línea formada por la función es 3. También sabemos que la intersección en y es Cualquier otra línea con una pendiente de 3 será paralela a Así que las líneas formadas por todas las funciones siguientes serán paralelas a
Supongamos entonces que queremos escribir la ecuación de una línea que es paralela a y pasa por el punto Ya sabemos que la pendiente es 3. Lo único que tenemos que hacer es determinar cuál valor para dará la línea correcta. Podemos empezar con la forma punto-pendiente de una ecuación para una línea, y luego reescribirla en la forma pendiente-intersección.
Así que es paralela a y pasa por el punto
### Escribir ecuaciones de líneas perpendiculares
Podemos utilizar un proceso muy similar para escribir la ecuación de una línea perpendicular a una línea dada. Sin embargo, en lugar de utilizar la misma pendiente, utilizamos el recíproco negativo de la pendiente dada. Supongamos que nos dan la siguiente función:
La pendiente de la línea es 2, y su recíproco negativo es Cualquier función con una pendiente de será perpendicular a Así que las líneas formadas por todas las siguientes funciones serán perpendiculares a
Al igual que antes, podemos reducir nuestras opciones para una línea perpendicular particular si sabemos que pasa por un punto determinado. Supongamos entonces que queremos escribir la ecuación de una línea que es perpendicular a y pasa por el punto Ya sabemos que la pendiente es Ahora podemos utilizar el punto para hallar la intersección en y al sustituir los valores dados en la forma pendiente-intersección de una línea y resolver para
La ecuación de la función con pendiente de y una intersección en y de 2 es
Así que es perpendicular a y pasa por el punto Tenga en cuenta que las líneas perpendiculares pueden no parecer obviamente perpendiculares en una calculadora gráfica, a menos que utilicemos la función de zoom cuadrado.
### Resolver un sistema de ecuaciones lineales mediante un gráfico
Un sistema de ecuaciones lineales incluye dos o más ecuaciones lineales. Los gráficos de dos líneas se intersecan en un mismo punto si no son paralelos. Dos líneas paralelas también pueden intersecarse si son coincidentes, lo que significa que son la misma línea y se cruzan en cada punto. En el caso de dos líneas que no son paralelas, el único punto de intersección satisfará ambas ecuaciones y, por lo tanto, representará la solución del sistema.
Para hallar este punto cuando las ecuaciones están dadas como funciones, podemos resolver para un valor de entrada de manera que En otras palabras, podemos establecer las fórmulas de las líneas iguales entre sí y resolver la entrada que satisface la ecuación.
### Conceptos clave
1. Las funciones lineales pueden graficarse trazando puntos o utilizando la intersección en y, además de la pendiente. Vea el y el .
2. Los gráficos de las funciones lineales pueden transformarse con desplazamientos hacia arriba, hacia abajo, hacia la izquierda o hacia la derecha, así como mediante estiramiento, compresión y reflexión. Vea el .
3. La intersección en y, además de la pendiente, pueden utilizarse para escribir la ecuación de una línea.
4. La intersección en x es el punto en el cual el gráfico de una función lineal cruza el eje x. Vea el y el .
5. Las líneas horizontales se escriben en la forma, Vea el .
6. Las líneas verticales se escriben en la forma, Vea el .
7. Las líneas paralelas tienen la misma pendiente.
8. Las líneas perpendiculares tienen pendientes recíprocas negativas, suponiendo que ninguna es vertical. Vea el .
9. Una línea paralela a otra, que pasa por un punto dado, puede hallarse al sustituir en la ecuación el valor de la pendiente de la línea y los valores de x y de y del punto dado en la ecuación y utilizando el resultante. Del mismo modo, también se puede utilizar la forma punto-pendiente de una ecuación. Vea el .
10. Una línea perpendicular a otra, que pasa por un punto dado, puede hallarse de la misma manera, con la excepción de utilizar la pendiente recíproca negativa. Vea el y el .
11. Un sistema de ecuaciones lineales puede resolverse al igualar las dos ecuaciones entre sí y resolver para El valor de y se halla al evaluar cualquiera de las ecuaciones originales y utilizando este valor de x.
12. Un sistema de ecuaciones lineales también puede resolverse al hallar el punto de intersección en un gráfico. Vea el y el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios determine si las líneas dadas por las ecuaciones de abajo son paralelas, perpendiculares o no son ni paralelas ni perpendiculares:
En los siguientes ejercicios, halle las intersecciones en x y en y de cada ecuación.
En los siguientes ejercicios, utilice las descripciones de cada par de líneas que se dan a continuación para calcular las pendientes de la línea 1 y la línea 2. ¿Cada par de líneas es paralelo, perpendicular o ninguno de los dos?
### Gráficos
En los siguientes ejercicios, relacione la ecuación lineal dada con su gráfico en la .
En los siguientes ejercicios, dibuje una línea con las características dadas.
En los siguientes ejercicios, dibuje el gráfico de cada ecuación.
En los siguientes ejercicios, escriba la ecuación de la línea que se muestra en el gráfico.
En los siguientes ejercicios, halle el punto de intersección de cada par de líneas, si existe. Si no existe, indique que no hay punto de intersección.
### Extensiones
En los siguientes ejercicios, utilice las funciones
### Aplicaciones en el mundo real
|
# Funciones lineales
## Modelado con funciones lineales
Elan es una estudiante universitaria que planea pasar el verano en Seattle. Ahorró 3.500 dólares para su viaje y prevé gastar 400 dólares cada semana en alquiler, comida y actividades. ¿Cómo podemos escribir un modelo lineal que represente la situación? ¿Cuál sería la intersección en x y qué puede aprender Elan de ella? Para responder estas y otras interrogantes por el estilo, podemos crear un modelo por medio de una función lineal. Los modelos como este pueden ser extremadamente útiles para analizar las relaciones y hacer predicciones basadas en estas. En esta sección, exploraremos ejemplos de modelos de función lineal.
### Identificar los pasos para modelar y resolver problemas
Cuando se modelan escenarios con funciones lineales y se resuelven problemas que implican cantidades con una tasa de cambio constante, solemos seguir las mismas estrategias de problemas que utilizaríamos para cualquier tipo de función. Repasémoslos brevemente:
1. Identifique las cantidades cambiantes y, a continuación, defina las variables descriptivas que representen esas cantidades. Cuando sea pertinente, haga un dibujo o defina un sistema de coordenadas.
2. Lea atentamente el problema para identificar la información importante. Busque información que proporcione valores para las variables o valores para partes del modelo funcional, como la pendiente y el valor inicial.
3. Lea detenidamente el problema para determinar qué es lo que queremos encontrar, identificar, resolver o interpretar.
4. A partir de la información suministrada, identifique una vía de solución a lo que tratamos de hallar. A menudo, esto implicará la comprobación y el seguimiento de las unidades, la construcción de una tabla o incluso la búsqueda de una fórmula para la función que se utiliza para modelar el problema.
5. Cuando sea necesario, escriba una fórmula para la función.
6. Resuelva o evalúe la función con la fórmula.
7. Reflexione si su respuesta es razonable para la situación dada y si tiene sentido matemático.
8. Exprese claramente su resultado con las unidades adecuadas, y responda con frases completas cuando sea necesario.
### Construir modelos lineales
Ahora echemos un vistazo a la estudiante en Seattle. En la situación de Elan hay dos cantidades cambiantes: el tiempo y el dinero. La cantidad de dinero que le queda mientras está de vacaciones depende del tiempo que se quede. Podemos utilizar esta información para definir nuestras variables, incluidas las unidades.
1. Salida:
dinero restante, en dólares
2. Entrada:
tiempo, en semanas
Por lo tanto, la cantidad de dinero restante depende del número de semanas:
También podemos identificar el valor inicial y la tasa de cambio.
1. Valor inicial: ahorró 3.500 dólares, por lo que 3.500 dólares es el valor inicial de
2. Tasa de cambio: prevé gastar 400 dólares cada semana, por lo que –400 dólares semanales es la tasa de cambio, o la pendiente.
Observe que la unidad de dólares por semana coincide con la unidad de nuestra variable de salida dividida entre nuestra variable de entrada. Además, dado que la pendiente es negativa, la función lineal es decreciente. Esto debería tener sentido porque gasta dinero cada semana.
La tasa de cambio es constante, por lo que podemos empezar con el modelo lineal
Entonces podemos sustituir la intersección y la pendiente que se han proporcionado.
Para calcular la intersección en
llevamos la salida a cero y resolvemos para la entrada.
Las intersecciones en
es de 8,75 semanas. Ya que esto representa el valor de entrada cuando la salida sea cero, podríamos decir que a Elan no le quedará dinero después de 8,75 semanas.
Al modelar cualquier situación de la vida real con funciones, suele haber un dominio limitado en el que ese modelo será válido: casi ninguna tendencia continúa indefinidamente. Aquí el dominio se refiere al número de semanas. En este caso, no tiene sentido hablar de valores de entrada inferiores a cero. Un valor negativo de entrada podría referirse a un número de semanas antes de que Elan ahorrara 3.500 dólares, pero el escenario analizado plantea la pregunta una vez que ahorró 3.500 dólares porque es cuando comienza su viaje y su gasto posterior. También es probable que este modelo no sea válido después de la intersección en
, a no ser que Elan utilice una tarjeta de crédito y se endeude. El dominio representa el conjunto de valores de entrada, por lo que el dominio razonable para esta función es:
En el ejemplo anterior, se nos dio una descripción escrita de la situación. Hemos seguido los pasos para el modelado de un problema con el fin de analizar la información. Sin embargo, no siempre se suministra la misma información. A veces se nos proporciona una intersección. Otras veces se nos da un valor de salida. Debemos tener cuidado de analizar la información que se nos suministra y utilizarla adecuadamente para construir un modelo lineal.
### Utilizar una intersección dada para construir un modelo
Algunos problemas del mundo real proporcionan la intersección en
, que es la constante o valor inicial. Una vez que se conoce la intersección en
, la intersección en
puede calcularse. Supongamos, por ejemplo, que Hannah planea pagar un préstamo sin intereses que contrajo de sus padres. El saldo de su préstamo es de 1.000 dólares. Tiene previsto pagar 250 dólares al mes hasta que su saldo sea de 0. La intersección en
es el importe inicial de su deuda, es decir, 1.000 dólares. La tasa de cambio, o pendiente, es de -250 dólares al mes. Podemos entonces utilizar la forma pendiente-intersección y la información dada para elaborar un modelo lineal.
Ahora podemos establecer la función igual a 0, y resolver para
para hallar la intersección en
.
Las intersecciones en
es el número de meses que tarde en llevar el saldo a 0 dólares. La intersección en
es 4 meses, por lo que Hannah tardará cuatro meses para pagar su préstamo.
### Utilizar una entrada y una salida dadas para construir un modelo
Muchas aplicaciones en el mundo real no son tan directas como las que acabamos de considerar. En cambio, nos exigen que identifiquemos algún aspecto de una función lineal. A veces se nos pide que evaluemos el modelo lineal con una entrada determinada o que establezcamos la ecuación del modelo lineal igual a una salida especificada.
### Utilizar un diagrama para modelar un problema
En muchas aplicaciones del mundo real es útil hacer un dibujo para tener una idea de cómo las variables que representan la entrada y la salida se utilizan para responder una pregunta. Para dibujar el cuadro, primero hay que considerar lo que pide el problema. A continuación, determine la entrada y la salida. El diagrama debería relacionar las variables. Con frecuencia se dibujan formas o figuras geométricas. A menudo, las distancias se trazan. Si se dibuja un triángulo rectángulo, el teorema de Pitágoras relaciona los lados. Si se dibuja un rectángulo, es útil etiquetar la anchura y la altura.
### Construir sistemas de modelos lineales
Las situaciones en el mundo real que incluyen dos o más funciones lineales pueden modelarse con un sistema de ecuaciones lineales. Recuerde que, al resolver un sistema de ecuaciones lineales, buscamos los puntos que tienen en común las dos líneas. Normalmente, hay tres tipos de respuestas posibles, como se indica en la .
1. Podemos utilizar las mismas estrategias de problemas que utilizaríamos para cualquier tipo de función.
2. Al modelar y resolver un problema, identifique las variables y busque los valores clave, incluso la pendiente y la intersección en y. Vea el .
3. Dibuje un diagrama, si procede. Vea el y el .
4. Compruebe si la respuesta es razonable.
5. Los modelos lineales pueden construirse al identificar o calcular la pendiente y utilizar la intersección en y.
6. La intersección en x se halla al establecer
que iguala la expresión
a 0.
7. El punto de intersección de un sistema de ecuaciones lineales es el punto en el que los valores de x y de y son iguales. Vea el .
8. Se puede utilizar un gráfico del sistema para identificar los puntos en los que una línea cae por debajo (o por encima) de la otra línea.
### Verbales
### Algebraicos
En los siguientes ejercicios, considere este escenario: La población de una ciudad ha disminuido a un ritmo constante. En 2010 la población era de 5.900 habitantes. Para 2012, la población había descendido a 4.700. Supongamos que esta tendencia se mantiene.
En los siguientes ejercicios, considere este escenario: La población de una ciudad ha aumentado a un ritmo constante. En 2010 la población era de 46.020 habitantes. En 2012 la población se había incrementado a 52.070 habitantes. Supongamos que esta tendencia se mantiene.
En los siguientes ejercicios, considere este escenario: Una ciudad tiene una población inicial de 75.000 habitantes. Crece a un ritmo constante de 2.500 al año durante 5 años.
En los siguientes ejercicios, considere este escenario: Un bebé pesa 7,5 libras al nacer. Aumenta media libra al mes durante su primer año.
En los siguientes ejercicios, considere este escenario: El número de personas afectadas por el resfriado común en los meses de invierno se redujo en 205 cada año desde 2005 hasta 2010. En 2005, 12.025 personas se vieron afectadas.
### Gráficos
En los siguientes ejercicios, utilice el gráfico de la , que muestra el beneficio,
en miles de dólares, de una empresa en un año determinado,
donde
representa el número de años desde 1980.
En los siguientes ejercicios, utilice el gráfico de la , que muestra el beneficio,
en miles de dólares, de una empresa en un año determinado,
donde
representa el número de años desde 1980.
### Numéricos
En los siguientes ejercicios, utilice la mediana del valor de la vivienda en Misisipi y Hawái (ajustado a la inflación) que aparece en la . Supongamos que el valor de la vivienda cambia linealmente.
En los siguientes ejercicios, utilice la mediana del valor de las vivienda en Indiana y Alabama (ajustado a la inflación) que aparece en la . Supongamos que el valor de la vivienda cambia linealmente.
### Aplicaciones en el mundo real
|
# Funciones lineales
## Ajuste de modelos lineales a los datos
Un profesor intenta identificar las tendencias entre las puntuaciones de los exámenes finales. En su clase hay una mezcla de alumnos, por lo que se pregunta si hay alguna relación entre la edad y las notas de los exámenes finales. Una forma de analizar las puntuaciones es crear un diagrama que relacione la edad de cada alumno con la puntuación recibida en el examen. En esta sección, examinaremos uno de estos diagramas, el cual se conoce como diagrama de dispersión.
### Dibujar e interpretar gráficos de dispersión
El diagrama de dispersión es un gráfico de puntos trazados capaz de mostrar una relación entre dos conjuntos de datos. Si la relación procede de un modelo lineal, o de un modelo casi lineal, el profesor puede sacar conclusiones por medio de su conocimiento acerca de funciones lineales. La muestra un ejemplo de gráfico de dispersión.
Observe que este gráfico de dispersión no indica ninguna relación lineal. Los puntos no parecen seguir ninguna tendencia. En otras palabras, no parece haber ninguna relación entre la edad del estudiante y la puntuación en el examen final.
### Hallar la línea de mejor ajuste
Una vez que reconocemos la necesidad de una función lineal para modelar esos datos, la pregunta obvia que sigue es "¿cuál es esa función lineal?”. Una forma de aproximar nuestra función lineal es trazar la línea que parezca ajustarse mejor a los datos. Entonces podemos extender la línea hasta que podamos verificar la intersección en y. Podemos calcular la pendiente de la línea al extenderla hasta que podamos estimar la
### Reconocer la interpolación o la extrapolación
Aunque los datos de la mayoría de los ejemplos no caen perfectamente sobre la línea, la ecuación es nuestra mejor conjetura sobre cómo se comportará la relación fuera de los valores para los que tenemos datos. Utilizamos un proceso conocido como interpolación cuando predecimos un valor dentro del dominio y el rango de los datos. La extrapolación se utiliza cuando predecimos un valor fuera del dominio y del rango de los datos.
La compara los dos procesos para los datos del chirrido de los grillos que se abordan en el . Podemos ver que la interpolación se produciría si utilizamos nuestro modelo para predecir la temperatura cuando los valores de los chirridos están entre 18,5 y 44. La extrapolación se produciría si utilizáramos nuestro modelo para predecir la temperatura cuando los valores de los chirridos fueran inferiores a 18,5 o superiores a 44.
Hay una diferencia entre hacer predicciones dentro del dominio y del rango de valores para los que tenemos datos y fuera de ese dominio y rango. Predecir un valor fuera del dominio y del rango tiene sus limitaciones. Cuando nuestro modelo deja de ser válido a partir de cierto momento, a veces se denomina ruptura del modelo. Por ejemplo, la predicción de una función de costos para un periodo de dos años implicaría el examen de los datos en los que la entrada es el tiempo en años y la salida es el costo. Sin embargo, si intentamos extrapolar un costo cuando que es dentro de 50 años, el modelo no se aplicaría porque no podríamos contabilizar factores a la vuelta de cincuenta años.
### Hallar la línea de mejor ajuste con una herramienta gráfica
Si bien es cierto que la observación de una línea funciona razonablemente bien, existen técnicas estadísticas para ajustar una línea a los datos que minimizan las diferencias entre la línea y los valores de los datosTécnicamente, el método minimiza la suma de las diferencias al cuadrado en la dirección vertical entre la línea y los valores de los datos.. Una de estas técnicas se denomina regresión de mínimos cuadrados y puede estimarse con muchas calculadoras gráficos, programas de hojas de cálculo, programas estadísticos y muchas calculadoras en líneaPor ejemplo, http://www.shodor.org/unchem/math/lls/leastsq.html. La regresión de mínimos cuadrados es un medio para determinar la línea que mejor se ajusta a los datos, y aquí nos referiremos a este método como regresión lineal.
### Distinguir entre modelos lineales y no lineales
Como hemos visto anteriormente con el modelo de grillo-chirrido, algunos datos muestran fuertes tendencias lineales. Sin embargo, otros datos, como las puntuaciones de los exámenes finales representadas por la edad, son claramente no lineales. La mayoría de las calculadoras y los programas informáticos también pueden proporcionarnos el coeficiente de correlación, que es una medida del grado de ajuste de la línea a los datos. Muchas calculadoras gráficas requieren que el usuario active una selección de "diagnóstico" para determinar el coeficiente de correlación, que los matemáticos denominan El coeficiente de correlación es una forma sencilla de hacerse una idea de lo cerca que están los datos de una línea.
Deberíamos calcular el coeficiente de correlación únicamente para los datos que siguen un patrón lineal o para determinar el grado en que un conjunto de datos es lineal. Si los datos presentan un patrón no lineal, el coeficiente de correlación de una regresión lineal no tiene sentido. Para tener una idea de la relación entre el valor de y el gráfico de los datos, la muestra algunos grandes conjuntos de datos con sus coeficientes de correlación. Recuerde que, en todos los gráficos, el eje horizontal muestra la entrada y el eje vertical la salida.
### Predecir con la línea de regresión
Una vez que determinamos que un conjunto de datos es lineal utilizando el coeficiente de correlación, podemos utilizar la línea de regresión para hacer predicciones. Como hemos aprendido anteriormente, la línea de regresión es la que más se acerca a los datos en el gráfico de dispersión, lo que significa que solo una de esas líneas es la que mejor se ajusta a los datos.
### Conceptos clave
1. Los gráficos de dispersión muestran la relación entre dos conjuntos de datos. Vea el .
2. Los gráficos de dispersión representan modelos lineales o no lineales.
3. La línea de mejor ajuste puede estimarse o calcularse con una calculadora o un software estadístico. Vea el .
4. La interpolación sirve para predecir valores dentro del dominio y del rango de los datos, mientras que la extrapolación sirve para predecir valores fuera del dominio y del rango de los datos. Vea el .
5. El coeficiente de correlación, indica el grado de relación lineal entre los datos. Vea el .
6. La línea de regresión es la que mejor se ajusta a los datos. Vea el .
7. La línea de regresión de mínimos cuadrados se halla al minimizar los cuadrados de las distancias de los puntos a una línea que pasa por los datos y puede utilizarse para hacer predicciones sobre cualquiera de las variables. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, dibuje un gráfico de dispersión para los datos proporcionados. ¿Parece que los datos están relacionados linealmente?
### Gráficos
En los siguientes ejercicios, haga coincidir cada gráfico de dispersión con una de las cuatro correlaciones especificadas en la y la .
En los siguientes ejercicios, dibuje una línea de mejor ajuste para los datos trazados.
### Numéricos
### En tecnología
En los siguientes ejercicios, utilice cada conjunto de datos para determinar la línea de regresión con una calculadora u otra herramienta tecnológica, y determine el coeficiente de correlación con una precisión de 3 decimales.
### Extensiones
En los siguientes ejercicios, considere este escenario: El beneficio de una empresa disminuyó de forma constante durante un periodo de diez años. Los siguientes pares ordenados muestran los dólares y el número de unidades vendidas en centenas, así como el beneficio en miles durante el periodo de diez años (número de unidades vendidas, beneficio) para determinados años registrados:
.
### Aplicaciones en el mundo real
En los siguientes ejercicios, considere este escenario: La población de una ciudad aumentó de forma constante durante un periodo de diez años. Los siguientes pares ordenados muestran la población y el año a lo largo de los diez años, (población, año) para determinados años registrados:
En los siguientes ejercicios, considere este escenario: El beneficio de una empresa aumentó de forma constante durante un período de diez años. Los siguientes pares ordenados muestran el número de unidades vendidas en centenas y el beneficio en miles durante el periodo de diez años (número de unidades vendidas, beneficio) para determinados años registrados:
.
En los siguientes ejercicios, considere este escenario: El beneficio de una empresa disminuyó de forma constante durante un periodo de diez años. Los siguientes pares ordenados muestran los dólares y el número de unidades vendidas en centenas y el beneficio en miles de durante el período de diez años (número de unidades vendidas, beneficio) para determinados años registrados:
### Ejercicios de repaso del capítulo
### Funciones lineales
### Gráficos de funciones lineales
En los siguientes ejercicios, determine si las líneas dadas por las ecuaciones de abajo son paralelas, perpendiculares o no son ni paralelas ni perpendiculares:
En los siguientes ejercicios, halle las intersecciones en x y en y de la ecuación dada
En los siguientes ejercicios, utilice las descripciones de los pares de líneas para hallar las pendientes de la Línea 1 y la Línea 2. ¿Cada par de líneas es paralelo, perpendicular o ninguno de los dos?
### Modelado con funciones lineales
En los siguientes ejercicios, utilice el gráfico de la que muestra el beneficio, en miles de dólares, de una empresa en un año determinado, donde representa los años desde 1980.
En el siguiente ejercicio, considere esta situación: En 2004, la población escolar era de 1.700 personas. En 2012 la población había crecido hasta las 2.500 personas.
En los siguientes ejercicios, considere este escenario: En el año 2000, la población de alces en el parque se midió en 6.500 ejemplares. En 2010, la población se contabilizó en 12.500 ejemplares. Supongamos que la población sigue cambiando linealmente.
En los siguientes ejercicios, considere este escenario: La mediana de los valores de las viviendas en las subdivisiones Pima Central y East Valley (ajustados a la inflación) se muestra en la . Supongamos que el valor de la vivienda cambia linealmente.
### Ajuste de modelos lineales a los datos
En los siguientes ejercicios, considere los datos en la , donde se muestra el porcentaje de desempleados en una ciudad de residentes mayores de 25 años de edad que son graduados universitarios, y que se ofrece a continuación, por año.
En los siguientes ejercicios, considere este escenario: La población de una ciudad aumentó de forma constante durante un periodo de diez años. Los siguientes pares ordenados muestran la población y el año en un período de diez años (población, año) para determinados años registrados:
### Prueba de práctica
En los siguientes ejercicios, determine si las líneas dadas por las ecuaciones de abajo son paralelas, perpendiculares o no son ni paralelas ni perpendiculares:
En los siguientes ejercicios, utilice el gráfico de la , que muestra el beneficio, , en miles de dólares, de una empresa en un año determinado, , donde representa los años desde 1980.
En los siguientes ejercicios, utilice la , que muestra el porcentaje de desempleados mayores de 25 años que son graduados universitarios en una ciudad en particular, por año.
En los siguientes ejercicios, considere este escenario: La población de una ciudad aumentó de forma constante durante un periodo de diez años. Los siguientes pares ordenados muestran la población (en centenas) y el año en el lapso de diez años, (población, año) para determinados años registrados:
|
# Funciones polinómicas y racionales
## Introducción
No hace falta sumergirse mucho para sentir los efectos de la presión. Cuando una persona en la piscina de su vecindario se desplaza ocho, diez, veinte pies hacia abajo, suele sentir dolor en los oídos como consecuencia de las diferenciales de presión del agua y del aire. La presión desempeña un papel mucho más importante en las profundidades de buceo del océano.
Los buceadores con escafandra autónoma y en apnea negocian constantemente los efectos de la presión para experimentar inmersiones agradables, seguras y productivas. Los gases del sistema respiratorio y del aparato de buceo de una persona interactúan según ciertas propiedades físicas, que al ser descubiertas y evaluadas se conocen colectivamente como las leyes de los gases. Algunas son conceptualmente sencillas, como la relación inversa entre presión y volumen, y otras son más complejas. Aunque sus fórmulas parecen más sencillas que muchas de las que se encontrarán en este capítulo, las leyes de los gases son generalmente expresiones polinómicas. |
# Funciones polinómicas y racionales
## Números complejos
El estudio de las matemáticas se construye continuamente sobre sí mismo. Los números enteros negativos, por ejemplo, llenan el vacío dejado por el conjunto de números enteros positivos. El conjunto de los números racionales, a su vez, llena el vacío dejado por el conjunto de los números enteros. El conjunto de los números reales llena el vacío dejado por el conjunto de los números racionales. No es de extrañar que el conjunto de los números reales también tenga vacíos. Por ejemplo, todavía no tenemos solución para ecuaciones como
Nuestras mejores suposiciones podrían ser +2 o –2. Sin embargo, si probamos +2 en esta ecuación, no funciona. Si probamos –2, no funciona. Si queremos tener una solución para esta ecuación, tendremos que ir más lejos de lo que hemos hecho hasta ahora. Después de todo, hasta ahora hemos descrito la raíz cuadrada de un número negativo como indefinida. Afortunadamente, existe otro sistema de números que proporciona soluciones a tales problemas. En esta sección, exploraremos este sistema numérico y cómo trabajar dentro de él.
### Expresar raíces cuadradas de los números negativos como múltiplos de i
Sabemos cómo hallar la raíz cuadrada de cualquier número real positivo. De forma similar, podemos hallar la raíz cuadrada de un número negativo. La diferencia es que la raíz no es real. Si el valor del radicando es negativo, se dice que la raíz es un número imaginario. El número imaginario
se define como la raíz cuadrada de 1 negativo.
Entonces, con las propiedades de los radicales,
Podemos escribir la raíz cuadrada de cualquier número negativo como un múltiplo de
Considere la raíz cuadrada de –25.
Utilizamos
y no
porque la raíz principal de
es la raíz positiva.
Un número complejo es la suma de un número real y un número imaginario. Un número complejo se expresa en forma estándar cuando se escribe
donde
es la parte real y
es la parte imaginaria. Por ejemplo,
es un número complejo. También lo es
Los números imaginarios se distinguen de los reales porque un número imaginario elevado al cuadrado produce un número real negativo. Recordemos que, cuando un número real positivo se eleva al cuadrado, el resultado es un número real positivo y cuando un número real negativo se eleva al cuadrado, de nuevo, el resultado es un número real positivo. Los números complejos son una combinación de números reales e imaginarios.
### Trazar un número complejo en el plano complejo
No podemos representar los números complejos en una línea numérica como lo haríamos con los números reales. Sin embargo, podemos representarlos gráficamente. Para representar un número complejo tenemos que abordar los dos componentes del número. Utilizamos el plano complejo, que es un sistema de coordenadas en el que el eje horizontal representa la componente real y el eje vertical representa el componente imaginario. Los números complejos son los puntos del plano, expresados como pares ordenados
donde
representa la coordenada del eje horizontal y
representa la coordenada del eje vertical.
Consideremos el número
La parte real del número complejo es
y la parte imaginaria es
Trazamos el par ordenado
para representar el número complejo
como se muestra en la .
### Sumar y restar números complejos
Al igual que con los números reales, podemos realizar operaciones aritméticas con los números complejos. Para sumar o restar números complejos, combinamos las partes reales y las partes imaginarias.
### Multiplicar números complejos
Multiplicar números complejos es muy parecido a multiplicar binomios. La principal diferencia es que trabajamos con las partes reales e imaginarias por separado.
### Multiplicar un número complejo por un número real
Empecemos por multiplicar un número complejo por un número real. Distribuimos el número real igual que lo haríamos con un binomio. Así, por ejemplo,
### Multiplicar números complejos juntos
Ahora, multipliquemos dos números complejos. Podemos utilizar la propiedad distributiva o el método FOIL. Recordemos que FOIL es el acrónimo en inglés de multiplicar juntos los términos Primero, Exterior, Interior y Último. Utilizando la propiedad distributiva o el método FOIL, obtenemos
Ya que
tenemos
Para simplificar, combinamos las partes reales y las partes imaginarias.
### Dividir números complejos
La división de dos números complejos es más complicada que la suma, la resta y la multiplicación porque no podemos dividir entre un número imaginario, lo que significa que cualquier fracción deberá tener un denominador de número real. Tenemos que hallar un término entre el cual podamos multiplicar el numerador y el denominador que elimine la parte imaginaria del denominador para que acabemos con un número real como denominador. Este término se llama conjugado complejo del denominador, que se encuentra al cambiar el signo de la parte imaginaria del número complejo. En otras palabras, el conjugado complejo de
es
Observe que los conjugados complejos tienen una relación recíproca: El conjugado complejo de
es
y el conjugado complejo de
es
Además, cuando una ecuación cuadrática con coeficientes reales tiene soluciones complejas, las soluciones son siempre conjugadas complejas entre sí.
Supongamos que queremos dividir
entre
donde ni
ni
son iguales a cero. Primero escribimos la división como una fracción, luego hallamos el conjugado complejo del denominador y multiplicamos.
Multiplicamos el numerador y el denominador por el conjugado complejo del denominador.
Aplicamos la propiedad distributiva.
Simplificamos, recordando que
### Simplificar las potencias de i
Las potencias de
son cíclicas. Veamos qué ocurre cuando elevamos
a potencias crecientes.
Podemos ver que, cuando llegamos a la quinta potencia de
es igual a la primera potencia. Mientras seguimos multiplicando
por sí mismo para potencias crecientes, veremos un ciclo de 4. Examinemos las siguientes 4 potencias de
### Conceptos clave
1. La raíz cuadrada de cualquier número negativo se puede escribir como múltiplo de
Vea el .
2. Para representar un número complejo, utilizamos dos líneas numéricas, cruzadas para formar el plano complejo. El eje horizontal es el eje real y el eje vertical es el eje imaginario. Vea el .
3. Los números complejos se pueden sumar y restar al combinar las partes reales y las partes imaginarias. Vea el .
4. Los números complejos se pueden multiplicar y dividir.
5. Para multiplicar números complejos, distribuya igual que con los polinomios. Vea el , el y el .
6. Para dividir números complejos, multiplique tanto el numerador como el denominador por el conjugado complejo del denominador para eliminar el número complejo del denominador. Vea el , el y el .
7. Las potencias de
son cíclicas, pues se repiten cada cuatro. Vea el .
### Verbales
### Algebraicos
En los siguientes ejercicios, evalúe las expresiones algebraicas.
### Gráficos
En los siguientes ejercicios, determine el número de soluciones reales y no reales de cada función cuadrática mostrada.
En los siguientes ejercicios, trace los números complejos en el plano complejo.
### Numéricos
En los siguientes ejercicios, realice la operación indicada y exprese el resultado como un número complejo simplificado.
### En tecnología
En los siguientes ejercicios, utilice una calculadora para responder las preguntas.
### Extensiones
En los siguientes ejercicios, evalúe las expresiones al escribir el resultado como un número complejo simplificado. |
# Funciones polinómicas y racionales
## Funciones cuadráticas
Las antenas curvas, como las que se muestran en la , se utilizan habitualmente para enfocar microondas y ondas de radio que transmiten señales de televisión y teléfono, así como para la comunicación por satélite y en naves espaciales. La sección transversal de la antena tiene forma de parábola, que se describe mediante una función cuadrática.
En esta sección, investigaremos las funciones cuadráticas, que modelan problemas que implican el movimiento de áreas y proyectiles. Trabajar con funciones cuadráticas puede ser menos complejo que trabajar con funciones de mayor grado; de allí que brindan una excelente oportunidad para el estudio detallado del comportamiento de las funciones.
### Reconocer las características de las parábolas
El gráfico de una función cuadrática es una curva en forma de U, denominada parábola. Una característica importante del gráfico es que tiene un punto extremo, denominado vértice. Si la parábola se abre, el vértice representa el punto más bajo en el gráfico o el valor mínimo de la función cuadrática. Si la parábola se abre hacia abajo, el vértice representa el punto más alto en el gráfico o el valor máximo. En cualquier caso, el vértice es un punto de inflexión en el gráfico. El gráfico también es simétrico, con una línea vertical trazada a través del vértice, denominada eje de simetría. Estas características se ilustran en la .
La intersección en y es el punto en el cual la parábola cruza el eje y. Las intersecciones en x son los puntos en los que la parábola cruza el eje x. Si existen, las intersecciones en x representan los ceros, o raíces, de la función cuadrática, los valores de
en los que
### Comprender cómo se relacionan los gráficos de las parábolas con sus funciones cuadráticas
La forma general de una función cuadrática presenta la función en la forma
donde
y
son números reales y
Si
la parábola se abre hacia arriba. Si los valores de
la parábola se abre hacia abajo. Podemos utilizar la forma general de una parábola para hallar la ecuación del eje de simetría.
El eje de simetría está definido por
Si utilizamos la fórmula cuadrática,
para resolver
para las intersecciones en
, o ceros, hallamos que el valor de
a mitad de camino siempre es
la ecuación del eje de simetría.
La representa el gráfico de la función cuadrática escrita en forma general como
En esta forma,
y
Dado que
la parábola se abre hacia arriba. El eje de simetría es
Esto también tiene sentido porque podemos ver en el gráfico que la línea vertical
divide el gráfico por la mitad. El vértice siempre se produce a lo largo del eje de simetría. Para una parábola que se abre hacia arriba, el vértice se encuentra en el punto más bajo del gráfico; en este caso,
La intersección en
, aquellos puntos en los que la parábola cruza el eje
, se producen en
y
La forma estándar de una función cuadrática presenta la función en la forma
donde
es el vértice. Dado que el vértice aparece en la forma estándar de la función cuadrática, esta forma también se conoce como la forma de vértice de una función cuadrática.
Al igual que con la forma general, si
la parábola se abre hacia arriba y el vértice es un mínimo. Si los valores de
la parábola se abre hacia abajo, y el vértice es un máximo. La representa el gráfico de la función cuadrática escrita en forma estándar como
Dado que
en este ejemplo,
En esta forma,
y
Dado que
la parábola se abre hacia abajo. El vértice está en
La forma estándar sirve para determinar cómo se transforma el gráfico de
La es el gráfico de esta función básica.
Si los valores de
el gráfico se desplaza hacia arriba, mientras que si
el gráfico se desplaza hacia abajo. En la ,
por lo que el gráfico se desplaza 4 unidades hacia arriba. Si los valores de
el gráfico se desplaza hacia la derecha y si
el gráfico se desplaza hacia la izquierda. En la ,
para que el gráfico se desplace 2 unidades a la izquierda. La magnitud de
indica el estiramiento del gráfico. Si los valores de
el punto asociado a un determinado valor de
se desplaza más lejos del eje x, por lo que el gráfico parece estrecharse, y hay un estiramiento vertical. Pero si
el punto asociado a un determinado valor de
se desplaza más cerca del eje x, por lo que el gráfico parece ampliarse, pero en realidad hay una compresión vertical. En la ,
por lo que el gráfico se estrecha.
La forma estándar y la forma general son métodos equivalentes para describir la misma función. Podemos verlo al ampliar la forma general y hacerla igual a la forma estándar.
Para que los términos lineales sean iguales, los coeficientes deberán ser iguales.
Este es el eje de simetría que definimos antes. Al igualar los términos constantes:
En la práctica, sin embargo, suele ser más fácil recordar que k es el valor de salida de la función cuando la entrada es
por lo que
### Hallar el dominio y el rango de una función cuadrática
Cualquier número puede ser el valor de entrada de la función cuadrática. Por lo tanto, el dominio de cualquier función cuadrática son todos los números reales. Dado que las parábolas tienen un punto máximo o mínimo, el rango está restringido. Dado que el vértice de una parábola será un máximo o un mínimo, el rango consistirá en todos los valores de y mayores o iguales a la coordenada de la y en el punto de giro o menores o iguales a la coordenada de la y en el punto de giro, dependiendo de si la parábola se abre hacia arriba o hacia abajo.
### Determinar los valores máximos y mínimos de las funciones cuadráticas
La salida de la función cuadrática en el vértice es el valor máximo o mínimo de la función, dependiendo de la orientación de la parábola. Podemos ver los valores máximos y mínimos en la .
Hay muchas situaciones en el mundo real que implican calcular el valor máximo o mínimo de una función cuadrática, como las aplicaciones que implican el área y los ingresos.
### Hallar las intersecciones en x y en y de la función cuadrática
Al igual que hicimos en los problemas de aplicación anteriores, también necesitamos hallar las intersecciones en las ecuaciones cuadráticas para graficar parábolas. Recordemos que hallamos la intersección en
de una cuadrática al evaluar la función en una entrada de cero, y hallamos la intersección en
en lugares donde la salida es cero. Observe en la que el número de intersecciones en
puede variar en función de la ubicación del gráfico.
### Reescribir cuadráticas en forma estándar
En el , la cuadrática se resolvió fácilmente mediante la factorización. Sin embargo, hay muchas cuadráticas que no se pueden factorizar. Podemos resolver estas cuadráticas al reescribirlas primero en forma estándar.
### Ecuaciones clave
### Conceptos clave
1. La función polinómica de grado dos se denomina función cuadrática.
2. El gráfico de una función cuadrática es una parábola. La parábola es una curva en forma de U que se abre hacia arriba o hacia abajo.
3. El eje de simetría es la línea vertical que pasa por el vértice. Los ceros, o intersecciones en
, son los puntos en los que la parábola cruza el eje
. La intersección en
es el punto en el que la parábola cruza el eje
. Vea el , el y el .
4. Las funciones cuadráticas suelen escribirse en forma general. La forma estándar o de vértice sirve para identificar fácilmente el vértice de una parábola. Cualquiera de las dos formas puede escribirse a partir de un gráfico. Vea el .
5. El vértice se halla a partir de una ecuación que representa una función cuadrática. Vea el .
6. El dominio de la función cuadrática son todos los números reales. La gama varía según la función. Vea el .
7. El valor mínimo o máximo de la función cuadrática viene dado por el valor de
del vértice.
8. El valor mínimo o máximo de la función cuadrática se utiliza para determinar el rango de la función y para resolver muchos tipos de problemas del mundo real, incluso de área e ingresos. Vea el y el .
9. Algunas ecuaciones cuadráticas deberán resolverse con la fórmula cuadrática. Vea el .
10. El vértice y las intersecciones pueden identificarse e interpretarse para resolver problemas del mundo real. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, reescriba las funciones cuadráticas en forma estándar e indique el vértice.
En los siguientes ejercicios, determine si existe un valor mínimo o máximo para cada función cuadrática. Halle el valor y el eje de simetría.
En los siguientes ejercicios, determine el dominio y el rango de la función cuadrática.
En los siguientes ejercicios, resuelva las ecuaciones en los números complejos.
En los siguientes ejercicios, utilice el vértice
y un punto en el gráfico
para hallar la forma general de la ecuación de la función cuadrática.
### Gráficos
En los siguientes ejercicios, dibuje un gráfico de la función cuadrática e indique el vértice, el eje de simetría y las intersecciones.
En los siguientes ejercicios, escriba la ecuación de la función graficada.
### Numéricos
En los siguientes ejercicios, utilice la tabla de valores que representan puntos en el gráfico de la función cuadrática. Al determinar el vértice y el eje de simetría, halle la forma general de la ecuación de la función cuadrática.
### En tecnología
En los siguientes ejercicios, utilice una calculadora para hallar la respuesta.
### Extensiones
En los siguientes ejercicios, utilice el vértice del gráfico de la función cuadrática y la dirección en que se abre el gráfico para hallar el dominio y el rango de la función.
En los siguientes ejercicios, escriba la ecuación de la función cuadrática que contiene el punto dado y tiene la misma forma que la función dada.
### Aplicaciones en el mundo real
|
# Funciones polinómicas y racionales
## Funciones potencia y funciones polinómicas
Supongamos que una determinada especie de ave prospera en una pequeña isla. Su población en los últimos años se muestra en la .
La población puede estimarse mediante la función
donde
representa la población de aves de la isla
años después de 2009. Podemos utilizar este modelo para estimar la población máxima de aves y cuándo se producirá. También podemos utilizar este modelo para predecir cuándo desaparecerá la población de aves de la isla. En esta sección, examinaremos las funciones que podemos utilizar para estimar y predecir este tipo de cambios.
### Identificar las funciones potencia
Para entender mejor el problema de los pájaros, necesitamos comprender un tipo específico de función. La función potencia es aquella con un solo término que es el producto de un número real, un coeficiente y una variable elevada a un número real fijo. (El número que multiplica una variable elevada a un exponente se conoce como coeficiente).
Como ejemplo, considere las funciones para el área o el volumen. La función para el área de un círculo con radio
se
y la función para el volumen de una esfera con radio
se
Ambas son ejemplos de funciones potencia porque constan de un coeficiente,
o
multiplicado por una variable
elevado a una potencia.
### Identificar el comportamiento final de las funciones potencia
La muestra los gráficos de
y
que son todas funciones potencia con números pares y enteros. Observe que estos gráficos tienen formas semejantes, muy parecidas a la de la función cuadrática en la caja de herramientas. Sin embargo, a medida que se incrementa la potencia, los gráficos se aplanan un poco cerca del origen y se vuelven más pronunciados lejos del mismo.
Para describir el comportamiento a medida que aumentan los números, utilizamos la idea del infinito. Utilizamos el símbolo
para el infinito positivo y
para el infinito negativo. Cuando decimos que "
se acerca al infinito", que puede escribirse simbólicamente como
describimos un comportamiento; decimos que
aumenta sin límites.
Con la función potencia par, a medida que la entrada aumenta o disminuye sin límite, los valores de salida se convierten en números positivos muy grandes. Por equivalencia, podríamos describir este comportamiento al afirmar que, a medida que
se acerca al infinito positivo o negativo, los valores
aumentan sin límite. En forma simbólica, podríamos escribir
La muestra los gráficos de
que son todas funciones potencia con potencias de números impares y enteros. Observe que estos gráficos son semejantes a los de la función cúbica en la caja de herramientas. De nuevo, a medida que aumenta la potencia, los gráficos se aplanan cerca del origen y se vuelven más pronunciados lejos del mismo.
Estos ejemplos ilustran que las funciones de la forma
revelan simetría de un tipo u otro. En primer lugar, en la observamos que incluso las funciones de la forma
son simétricas con respecto al eje
. En la observamos que las funciones impares de la forma
son simétricas respecto al origen.
En estas funciones potencia con números impares, a medida que
se acerca al infinito negativo,
disminuye sin límites. A medida que
se acerca al infinito positivo,
aumenta sin límites. En forma simbólica escribimos
El comportamiento del gráfico de una función a medida que los valores de entrada disminuyen (
) y aumentan mucho (
) se denomina comportamiento final de la función. Podemos utilizar palabras o símbolos para describir el comportamiento final.
La muestra el comportamiento final de las funciones de potencia en la forma
donde
es un número entero no negativo que depende de la potencia y de la constante.
### Identificar funciones polinómicas
Un oleoducto estalla en el golfo de México, lo que provoca un derrame de petróleo aproximadamente circular. La mancha tiene actualmente un radio de 24 millas, pero ese radio aumenta 8 millas cada semana. Queremos escribir una fórmula para la superficie cubierta por el derrame de petróleo al combinar dos funciones. El radio
del derrame de petróleo depende del número de semanas
que han pasado. Esta relación es lineal.
Podemos combinar esto con la fórmula del área
de un círculo.
Al componer estas funciones se obtiene una fórmula para el área en términos de semanas.
Multiplicando se obtiene la fórmula.
Esta fórmula es un ejemplo de función polinómica. Una función polinómica se compone de cero o de la suma de un número finito de términos distintos de cero, cada uno de los cuales es el producto de un número, llamado coeficiente del término, y una variable elevada a la potencia de un número entero no negativo.
### Identificar el grado y el coeficiente principal de una función polinómica
Debido a la forma de una función polinómica, podemos ver una variedad infinita en el número de términos y la potencia de la variable. Aunque el orden de los términos de la función polinómica no es importante para realizar las operaciones, solemos ordenar los términos en orden descendente de potencia o en forma general. El grado del polinomio es la potencia más elevada de la variable que aparece en el polinomio; es la potencia de la primera variable si la función tiene forma general. El término principal es aquel que contiene la potencia más elevada de la variable o el término del grado más alto. El coeficiente principal es el coeficiente del término principal.
### Identificar el comportamiento final de las funciones polinómicas
Conocer el grado de una función polinómica nos sirve para predecir su comportamiento final. Para determinar su comportamiento final, preste atención al término principal de la función polinómica. Dado que la potencia del término principal es la más alta, ese término crecerá mucho más rápido que los demás términos, a medida que
aumenta o disminuye mucho, por lo que su comportamiento dominará el gráfico. En cualquier polinomio, su comportamiento final coincidirá con el del término del grado más alto. Vea el .
### Identificar el comportamiento local de las funciones polinómicas
Además del comportamiento final de las funciones polinómicas, también nos interesa lo que ocurre en el "medio" de la función. En particular, nos interesan los lugares donde cambia el comportamiento del gráfico. El punto de inflexión es aquel donde los valores de la función pasan de ser crecientes a decrecientes o de decrecientes a crecientes.
También nos interesan las intersecciones. Al igual que en todas las funciones, la intersección en y es el punto en el que el gráfico se cruza con el eje vertical. El punto corresponde al par de coordenadas donde el valor de entrada es cero. Ya que el polinomio es una función, solo un valor de salida corresponde a cada valor de entrada, por lo que únicamente puede haber una intersección en y
Las intersecciones en x se producen en los valores de entrada que corresponden a un valor de salida de cero. Puede haber más de una intersección en x. Vea la .
### Comparar gráficos suaves y continuos
El grado de una función polinómica nos permite determinar el número de intersecciones en
y el número de puntos de inflexión. Una función polinómica de grado
es el producto de
factores, por lo que tendrá como máximo
raíces o ceros, o bien intersecciones en
. El gráfico de la función polinómica de grado
deberá tener como máximo
puntos de inflexión. Esto significa que el gráfico tiene como máximo un punto de inflexión menos que el grado del polinomio o uno menos que el número de factores.
La función continua no tiene interrupciones en su gráfico, el cual puede dibujarse sin levantar el bolígrafo del papel. La curva suave es un gráfico que no tiene aristas. Los puntos de inflexión de un gráfico suave deberán producirse siempre en curvas redondeadas. Los gráficos de las funciones polinómicas son continuos y suaves.
### Ecuaciones clave
### Conceptos clave
1. La función potencia es una base variable elevada a una potencia numérica. Vea el .
2. El comportamiento de un gráfico cuando la entrada disminuye más allá del límite y aumenta más allá del límite se denomina comportamiento final.
3. El comportamiento final depende de que la potencia sea par o impar. Vea el y el .
4. La función polinómica es la suma de términos, cada uno de los cuales consiste en una función potencia transformada con número entero positivo. Vea el .
5. El grado de una función polinómica es la potencia más elevada de la variable que aparece en un polinomio. El término que contiene la potencia más elevada de la variable se denomina término principal. El coeficiente del término principal se denomina coeficiente principal. Vea el .
6. El comportamiento final de una función polinómica es el mismo que el de la función potencia representada por el término principal de la función. Vea el y el .
7. Un polinomio de grado
tendrá como máximo
intersecciones en x y a lo sumo
puntos de inflexión. Vea el , el , el , el y el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, identifique la función como función potencia, función polinómica o ninguna de las dos.
En los siguientes ejercicios, halle el grado y el coeficiente principal del polinomio dado.
En los siguientes ejercicios, determine el comportamiento final de las funciones.
En los siguientes ejercicios, halle las intersecciones de las funciones.
### Gráficos
En los siguientes ejercicios, determine el menor grado posible de la función polinómica indicada.
En los siguientes ejercicios, determine si el gráfico de la función proporcionada es la de una función polinómica. Si es así, determine el número de puntos de inflexión y el menor grado posible para la función.
### Numéricos
En los siguientes ejercicios, construya una tabla para confirmar el comportamiento final de la función.
### En tecnología
En los siguientes ejercicios, grafique las funciones polinómicas con la ayuda de la calculadora. A partir del gráfico, determine las intersecciones y el comportamiento final.
### Extensiones
En los siguientes ejercicios, disponga de la información acerca del gráfico de una función polinómica para determinar la función. Supongamos que el coeficiente principal es 1 o -1. Puede haber más de una respuesta correcta.
### Aplicaciones en el mundo real
En los siguientes ejercicios, utilice los enunciados escritos para construir una función polinómica que represente la información requerida. |
# Funciones polinómicas y racionales
## Gráfico de funciones polinómicas
Los ingresos en millones de dólares desde 2006 hasta 2013 de una empresa de cable ficticia se muestran en la .
Los ingresos pueden modelarse con la función polinómica
donde
representa los ingresos en millones de dólares y
representa el año, con
correspondiente a 2006. ¿En qué intervalos aumentan los ingresos de la empresa? ¿En qué intervalos disminuyen los ingresos de la empresa? Estas preguntas, junto con muchas otras, pueden responderse al examinar el gráfico de la función polinómica. Ya hemos explorado el comportamiento local de las cuadráticas, que es un caso especial de los polinomios. En esta sección exploraremos el comportamiento local de los polinomios en general.
### Reconocer las características de los gráficos de las funciones polinómicas
Las funciones polinómicas de grado 2 o más constan de gráficos que no tienen ángulos agudos; recuerde que estos gráficos se denominan curvas fluidas. Las funciones polinómicas también muestran gráficos que no tienen cortes. Las curvas sin cortes se denominan continuas. La muestra un gráfico que representa una función polinómica y un gráfico que representa una función que no es un polinomio.
### Usar la factorización para hallar los ceros de las funciones polinómicas
Recordemos que si
es una función polinómica, los valores de
en el que
se llaman ceros de
Si la ecuación de la función polinómica se puede factorizar, podemos poner cada factor igual a cero y resolver los ceros.
Podemos utilizar este método para hallar las intersecciones en
porque en las intersecciones en
hallamos los valores de entrada cuando el valor de salida es cero. En los polinomios generales, esto puede ser un desafío. Mientras que las cuadráticas pueden resolverse mediante la fórmula cuadrática, relativamente sencilla, las fórmulas correspondientes para los polinomios cúbicos y de cuarto grado no son tan sencillas de recordar, y no existen fórmulas para los polinomios generales de grado superior. En consecuencia, en esta sección nos limitaremos a tres casos:
1. El polinomio se puede factorizar con métodos conocidos: máximo común divisor y factorización de trinomios.
2. El polinomio se da en forma factorizada.
3. La tecnología se utiliza para determinar las intersecciones.
### Identificar los ceros y sus multiplicidades
Los gráficos se comportan de manera diferente en diversas intersecciones en
. A veces, el gráfico cruza el eje horizontal en una intersección. Otras veces, el gráfico toca el eje horizontal y rebota.
Supongamos, por ejemplo, que graficamos la función
Observe que en la el comportamiento de la función en cada una de las intersecciones en
es diferente.
La intersección en
es la solución de la ecuación
El gráfico pasa directamente por la intersección en
en
El factor es lineal (tiene un grado de 1), por lo que el comportamiento cerca de la intersección es como el de una línea: pasa directamente por la intersección. Llamamos a esto un solo cero porque el cero corresponde a un solo factor de la función.
La intersección en
es la solución repetida de la ecuación
El gráfico toca el eje en la intersección y cambia de dirección. El factor es cuadrático (grado 2), por lo que el comportamiento cerca de la intersección es como el de un cuadrático: rebota del eje horizontal en la intersección.
El factor se repite, es decir, el factor
aparece dos veces. El número de veces que aparece un factor determinado en la forma factorizada de la ecuación de un polinomio se denomina multiplicidad. El cero asociado a este factor,
tiene multiplicidad 2 porque el factor
ocurre dos veces.
La intersección en
es la solución repetida del factor
El gráfico pasa por el eje en la intersección, pero se aplana un poco primero. Este factor es cúbico (grado 3), por lo que el comportamiento cerca de la intersección es como el de una cúbica, con la misma forma de S cerca de la intersección que la función de la caja de herramientas
A esto lo denominamos triple cero, o un cero con multiplicidad 3.
En los ceros con multiplicidades pares, los gráficos tocan o son tangentes al eje
. En los ceros con multiplicidades impares, los gráficos cruzan o se intersecan con el eje
. Consulte en la ejemplos de gráficos de funciones polinómicas con multiplicidad 1, 2 y 3.
Para potencias pares más altas, como 4, 6 y 8, el gráfico seguirá tocando y rebotando en el eje horizontal. Sin embargo, por cada potencia par creciente, el gráfico aparecerá más plano a medida que se acerque y abandone el eje
.
En las potencias impares más altas, como 5, 7 y 9, el gráfico seguirá cruzando el eje horizontal. Sin embargo, por cada potencia impar creciente, el gráfico aparecerá más plano a medida que se acerque y abandone el eje
.
### Determinar el comportamiento final
Como ya hemos aprendido, el comportamiento del gráfico de una función polinómica de la forma
al final sube o baja en la medida en que
aumenta sin límites, y sube o bajar a medida que
disminuye sin límites. Esto se debe a que, en el caso de las entradas muy grandes, por ejemplo 100 o 1.000, el término principal domina el tamaño de la salida. Lo mismo ocurre con entradas muy pequeñas, por ejemplo -100 o -1.000.
Recordemos que llamamos a este comportamiento el comportamiento final de una función. Como señalamos al hablar de las ecuaciones cuadráticas, cuando el término principal de una función polinómica,
es una función potencia par, a medida que
aumenta o disminuye sin límites,
aumenta sin límites. Cuando el término principal es una función potencia impar, a medida que
disminuye sin límites,
también disminuye sin límite; a medida que
aumenta sin límites,
también aumenta sin límites. Si el término principal es negativo, cambia la dirección del comportamiento final. La resume los cuatro casos.
### Comprender la relación entre el grado y los puntos de inflexión
Además del comportamiento final, recordemos que podemos analizar el comportamiento local de una función polinómica. Puede tener un punto de inflexión en el que el gráfico pasa de ser creciente a ser decreciente (de aumento a disminución) o de decreciente a creciente (de disminución a aumento). Observe el gráfico de la función polinómica
en la . El gráfico tiene tres puntos de inflexión.
Esta función
es una función polinómica de 4.º grado y tiene 3 puntos de inflexión. El número máximo de puntos de inflexión de una función polinómica es siempre uno menos que el grado de la función.
### Graficar funciones polinómicas
Podemos utilizar lo que hemos aprendido acerca de las multiplicidades, el comportamiento final y los puntos de inflexión para trazar gráficos de funciones polinómicas. Pongamos todo esto en orden y veamos los pasos necesarios para graficar funciones polinómicas.
### Usar el teorema del valor intermedio
En algunas situaciones, podemos conocer dos puntos de un gráfico, pero no los ceros. Si esos dos puntos están en lados opuestos del eje x, podemos confirmar que hay un cero entre ellos. Consideremos una función polinómica
cuyo gráfico es fluido y continuo. El teorema del valor intermedio establece que para dos números
y
en el dominio de
si
y
entonces la función
adopta cualquier valor entre
y
Podemos aplicar este teorema a un caso especial que sirva para graficar funciones polinómicas. Si un punto del gráfico de una función continua
en
se encuentra por encima del eje
y otro punto en
se encuentra por debajo del eje
, debe existir un tercer punto entre
y
donde el gráfico cruza el eje
. Llamemos a este punto
Esto significa que estamos seguros de que hay una solución
donde
En otras palabras, el teorema del valor intermedio nos señala que cuando una función polinómica pasa de un valor negativo a un valor positivo, la función deberá cruzar el eje
. La revela que hay un cero entre
y
### Escribir fórmulas para funciones polinómicas
Ahora que sabemos cómo hallar los ceros de las funciones polinómicas, podemos utilizarlos para escribir fórmulas basadas en los gráficos. Debido a que una función polinómica escrita en forma factorizada tendrá una intersección en
, donde cada factor es igual a cero, podemos formar una función que pase por un conjunto de intersecciones en
al introducir el correspondiente conjunto de factores.
### Usar los extremos locales y globales
Con las cuadráticas calculamos algebraicamente el valor máximo o mínimo de la función al hallar el vértice. En los polinomios generales, no es posible hallar estos puntos de inflexión sin técnicas más avanzadas de cálculo. Incluso entonces, hallar dónde se producen los extremos puede ser retador desde el punto de vista del álgebra. Por ahora, estimaremos las ubicaciones de los puntos de inflexión con la tecnología para generar un gráfico.
Cada punto de inflexión representa un mínimo o un máximo local. A veces, el punto de inflexión es el punto más alto o más bajo de todo el gráfico. En estos casos, decimos que el punto de inflexión es un máximo global o un mínimo global. También se denominan valores máximos y mínimos absolutos de la función.
### Conceptos clave
1. Las funciones polinómicas de grado 2 o más son fluidas y continuas. Vea el .
2. Para hallar los ceros de una función polinómica, si se puede, factorice la función y lleve a cero cada factor. Vea el , el y el .
3. Otra forma de hallar las intersecciones en
de una función polinómica es graficar la función e identificar los puntos en los que el gráfico cruza el eje
. Vea el .
4. La multiplicidad de un cero determina cómo se comporta el gráfico en las intersecciones en
. Vea el .
5. El gráfico de un polinomio cruza el eje horizontal en un cero con multiplicidad impar.
6. El gráfico de un polinomio toca el eje horizontal en un cero con multiplicidad par.
7. El comportamiento final de la función polinómica depende del término principal.
8. El gráfico de una función polinómica cambia de dirección en sus puntos de inflexión.
9. Una función polinómica de grado
tiene como máximo
puntos de inflexión. Vea el .
10. Para graficar funciones polinómicas, halle los ceros y sus multiplicidades, determine el comportamiento final y verifique que el gráfico final tenga como máximo
puntos de inflexión. Vea el y el .
11. Graficar una función polinómica ayuda a estimar los extremos locales y globales. Vea el .
12. El teorema del valor intermedio nos indica que, si
tienen signos opuestos, entonces existe al menos un valor
entre
y
para los cuales
Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, halle las intersecciones en
o las intersecciones en tde las funciones polinómicas.
En los siguientes ejercicios, utilice el teorema del valor intermedio para confirmar que el polinomio dado tiene al menos un cero dentro del intervalo dado.
En los siguientes ejercicios, halle los ceros y dé la multiplicidad de cada uno.
### Gráficos
En los siguientes ejercicios, grafique las funciones polinómicas. Tome nota de las intersecciones en
y en
, la multiplicidad y el comportamiento final.
En los siguientes ejercicios, utilice los gráficos para escribir la fórmula de una función polinómica de grado mínimo.
En los siguientes ejercicios, utilice el gráfico para identificar los ceros y la multiplicidad.
En los siguientes ejercicios, disponga de la información dada acerca del gráfico del polinomio para escribir la ecuación.
### En tecnología
En los siguientes ejercicios, utilice una calculadora para estimar los mínimos y máximos locales o el mínimo y el máximo global.
### Extensiones
En los siguientes ejercicios, utilice los gráficos para escribir una función polinómica de grado mínimo.
### Aplicaciones en el mundo real
En los siguientes ejercicios, escriba la función polinómica que modele la situación dada. |
# Funciones polinómicas y racionales
## Dividir polinomios
El exterior del Monumento a Lincoln en Washington, D.C., es un gran sólido rectangular con 61,5 metros (m) de largo, 40 m de ancho y 30 m de alto.Servicio de Parques Nacionales. "Estadísticas del edificio Monumento a Lincoln". http://www.nps.gov/linc/historyculture/lincoln-memorial-building-statistics.htm. Consultado el 3 de abril de 2014 Podemos calcular fácilmente el volumen con la geometría elemental.
Así que el volumen es de 73.800 metros cúbicos
Supongamos que conocemos el volumen, la longitud y la anchura. Podríamos dividir para determinar la altura.
Por lo que podemos confirmar a partir de las dimensiones anteriores, la altura es de 30 m. Podemos utilizar métodos similares para dar con cualquiera de las dimensiones que faltan. También podemos utilizar el mismo método si alguna o todas las medidas contienen expresiones variables. Por ejemplo, supongamos que el volumen de un sólido rectangular viene dado por el polinomio
La longitud del sólido viene dada por
la anchura viene dada por
Para hallar la altura del sólido, podemos utilizar la división polinómica, que es el objetivo de esta sección.
### Usar la división larga para dividir polinomios
Conocemos el algoritmo de la división larga para la aritmética ordinaria. Comenzamos por dividir entre los dígitos del dividendo que tienen el mayor valor posicional. Dividimos, multiplicamos, restamos, incluimos el dígito en la siguiente posición de valor posicional y repetimos. Por ejemplo, dividamos 178 entre 3 mediante la división larga.
Otra forma de ver la solución es como la suma de las partes. Esto debería resultarle familiar, ya que es el mismo método que se utiliza para comprobar la división en la aritmética elemental.
Lo denominamos algoritmo de la división y lo analizaremos más formalmente después de ver un ejemplo.
La división de polinomios que contienen más de un término tiene similitudes con la división larga de números enteros. Podemos escribir el dividendo de un polinomio como el producto del divisor y el cociente sumado al restante. Los términos de la división polinómica corresponden a los dígitos (y valores posicionales) de la división de números enteros. Este método nos permite dividir dos polinomios. Por ejemplo, si dividimos
entre
mediante el algoritmo de la división larga, quedaría así:
Hemos calculado
o
Podemos identificar el dividendo, el divisor, el cociente y el restante.
Escribir el resultado de esta manera ilustra el algoritmo de la división.
### Usar la división sintética para dividir polinomios
Como hemos visto, la división larga de polinomios implica muchos pasos y puede resultar bastante engorrosa. La división sintética es un método abreviado de dividir polinomios para el caso especial de dividir entre un factor lineal cuyo coeficiente principal es 1.
Para ilustrar el proceso, recuerde el ejemplo al principio de la sección.
Divida
entre
con el algoritmo de la división larga.
La forma final del proceso lucía así:
Hay mucha repetición en la tabla. Si no escribimos las variables, sino que alineamos sus coeficientes en columnas bajo el signo de la división y además eliminamos los productos parciales, ya tenemos una versión simplificada de todo el problema.
La división sintética lleva esta simplificación incluso unos cuantos pasos más. Colapse la tabla al mover cada una de las filas hacia arriba para llenar los espacios vacíos. Además, en lugar de dividir entre 2, como haríamos en la división de números enteros, y luego multiplicar y restar el producto medio, cambiamos el signo del "divisor" a –2, multiplicamos y sumamos. El proceso se inicia con la reducción del coeficiente principal.
A continuación, lo multiplicamos por el "divisor" y sumamos, repitiendo este proceso columna a columna, hasta que no queden entradas. La fila inferior representa los coeficientes del cociente; la última entrada de la fila inferior es el restante. En este caso, el cociente es
y el restante es
El proceso se aclarará en el .
### Uso de la división polinómica para resolver problemas de aplicación
La división polinómica se utiliza para resolver una variedad de problemas de aplicación que implican expresiones de área y volumen. Al principio de esta sección hemos visto una aplicación. Ahora resolveremos ese problema en el siguiente ejemplo.
### Ecuaciones clave
### Conceptos clave
1. La división larga de polinomios se utiliza para dividir un polinomio entre cualquier polinomio de grado igual o inferior. Vea el y el .
2. El algoritmo de la división nos señala que un dividendo polinómico se puede escribir como el producto del divisor y el cociente sumado al restante.
3. La división sintética es un atajo que se utiliza para dividir un polinomio entre un binomio en la forma
Vea el , el y el .
4. La división polinómica se utiliza para resolver problemas de aplicación, como el área y el volumen. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, utilice la división larga. Especifique el cociente y el restante.
En los siguientes ejercicios, utilice la división sintética para calcular el cociente.
En los siguientes ejercicios, utilice la división sintética para determinar si la primera expresión es un factor de la segunda. Si es así, indique la factorización.
### Gráficos
En los siguientes ejercicios, utilice el gráfico del polinomio de tercer grado y un factor para escribir la forma factorizada del polinomio que se sugiere en el gráfico. El coeficiente principal es uno.
En los siguientes ejercicios, utilice la división sintética para calcular el cociente y el restante.
### En tecnología
En los siguientes ejercicios, utilice una calculadora con sistema de álgebra computacional (Computer Algebra Systems, CAS)) para responder las preguntas.
### Extensiones
En los siguientes ejercicios, utilice la división sintética para determinar el cociente que implica un número complejo.
### Aplicaciones en el mundo real
En los siguientes ejercicios, utilice la longitud y el área dadas de un rectángulo para expresar la anchura algebraicamente.
En los siguientes ejercicios, utilice el volumen dado de una caja y su longitud y anchura para expresar algebraicamente la altura.
En los siguientes ejercicios, utilice el volumen y el radio dados de un cilindro para expresar algebraicamente su altura. |
# Funciones polinómicas y racionales
## Ceros de funciones polinómicas
Una nueva panadería ofrece pasteles decorados de varios pisos para exponerlos y cortarlos en celebraciones de quinceañeras y bodas, así como pasteles en bandeja para servir a la mayoría de los invitados. La panadería quiere que el volumen de un pastel pequeño de bandeja sea de 351 pulgadas cúbicas. El pastel tiene forma de sólido rectangular. Quieren que la longitud del pastel sea diez centímetros más larga que la anchura y que la altura del pastel sea un tercio de la anchura. ¿Cuáles deben ser las dimensiones del molde?
Este problema se resuelve al escribir una función cúbica y resolver una ecuación cúbica para el volumen del pastel. En esta sección, abordaremos una variedad de herramientas para escribir funciones polinómicas y resolver ecuaciones polinómicas.
### Evaluar un polinomio con el teorema del resto
En la última sección, aprendimos a dividir polinomios. Ahora podemos utilizar la división de polinomios para evaluarlos con el teorema del resto. Si el polinomio se divide entre
el resto se puede hallar rápidamente si evaluamos la función polinómica en
es decir,
Repasemos la demostración del teorema.
Recordemos que el algoritmo de la división establece que, dado un dividendo polinómico
y un divisor polinómico distinto de cero
donde el grado de
es menor o igual que el grado de
existen polinomios únicos
y
tal que
Si el divisor,
es
esto asume la forma
Dado que el divisor
es lineal, el resto será una constante,
Si evaluamos esto para
tenemos
En otras palabras,
es el resto que se obtiene al dividir
entre
### Usar el teorema del factor para resolver una ecuación polinómica
El teorema del factor es otro teorema que nos permite analizar las ecuaciones polinómicas. Nos indica cómo se relacionan los ceros de un polinomio con los factores. Recordemos que el algoritmo de la división nos señala que
Si los valores de
es un cero, entonces el restante
es
y
o
Observe que, escrito en esta forma,
es un factor de
Podemos concluir que, si
es un cero de
entonces
es un factor de
Del mismo modo, si
es un factor de
entonces el restante del algoritmo de la división
es 0. Esto nos dice que
es un cero.
Este par de implicaciones constituye el teorema del factor. Como veremos más adelante, un polinomio de grado
en el sistema de números complejos tendrá
ceros. Podemos utilizar el teorema del factor para factorizar completamente un polinomio en el producto de
factores. Una vez que el polinomio se ha factorizado por completo, podemos determinar fácilmente los ceros.
### Usar el teorema del cero racional para hallar los ceros racionales
Otro uso del teorema del resto es probar si un número racional es un cero para un polinomio dado. No obstante, primero necesitamos un conjunto de números racionales para probar. El teorema del cero racional nos permite reducir el número de posibles ceros racionales mediante la relación de los factores del término constante y los factores del coeficiente principal del polinomio.
Consideremos una función cuadrática con dos ceros,
y
Según el teorema del factor, estos ceros tienen factores asociados. Supongamos que cada factor es igual a 0, y luego construyamos la función cuadrática original sin su factor de estiramiento.
Observe que dos de los factores del término constante, 6, son los dos numeradores de las raíces racionales originales: 2 y 3. Del mismo modo, dos de los factores del coeficiente principal, 20, son los dos denominadores de las raíces racionales originales: 5 y 4.
Podemos deducir que los numeradores de las raíces racionales serán siempre factores del término constante y los denominadores serán factores del coeficiente principal. Esta es la esencia del teorema del cero racional; es un medio para darnos un conjunto de posibles ceros racionales.
### Hallar los ceros de las funciones polinómicas
El teorema del cero racional nos permite reducir la lista de posibles ceros racionales de una función polinómica. Una vez hecho esto, podemos utilizar la división sintética repetidamente para determinar todos los ceros de una función polinómica.
### Usar el teorema fundamental del álgebra
Ahora que podemos hallar los ceros racionales de una función polinómica, veremos un teorema que aborda el número de ceros complejos de una función polinómica. El teorema fundamental del álgebra nos instruye que toda función polinómica tiene al menos un cero complejo. Este teorema constituye la base para la resolución de ecuaciones polinómicas.
Supongamos que
es una función polinómica de grado cuatro, y
El teorema fundamental del álgebra establece que existe al menos una solución compleja, llámese
Por el teorema del factor, podemos escribir
como producto de
y un cociente polinómico. Dado que
es lineal, el cociente polinómico será de grado tres. Ahora aplicamos el teorema fundamental del álgebra al cociente del polinomio de tercer grado. Tendrá al menos un cero complejo, llámese
Así que podemos escribir el cociente de polinomios como un producto de
y un nuevo cociente polinómico de grado dos. Continúe aplicando el teorema fundamental del álgebra hasta hallar todos los ceros. Serán cuatro y cada uno de ellos arrojará un factor de
### Usar el teorema de la factorización lineal para hallar polinomios con ceros dados
Una implicación vital del teorema fundamental del álgebra, como mencionamos anteriormente, es que una función polinómica de grado
tendrá
ceros en el conjunto de los números complejos, si permitimos las multiplicidades. Esto significa que podemos factorizar la función polinómica en
factores. El teorema de la factorización lineal nos señala que una función polinómica tendrá el mismo número de factores que su grado, y que cada factor estará en la forma
donde
es un número complejo.
Supongamos que
es una función polinómica con coeficientes reales, y supongamos que
es un cero de
Entonces, según el teorema del factor,
es un factor de
Para que
tenga coeficientes reales,
también deberá ser un factor de
Esto es así porque cualquier factor que no sea
cuando se multiplica por
dejará componentes imaginarios en el producto. Solo la multiplicación con pares conjugados eliminará las partes imaginarias y dará lugar a coeficientes reales. En otras palabras, si una función polinómica
con coeficientes reales tiene un cero complejo
entonces el conjugado complejo
también será un cero de
Esto se denomina el teorema del conjugado complejo.
### Usar la regla de los signos de Descartes
Existe una forma directa de determinar el número posible de ceros reales positivos y negativos de cualquier función polinómica. Si el polinomio se escribe en orden descendente, la regla de los signos de Descartes nos habla de una relación entre el número de cambios de signo en
y el número de ceros reales positivos. Por ejemplo, la función polinómica siguiente tiene un cambio de signo.
Esto nos indica que la función tendrá 1 cero real positivo.
Existe una relación similar entre el número de cambios de signo en
y el número de ceros reales negativos.
En este caso,
tiene 3 cambios de signo. Esto nos dice que
puede tener 3 o 1 ceros reales negativos.
### Resolver aplicaciones del mundo real
Ahora hemos introducido una variedad de herramientas para resolver ecuaciones polinómicas. Utilicemos estas herramientas para resolver el problema de la panadería al principio de la sección.
### Conceptos clave
1. Para hallar
determine el restante del polinomio
cuando se divide entre
Vea el .
2.
es un cero de
si y solo si
es un factor de
Vea el .
3. Cada cero racional de una función polinómica con coeficientes enteros será igual a un factor del término constante dividido entre un factor del coeficiente principal. Vea el y el .
4. Cuando el coeficiente principal es 1, los posibles ceros racionales son los factores del término constante.
5. La división sintética puede utilizarse para hallar los ceros de una función polinómica. Vea el .
6. Según el teorema fundamental, toda función polinómica tiene al menos un cero complejo. Vea el .
7. Toda función polinómica de grado superior a 0 tiene al menos un cero complejo.
8. Teniendo en cuenta las multiplicidades, una función polinómica tendrá el mismo número de factores que su grado. Cada factor tendrá la forma
donde
es un número complejo. Vea el .
9. El número de ceros reales positivos de una función polinómica es o bien el número de cambios de signo de la función o bien menor que el número de cambios de signo en un número entero par.
10. El número de ceros reales negativos de una función polinómica es el número de cambios de signo de
o menos que el número de cambios de signo por un número entero par. Vea el .
11. Las ecuaciones polinómicas modelan muchas situaciones en el mundo real. La resolución de las ecuaciones es más fácil de realizar mediante la división sintética. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, utilice el teorema del resto para hallar el restante.
En los siguientes ejercicios, utilice el teorema del factor para hallar todos los ceros reales de la función polinómica dada y un factor.
En los siguientes ejercicios, utilice el teorema del cero racional para hallar todos los ceros reales.
En los siguientes ejercicios, halle todas las soluciones complejas (reales y no reales).
### Gráficos
En los siguientes ejercicios, utilice la regla de Descartes para determinar el número posible de soluciones positivas y negativas. A continuación, trace un gráfico para confirmar cuál de esas posibilidades es la combinación real.
### Numéricos
En los siguientes ejercicios, enumere todos los posibles ceros racionales de las funciones.
### En tecnología
En los siguientes ejercicios, utilice la calculadora para graficar la función polinómica. A partir del gráfico, halle los ceros racionales. Todas las soluciones reales son racionales.
### Extensiones
En los siguientes ejercicios, construya una función polinómica del menor grado posible con la información dada.
### Aplicaciones en el mundo real
En los siguientes ejercicios, halle las dimensiones de la caja descrita.
En los siguientes ejercicios, halle las dimensiones del cilindro circular descrito. |
# Funciones polinómicas y racionales
## Funciones racionales
Supongamos que sabemos que el costo de fabricación de un producto depende del número de artículos,
producidos. Esto viene dado por la ecuación
Si queremos saber el costo promedio de producir
artículos, dividiríamos la función de costo entre el número de artículos,
La función de costo promedio, que arroja el costo promedio por artículo para
artículos producidos, es
Muchos otros problemas de aplicación requieren hallar un valor promedio de forma similar, para darnos variables en el denominador. Esta función, escrita sin ninguna variable en el denominador, contendrá una potencia entera negativa.
En las últimas secciones, hemos trabajado con funciones polinómicas, que son funciones con enteros no negativos para los exponentes. En esta sección, exploramos las funciones racionales, que tienen variables en el denominador.
### Usar la notación de flechas
Hemos visto los gráficos de la función recíproca básica y de la función recíproca al cuadrado a partir de nuestro estudio de las funciones de la caja de herramientas. Examine estos gráficos, como se muestra en la , y observe algunas de sus características.
Varios aspectos son evidentes si examinamos el gráfico de
1. En la rama izquierda del gráfico, la curva se acerca al eje x
2. A medida que el gráfico se acerca a
desde la izquierda, la curva desciende; sin embargo, a medida que nos acercamos a cero desde la derecha, la curva sube.
3. Finalmente, en la rama derecha del gráfico, las curvas se acercan al eje x
Para resumir, utilizamos la notación de flecha para mostrar que
o
se acerca a un valor determinado. Vea la .
### Comportamiento local de
Empecemos por ver la función recíproca,
No podemos dividir entre cero, lo que significa que la función es indefinida en
por lo que el cero no está en el dominio. A medida que los valores de entrada se acercan a cero desde el lado izquierdo (para convertirse en valores muy pequeños y negativos), los valores de la función disminuyen sin límite (en otras palabras, se acercan al infinito negativo). Podemos ver este comportamiento en la .
Escribimos en la notación de flechas
A medida que los valores de entrada se acercan a cero desde el lado derecho (para convertirse en valores positivos muy pequeños), los valores de la función aumentan sin límite (se acercan al infinito). Podemos ver este comportamiento en la .
Escribimos en la notación de flechas
Vea la .
Este comportamiento crea una asíntota vertical, que es una línea vertical a la que se acerca el gráfico, pero nunca cruza. En este caso, el gráfico se acerca a la línea vertical
a medida que la entrada se acerca a cero. Vea la .
### Comportamiento final de
Dado que los valores de
se acercan al infinito, los valores de la función se acercan a 0. Dado que los valores de
se acercan al infinito negativo, los valores de la función se acercan a 0. Vea la . Simbólicamente, mediante la notación de flechas
Con base en este comportamiento general y en el gráfico, vemos que la función se acerca a 0, pero nunca llega realmente a 0; parece que se nivela a medida que aumentan las entradas. Este comportamiento crea una asíntota horizontal, una línea horizontal a la que se acerca el gráfico a medida que la entrada aumenta o disminuye sin límite. En este caso, el gráfico se acerca a la línea horizontal
Vea la .
### Resolver problemas aplicados con funciones racionales
En el , hemos desplazado una función de la caja de herramientas de manera que la función
Este es un ejemplo de función racional. La función racional es aquella que se escribe como el cociente de dos funciones polinómicas. Muchos problemas del mundo real exigen que hallemos el cociente de dos funciones polinómicas. Los problemas que implican tasas y concentraciones a menudo implican funciones racionales.
### Hallar los dominios de las funciones racionales
La asíntota vertical representa un valor en el que una función racional es indefinida, por lo que ese valor no está en el dominio de la función. La función recíproca no puede tener valores en su dominio que hagan que el denominador sea igual a cero. En general, para hallar el dominio de la función racional, necesitamos determinar qué entradas provocarían la división entre cero.
### Identificar las asíntotas verticales de las funciones racionales
Al observar el gráfico de una función racional, podemos investigar su comportamiento local y ver fácilmente si hay asíntotas. Puede que incluso seamos capaces de calcular aproximadamente su ubicación. Sin embargo, incluso sin el gráfico, podemos determinar si una función racional dada tiene alguna asíntota y calcular su ubicación.
### Asíntotas verticales
Las asíntotas verticales de una función racional se hallan al examinar los factores del denominador que no son comunes a los factores del numerador. Las asíntotas verticales se producen en los ceros de dichos factores.
### Discontinuidades removibles
En ocasiones, un gráfico contiene un agujero: un único punto en el que el gráfico no está definido, indicado por un círculo abierto. Denominamos a tal agujero discontinuidad removible.
Por ejemplo, la función
puede reescribirse mediante la factorización del numerador y del denominador.
Observe que
es un factor común al numerador y al denominador. El cero de este factor,
es la ubicación de la discontinuidad removible. Observe también que
no es un factor ni en el numerador ni en el denominador. El cero de este factor,
es la asíntota vertical. Vea la .
### Identificar las asíntotas horizontales de las funciones racionales
Mientras que las asíntotas verticales describen el comportamiento de un gráfico cuando la salida es muy grande o muy pequeña, las asíntotas horizontales describen el comportamiento de un gráfico cuando la entrada es muy grande o muy pequeña. Recordemos que el comportamiento final de un polinomio reflejará el del término principal. Asimismo, el comportamiento final de la función racional reflejará el del cociente de los términos principales de las funciones del numerador y del denominador.
Hay tres resultados distintos al comprobar las asíntotas horizontales:
Caso 1: Si el grado del denominador > grado del numerador, existe una asíntota horizontal en
En este caso, el comportamiento final es
Esto nos indica que, a medida que las entradas aumentan o disminuyen sin límite, esta función se comportará de forma similar a la función
y las salidas se acercarán a cero, lo que dará lugar a una asíntota horizontal en
Vea la . Observe que este gráfico cruza la asíntota horizontal.
Caso 2: Si el grado del denominador < grado del numerador en uno, obtenemos una asíntota oblicua.
En este caso, el comportamiento final es
Esto nos indica que, a medida que las entradas aumentan o disminuyen sin límite, esta función se comportará de forma similar a la función
A medida que las entradas crezcan, las salidas crecerán y no se nivelarán, por lo que este gráfico no tiene asíntota horizontal. Sin embargo, el gráfico de
parece una línea diagonal, y dado que
se comportará de forma similar a
se aproximará a una línea cercana a
Esta línea es una asíntota oblicua.
Para hallar la ecuación de la asíntota oblicua, divida
El cociente es
y el restante es 2. La asíntota oblicua es el gráfico de la recta
Vea la .
Caso 3: Si el grado del denominador = grado del numerador, existe una asíntota horizontal en
donde
y
son los coeficientes principales de
como
por
En este caso, el comportamiento final es
Esto nos indica que, a medida que las entradas crezcan, esta función se comportará como la función
que es una línea horizontal. Dado que
lo que da lugar a una asíntota horizontal en
Vea la . Observe que este gráfico cruza la asíntota horizontal.
Observe que, mientras que el gráfico de una función racional nunca cruzará una asíntota vertical, el gráfico puede o no cruzar una asíntota horizontal u oblicua. Además, aunque el gráfico de una función racional puede tener muchas asíntotas verticales, el gráfico tendrá como mucho una asíntota horizontal (u oblicua).
Hay que tener en cuenta que, si el grado del numerador es mayor que el grado del denominador en más de uno, el comportamiento final del gráfico imitará el comportamiento de la fracción reducida de comportamiento final. Por ejemplo, si tuviéramos la función
con comportamiento final
el comportamiento final del gráfico sería semejante al de un polinomio par con coeficiente principal positivo.
### Graficar funciones racionales
En el , vemos que el numerador de la función racional revela las intersecciones en x del gráfico, mientras que el denominador revela las asíntotas verticales. Al igual que con los polinomios, los factores del numerador pueden tener potencias enteras mayores que uno. Afortunadamente, el efecto sobre la forma del gráfico en esas intersecciones es el mismo que vimos con los polinomios.
Las asíntotas verticales asociadas a los factores del denominador reflejarán una de las dos funciones recíprocas de la caja de herramientas. Cuando el grado del factor en el denominador es impar, la característica distintiva es que, a un lado de la asíntota vertical, el gráfico se dirige hacia el infinito positivo, mientras que, al otro lado, el gráfico se dirige hacia el infinito negativo. Vea la .
Cuando el grado del factor en el denominador es par, la característica distintiva es que el gráfico se dirige hacia el infinito positivo en ambos lados de la asíntota vertical o se dirige hacia el infinito negativo en ambos lados. Vea la .
Por ejemplo, el gráfico de
se muestra en la .
1. En la intersección en x
correspondiente al factor
del numerador, el gráfico rebota, en consonancia con la naturaleza cuadrática del factor.
2. En la intersección en x
correspondiente al factor
del numerador, el gráfico pasa por el eje, como cabría esperarse de un factor lineal.
3. En la asíntota vertical
correspondiente al factor
del denominador, el gráfico se dirige hacia el infinito positivo a ambos lados de la asíntota, lo que es compatible con el comportamiento de la función
4. En la asíntota vertical
correspondiente al factor
del denominador, el gráfico se dirige hacia el infinito positivo en el lado izquierdo de la asíntota y hacia el infinito negativo en el lado derecho.
### Escribir funciones racionales
Ahora que hemos analizado las ecuaciones de las funciones racionales y cómo se relacionan con un gráfico de la función, podemos utilizar la información dada por un gráfico para escribir la función. La función racional escrita en forma factorizada tendrá una intersección en x, donde cada factor del numerador es igual a cero. (Se produce una excepción en el caso de discontinuidad removible). En consecuencia, podemos formar el numerador de una función cuyo gráfico pase por un conjunto de intersecciones en x, al introducir el correspondiente conjunto de factores. Asimismo, dado que la función tendrá una asíntota vertical en la que cada factor del denominador es igual a cero, podemos formar un denominador que produzca las asíntotas verticales al introducir el correspondiente conjunto de factores.
### Ecuaciones clave
### Conceptos clave
1. Podemos utilizar la notación de flecha para describir el comportamiento local y el comportamiento final de las funciones de la caja de herramientas
y
Vea el .
2. Una función que se nivela en un valor horizontal tiene una asíntota horizontal. Una función puede tener más de una asíntota vertical. Vea el .
3. Los problemas de aplicación que implican tasas y concentraciones a menudo implican funciones racionales. Vea el .
4. El dominio de una función racional incluye todos los números reales excepto aquellos que hacen que igualan el denominador a cero. Vea el .
5. Las asíntotas verticales de una función racional se darán cuando el denominador de la función sea igual a cero y el numerador sea distinto a cero. Vea el .
6. Puede producirse una discontinuidad removible en el gráfico de una función racional si una entrada hace que tanto el numerador como el denominador sean cero. Vea el .
7. El comportamiento final de una función racional reflejará el de la relación de los términos principales de las funciones del numerador y del denominador. Vea el , el , el y el .
8. Grafique funciones racionales al hallar las intersecciones, el comportamiento en las intersecciones y las asíntotas, así como el comportamiento final. Vea el .
9. Si una función racional tiene intersecciones en x en
asíntotas verticales en
y ninguna
entonces la función se puede escribir de la forma
Vea el
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, halle el dominio de las funciones racionales.
En los siguientes ejercicios, halle el dominio, las asíntotas verticales y las asíntotas horizontales de las funciones.
En los siguientes ejercicios, halle las intersecciones en x y en y de las funciones.
En los siguientes ejercicios, describa el comportamiento local y final de las funciones.
En los siguientes ejercicios, halle la asíntota oblicua de las funciones.
### Gráficos
En los siguientes ejercicios, utilice la transformación dada para graficar la función. Observe las asíntotas verticales y horizontales.
En los siguientes ejercicios, halle las intersecciones horizontales, la intersección vertical, las asíntotas verticales y la asíntota horizontal u oblicua de las funciones. Dibuje un gráfico con esta información.
En los siguientes ejercicios, escriba una ecuación para una función racional con las características dadas.
En los siguientes ejercicios, utilice los gráficos para escribir una ecuación de la función.
### Numéricos
En los siguientes ejercicios, haga tablas que muestren el comportamiento de la función cerca de la asíntota vertical y que reflejen la asíntota horizontal
### En tecnología
En los siguientes ejercicios, utilice una calculadora para graficar
Utilice el gráfico para resolver
### Extensiones
En los siguientes ejercicios, identifique la discontinuidad removible.
### Aplicaciones en el mundo real
En los siguientes ejercicios, exprese una función racional que describa la situación.
En los siguientes ejercicios, utilice la función racional dada para responder la pregunta.
En los siguientes ejercicios, construya una función racional para resolver el problema. A continuación, utilice una calculadora para responder la pregunta. |
# Funciones polinómicas y racionales
## Inversas y funciones radicales
Los guardaparques y otros administradores de senderos pueden construir pilas de rocas, apilamientos u otros arreglos, normalmente llamados mojones, para marcar senderos u otros puntos de referencia (los guardaparques y los científicos medioambientales desaconsejan que los excursionistas hagan lo mismo, para evitar confusiones y preservar los hábitats de plantas y animales). Un mojón en forma de montículo de grava tiene forma de cono con una altura igual al doble del radio.
El volumen se calcula con una fórmula de geometría elemental.
Hemos escrito el volumen
en términos de radio
Sin embargo, en algunos casos, podemos empezar con el volumen y querer determinar el radio. Por ejemplo: Un cliente compra 100 pies cúbicos de grava para construir un montículo en forma de cono con una altura del doble del radio. ¿Cuáles son el radio y la altura del nuevo cono? Para responder esta pregunta, utilizamos la fórmula
Esta función es la inversa de la fórmula de
en términos de
En esta sección, exploraremos las inversas de las funciones polinómicas y racionales y, en particular, las funciones radicales que encontramos en el proceso.
### Hallar la inversa de una función polinómica
Dos funciones
y
son funciones inversas si para cada par de coordenadas en
existe un par de coordenadas correspondiente en la función inversa,
En otras palabras, los pares de coordenadas de las funciones inversas tienen la entrada y la salida intercambiadas.
Para que una función tenga una inversa, debe crear una función que sea biunívoca y que tendría una inversa.
Por ejemplo, supongamos que el Club de Sostenibilidad construye un colector de escorrentía con forma de artesa parabólica, como se ilustra en la . Podemos utilizar la información en la figura para hallar el área superficial en la artesa como función de la profundidad del agua.
Ya que será útil tener una ecuación para la forma de sección transversal parabólica, impondremos un sistema de coordenadas, donde
se mide horizontalmente, mientras que
se mide verticalmente, con el origen en el vértice de la parábola. Vea la .
A partir de esto hallamos una ecuación para la forma parabólica. Hemos situado el origen en el vértice de la parábola, por lo que sabemos que la ecuación tendrá la forma
Nuestra ecuación deberá pasar por el punto (6, 18), a partir del cual podemos resolver el factor de estiramiento
Nuestra sección transversal parabólica tiene la ecuación
Nos interesa el área superficial del agua, por lo que debemos determinar la anchura en la parte de arriba como función de la profundidad del agua. Para cualquier profundidad
la anchura vendrá dada por
así que tenemos que resolver la ecuación anterior para
y hallar la función inversa. Sin embargo, observe que la función original no es biunívoca, y de hecho, dada cualquier salida hay dos entradas que producen la misma salida: una positiva y otra negativa.
Para hallar una inversa, podemos restringir nuestra función original a un dominio limitado en el que sea biunívoca. En este caso, tiene sentido limitarse a los valores positivos de
. En este dominio, podemos hallar una inversa al resolver la variable de entrada:
Esto no es una función tal y como está escrita. Nos limitamos a los valores positivos de
, por lo que eliminamos la solución negativa, lo que arroja la función inversa que buscamos.
Dado que
es la distancia desde el centro de la parábola hasta cualquier lado, toda la anchura del agua en la parte superior será
La artesa tiene 3 pies (36 pulgadas) de largo, por lo que el área superficial será entonces:
Este ejemplo ilustra dos puntos importantes:
1. Al momento de hallar la inversa de una cuadrática, tenemos que limitarnos a un dominio en el que la función sea biunívoca.
2. La inversa de una función cuadrática es una función de raíz cuadrada. Ambas son funciones de la caja de herramientas y diferentes tipos de funciones de potencia.
Las funciones que implican raíces suelen llamarse funciones radicales. Aunque no es posible hallar la inversa de la mayoría de las funciones polinómicas, algunos polinomios básicos tienen inversa. Tales funciones se denominan funciones invertibles y utilizamos la notación
Advertencia:
no es lo mismo que el recíproco de la función
Este uso de "–1" está reservado para denotar funciones inversas. Para denotar el recíproco de una función
tendríamos que escribir
Una relación importante entre las funciones inversas es que se "deshacen" entre sí. Si los valores de
es la inversa de una función
entonces
es la inversa de la función
En otras palabras, lo que sea que la función
haga a
lo deshace, y viceversa. Más formalmente, escribimos
y
### Delimitar del dominio para calcular la inversa de una función polinómica
Hasta ahora, hemos hallado las inversas de las funciones cúbicas sin tener que restringir sus dominios. Sin embargo, como sabemos, no todos los polinomios cúbicos son biunívocos. Puede que el dominio en algunas funciones que no son biunívocas se restrinja para que sea biunívoco, pero únicamente con respecto a ese dominio. La función sobre el dominio restringido tendría entonces una función inversa. Dado que las funciones cuadráticas no biunívocas, debemos restringir su dominio para hallar sus inversas.
### Resolver aplicaciones de funciones radicales
Observe que las funciones de los ejemplos anteriores eran todas polinomios, y sus inversas eran funciones radicales. Si queremos hallar la inversa de una función radical, tendremos que restringir el dominio de la respuesta porque el rango de la función original es limitado.
###
Las funciones radicales son comunes en los modelos físicos, como vimos en la sección inicial. Ahora tenemos suficientes herramientas para poder resolver el problema planteado al principio de la sección.
### Determinar el dominio de una función radical compuesta con otras funciones
Cuando las funciones radicales se componen con otras funciones, puede complicarse la determinación del dominio.
### Hallar las inversas de las funciones racionales
Al igual que con la búsqueda de las inversas de las funciones cuadráticas, a veces es deseable hallar la inversa de una función racional, especialmente de las que son el cociente de las funciones lineales, como en las aplicaciones de concentración.
### Conceptos clave
1. La inversa de una función cuadrática es una función de raíz cuadrada.
2. Si los valores de
es la inversa de una función
entonces
es la inversa de la función
Vea el .
3. Aunque no es posible hallar la inversa de la mayoría de las funciones polinómicas, algunos polinomios básicos son invertibles. Vea el .
4. Para hallar la inversa de determinada función, debemos restringirla a un dominio en el que sea biunívoca. Vea el y el .
5. Cuando hallamos la inversa de una función radical, necesitamos una restricción en el dominio de la respuesta. Vea el y el .
6. Las funciones inversas y radicales se utilizan para resolver problemas de aplicación. Vea el y el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, halle la inversa de la función en el dominio dado.
En los siguientes ejercicios, calcule la inversa de las funciones.
En los siguientes ejercicios, calcule la inversa de las funciones.
### Gráficos
En los siguientes ejercicios, halle la inversa de la función y grafique tanto la función como su inversa.
En los siguientes ejercicios, utilice un gráfico para determinar el dominio de las funciones.
### En tecnología
En los siguientes ejercicios, utilice la calculadora para graficar la función. A continuación, indique tres puntos en el gráfico de la inversa con las coordenadas dadas de y.
### Extensiones
En los siguientes ejercicios, halle la inversa de las funciones con
números reales positivos.
### Aplicaciones en el mundo real
En los siguientes ejercicios, determine la función descrita y luego utilícela para responder la pregunta. |
# Funciones polinómicas y racionales
## Modelado mediante la variación
Un concesionario de automóviles usados acaba de ofrecer a su mejor candidata, Nicole, un cargo en ventas. El cargo ofrece una comisión del 16 % sobre sus ventas. Sus ganancias dependen del importe de sus ventas. Por ejemplo, si vende un vehículo por 4.600 dólares, ganará 736 dólares. Al considerar la oferta, tiene en cuenta el precio típico de los automóviles del concesionario, el mercado en general y cuántos puede esperar vender razonablemente. En esta sección, examinaremos las relaciones, como esta, entre las ganancias, las ventas y la tasa de comisión.
### Resolver problemas de variación directa
En el ejemplo anterior, las ganancias de Nicole se hallan al multiplicar sus ventas por su comisión. La fórmula
nos cuenta sus ganancias,
provienen del producto de 0,16, su comisión, y el precio de venta del vehículo. Si creamos una tabla, observamos que, a medida que aumenta el precio de venta, también aumentan las ganancias, lo que debería ser intuitivo. Vea la .
Observe que las ganancias son un múltiplo de las ventas. A medida que aumentan las ventas, las ganancias se incrementan de forma previsible. Duplicamos las ventas del vehículo de 4.600 a 9.200 dólares, y duplicamos las ganancias de 736 a 1.472 dólares. A medida que aumenta la entrada, la salida aumenta como un múltiplo de la entrada. La relación en la que una cantidad es una constante multiplicada por otra cantidad se denomina variación directa. Cada variable en este tipo de relación varía directamente con la otra.
La representa los datos de las posibles ganancias de Nicole. Decimos que las ganancias varían directamente con el precio de venta del automóvil. La fórmula
se utiliza para la variación directa. El valor
es una constante no nula mayor que cero y se denomina constante de variación. En este caso,
y
### Resolver problemas de variación inversa
La temperatura del agua en un océano varía inversamente a la profundidad del agua. Entre las profundidades de 250 pies y 500 pies, la fórmula
nos da la temperatura en grados Fahrenheit a una profundidad en pies bajo la superficie de la Tierra. Consideremos el Océano Atlántico, que cubre el 22 % de la superficie de la Tierra. En un lugar determinado, a una profundidad de 500 pies, la temperatura puede ser de 28 °F.
Si creamos la , observamos que, a medida que aumenta la profundidad, la temperatura del agua disminuye.
Observamos en la relación entre estas variables que, a medida que una cantidad aumenta, la otra disminuye. Se dice que las dos cantidades son inversamente proporcionales y que cada término varía inversamente con el otro. Las relaciones inversamente proporcionales también se denominan variaciones inversas.
Para nuestro ejemplo, la representa la variación inversa. Decimos que la temperatura del agua varía inversamente a la profundidad del agua porque, a medida que la profundidad aumenta, la temperatura disminuye. La fórmula
para la variación inversa en este caso utiliza
### Resolver problemas que implican una variación conjunta
Muchas situaciones son más complicadas que un modelo básico de variación directa o de variación inversa. Una variable suele depender de varias otras variables. Cuando una variable depende del producto o cociente de dos o más variables, se denomina variación conjunta. Por ejemplo, el costo del transporte en autobús de los alumnos por cada viaje escolar varía en función del número de alumnos que asisten y de la distancia de la escuela. La variable
costo, varía junto con el número de estudiantes,
y la distancia,
### Ecuaciones clave
### Conceptos clave
1. La relación en la que una cantidad es una constante multiplicada por otra cantidad se denomina variación directa. Vea el .
2. Dos variables que son directamente proporcionales entre sí tendrán una relación constante.
3. La relación en la que una cantidad es una constante dividida entre otra cantidad se denomina variación inversa. Vea el .
4. Dos variables que son inversamente proporcionales entre sí tendrán un múltiplo constante. Vea el .
5. En muchos problemas, la variable varía directa o inversamente con múltiples variables. Este tipo de relación recibe el nombre de variación conjunta. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, escriba una ecuación que describa la relación de las variables dadas.
### Numéricos
En los siguientes ejercicios, utilice la información dada para determinar el valor desconocido.
### En tecnología
En los siguientes ejercicios, utilice la calculadora para graficar la ecuación implícita en la variación dada.
### Extensiones
En los siguientes ejercicios, utilice la ley de Kepler, que establece que el cuadrado del tiempo,
que se necesita para que un planeta orbite alrededor del Sol varía directamente con el cubo de la distancia media,
que el planeta es del Sol.
### Aplicaciones en el mundo real
En los siguientes ejercicios, utilice la información dada para responder las preguntas.
### Ejercicios de repaso del capítulo
Ha llegado al final del capítulo 3: Funciones polinómicas y racionales. Repasemos algunos de los términos, conceptos y ecuaciones clave que aprendió.
### Números complejos
Realice la operación indicada con números complejos.
Resuelva las siguientes ecuaciones sobre el sistema de números complejos.
### Funciones cuadráticas
En los siguientes ejercicios, escriba la función cuadrática en forma estándar. A continuación, dé los vértices y las intersecciones de los ejes. Por último, grafique la función.
En los siguientes problemas, halle la ecuación de la función cuadrática con la información dada.
Responda las siguientes preguntas.
### Funciones de potencia y funciones polinómicas
En los siguientes ejercicios, determine si la función es polinómica y, de ser así, dé el grado y el coeficiente principal.
En los siguientes ejercicios, determine el comportamiento final de la función polinómica.
### Gráfico de funciones polinómicas
En los siguientes ejercicios, halle todos los ceros de la función polinómica; tome nota de las multiplicidades.
En los siguientes ejercicios, a partir del gráfico dado, determine los ceros de la función y tome nota de la multiplicidad.
### Dividir polinomios
En los siguientes ejercicios, utilice la división larga para hallar el cociente y el restante.
En los siguientes ejercicios, utilice la división sintética para calcular el cociente. Si el divisor es un factor, entonces escriba la forma factorizada.
### Ceros de funciones polinómicas
En los siguientes ejercicios, utilice el teorema del cero racional para resolver la ecuación polinómica.
En los siguientes ejercicios, utilice la regla de los signos de Descartes para calcular el número posible de soluciones positivas y negativas.
### Funciones racionales
En las siguientes funciones racionales, halle las intersecciones y las asíntotas verticales y horizontales, y luego úsales para trazar un gráfico.
En los siguientes ejercicios, halle la asíntota oblicua.
### Funciones inversas y radicales
En los siguientes ejercicios, halle la inversa de la función con el dominio dado.
### Modelado mediante la variación
En los siguientes ejercicios, calcule el valor de la incógnita.
En los siguientes ejercicios, resuelva el problema de aplicación.
### Examen del capítulo
Realice la operación indicada o resuelva la ecuación.
Diga el grado y el coeficiente principal de la siguiente función polinómica.
Determine el comportamiento final de la función polinómica.
Escriba la función cuadrática en forma estándar. Determine el vértice y las intersecciones de los ejes y grafique la función.
Dada la información acerca del gráfico de una función cuadrática, halle su ecuación.
Resuelva el siguiente problema de aplicación.
Halle todos los ceros de las siguientes funciones polinómicas; tome nota de las multiplicidades.
A partir del gráfico, determine los ceros de la función y las multiplicidades.
Utilice la división larga para hallar el cociente.
Utilice la división sintética para hallar el cociente. Si el divisor es un factor, escriba la forma factorizada.
Utilice el teorema del cero racional para hallar los ceros de las funciones polinómicas.
Dada la siguiente información en torno a una función polinómica, halle la función.
Utilice la regla de los signos de Descartes para determinar el número posible de soluciones positivas y negativas.
En las siguientes funciones racionales, halle las intersecciones y las asíntotas horizontales y verticales, y trace un gráfico.
Halle la asíntota oblicua de la función racional.
Halle la inversa de la función.
Calcule el valor de la incógnita.
Resuelva el siguiente problema de aplicación. |
# Funciones exponenciales y logarítmicas
## Introducción
Concéntrese en un centímetro cuadrado de su piel. Mire más de cerca. Más cerca aún. Si se pudiera mirar con suficiente atención, se verían cientos de miles de organismos microscópicos. Son bacterias, y no solo están en la piel, sino también en la boca, en la nariz y hasta en los intestinos. De hecho, las células bacterianas en su cuerpo superan a sus propias células en cualquier momento. Sin embargo, eso no es motivo para sentirse mal consigo mismo. Aunque algunas bacterias pueden causar enfermedades, muchas son saludables y hasta esenciales para el organismo.
Las bacterias se reproducen en un proceso denominado fisión binaria, durante el cual una célula bacteriana se divide en dos. Cuando las condiciones son adecuadas, las bacterias se reproducen muy rápidamente. A diferencia de los humanos y otros organismos complejos, el tiempo necesario para formar una nueva generación de bacterias suele ser cuestión de minutos u horas, en lugar de días o años.Todar, PhD, Kenneth. Todar's Online Textbook of Bacteriology. http://textbookofbacteriology.net/growth_3.html.
Para simplificar, supongamos que empezamos con un cultivo de una célula bacteriana que se divide cada hora. La muestra el número de células bacterianas al final de cada hora. Vemos que la única célula bacteriana da lugar a ¡más de mil células bacterianas en solo diez horas! Si extrapolamos la tabla a veinticuatro horas, ¡tendríamos más de 16 millones!
En este capítulo, exploraremos las funciones exponenciales, que se utilizan, entre otros aspectos, para modelar patrones de crecimiento como los que se encuentran en las bacterias. También investigaremos las funciones logarítmicas, que guardan estrecha relación con las funciones exponenciales. Ambos tipos de funciones tienen numerosas aplicaciones en el mundo real a la hora de modelar e interpretar datos. |
# Funciones exponenciales y logarítmicas
## Funciones exponenciales
### Objetivos de aprendizaje
1. Hallar el valor de una función (exponencial). (IA 3.5.3)
2. Graficar las funciones exponenciales. (IA 10.2.1)
### Objetivo 1: Hallar el valor de una función (exponencial). (IA 3.5.3)
### La práctica hace la perfección
Halle el valor de una función exponencial.
### Objetivo 2: Graficar las funciones exponenciales. (IA 10.2.1)
### La práctica hace la perfección
Graficar las funciones exponenciales.
El número e, e ≈ 2,718281827, es como el número π en el sentido de que utilizamos un símbolo para representarlo porque su representación decimal nunca se detiene ni se repite. El número irracional e se denomina base natural o número de Euler en honor al matemático suizo Leonhard Euler.
La función exponencial cuya base es e, se denomina función exponencial natural.
### La práctica hace la perfección
La India es el segundo país más poblado del mundo, con unos
mil millones de habitantes en 2021. La población crece a un ritmo de aproximadamente
cada añohttp://www.worldometers.info/world-population/. Consultado el 24 de febrero de 2014.. Si este ritmo continúa, la población de la India superará a la de China en el año
Cuando las poblaciones crecen rápidamente, a menudo decimos que el crecimiento es "exponencial", lo que significa que algo asciende muy rápidamente. Sin embargo, para un matemático, el término crecimiento exponencial tiene un significado muy específico. En esta sección, echaremos un vistazo a las funciones exponenciales, que modelan este tipo de crecimiento rápido.
### Identificación de funciones exponenciales
Al explorar el crecimiento lineal, observamos una tasa de cambio constante: una cifra constante en la que la producción aumenta por cada incremento de unidad en la entrada. Por ejemplo, en la ecuación
la pendiente nos indica que la salida aumenta en 3 cada vez que la entrada aumenta en 1. El escenario del ejemplo de la población de la India es diferente porque tenemos un cambio porcentual por unidad de tiempo (en lugar de un cambio constante) en el número de personas.
### Definir una función exponencial
Un estudio reveló que el porcentaje de la población que es vegana en Estados Unidos se duplicó de 2009 a 2011. En 2011, el 2,5 % de la población era vegana, tras adherirse a una dieta que no incluye ningún producto de origen animal: sin carne, aves, pescado, lácteos ni huevos. Si este ritmo continúa, los veganos representarán el 10 % de la población estadounidense en 2015, el 40 % en 2019 y el 80 % en 2021.
¿Qué significa exactamente crecer exponencialmente? ¿Qué tiene en común la palabra doble con el porcentaje de aumento? La gente usa estas palabras erróneamente. ¿Se utilizan correctamente estas palabras? Ciertamente, las palabras aparecen con frecuencia en los medios de comunicación.
Para entender claramente el crecimiento exponencial, contrastémoslo con el crecimiento lineal. Construiremos dos funciones. La primera función es exponencial. Empezaremos con una entrada de 0 y aumentaremos cada entrada en 1. Duplicaremos las correspondientes salidas consecutivas. La segunda función es lineal. Empezaremos con una entrada de 0 y aumentaremos cada entrada en 1. Sumaremos 2 a las salidas consecutivas correspondientes. Vea la .
A partir de la , podemos deducir que, en lo que respecta a estas dos funciones, el crecimiento exponencial empequeñece al crecimiento lineal.
1. El crecimiento exponencial se refiere a que el valor original a partir del rango aumenta en el mismo porcentaje en incrementos iguales, hallados en el dominio.
2. El crecimiento lineal se refiere a que el valor original a partir del rango se incrementa en la misma cantidad en incrementos iguales, hallados en el dominio.
Aparentemente, la diferencia entre "el mismo porcentaje" y "la misma cantidad" es bastante significativa. En el caso del crecimiento exponencial, en incrementos iguales, la tasa de cambio multiplicativa constante daba como resultado la duplicación de la producción cada vez que la entrada aumentaba en uno. En el caso del crecimiento lineal, la tasa de cambio sumatoria constante sobre incrementos iguales daba como resultado la suma de 2 a la salida cada vez que la entrada se incrementaba en uno.
La forma general de la función exponencial es
donde
es cualquier número distinto a cero,
es un número real positivo, que no sea igual a 1.
1. Si los valores de
la función crece a un ritmo proporcional a su tamaño.
2. Si los valores de
la función decae a un ritmo proporcional a su tamaño.
Veamos la función
de nuestro ejemplo. Crearemos una tabla () para determinar las salidas correspondientes durante un intervalo en el dominio de
con
Examinemos el gráfico de
al trazar los pares ordenados que observamos en la tabla en la , y luego hagamos algunas observaciones.
Definamos el comportamiento del gráfico de la función exponencial
y destaquemos algunas de sus características principales.
1. el dominio es
2. el rango es
3. a medida que
4. a medida que
5.
es siempre creciente,
6. el gráfico de
nunca tocará el eje x porque la base dos elevada a cualquier exponente nunca tiene el resultado de cero.
7.
es la asíntota horizontal.
8. la intersección en y es 1.
### Evaluar funciones exponenciales
Recordemos que la base de la función exponencial debe ser un número real positivo, distinto a
¿Por qué limitamos la base
a valores positivos? Para garantizar que las salidas sean números reales. Observe lo que ocurre si la base no es positiva:
1. Supongamos que
y
Entonces
que no es un número real.
¿Por qué limitamos la base a valores positivos que no sean
Porque la base
da como resultado la función constante. Observe lo que ocurre si la base es
1. Supongamos que
Entonces
para cualquier valor de
Para evaluar una función exponencial con la forma
simplemente sustituimos
con el valor dado, y calculamos la potencia resultante. Por ejemplo:
Supongamos que
¿Qué es
Para evaluar una función exponencial con una forma distinta a la básica, es importante seguir el orden de las operaciones. Por ejemplo:
Supongamos que
¿Qué es
Observe que, de no seguirse el orden de las operaciones, el resultado sería incorrecto:
### Definir el crecimiento exponencial
Dado que el resultado de las funciones exponenciales aumenta muy rápidamente, el término "crecimiento exponencial" se utiliza a menudo en el lenguaje cotidiano para describir cualquier cosa que crezca o aumente rápidamente. Sin embargo, el crecimiento exponencial puede definirse con mayor precisión en un sentido matemático. Si la tasa de crecimiento es proporcional a la cantidad presente, la función modela un crecimiento exponencial.
En términos generales, tenemos una función exponencial, en la que una base constante se eleva a un exponente variable. Para diferenciar entre funciones lineales y exponenciales, consideremos dos empresas, A y B. La empresa A tiene 100 tiendas y se expande con la inauguración de 50 tiendas al año, por lo que su crecimiento puede representarse mediante la función
La empresa B tiene 100 tiendas y se expande al aumentar el número de tiendas en un 50 % cada año, por lo que su crecimiento puede representarse mediante la función
Algunos años de crecimiento de estas empresas se ilustran en la .
Los gráficos que comparan el número de tiendas de cada empresa en el lapso de cinco años se muestran en la . Podemos ver que, con el crecimiento exponencial, el número de tiendas aumenta mucho más rápidamente que con el crecimiento lineal.
Observe que el dominio de ambas funciones es
y el rango en ambas funciones es
Después del año 1, la empresa B siempre tiene más tiendas que la empresa A.
Ahora, nos centraremos en la función que representa el número de tiendas de la empresa B,
En esta función exponencial, 100 representa el número inicial de tiendas, 0,50 representa la tasa de crecimiento y
representa el factor de crecimiento. En términos más generales, podemos escribir esta función como
donde 100 es el valor inicial,
se denomina la base, y
se denomina el exponente.
### Hallar ecuaciones de funciones exponenciales
En los ejemplos anteriores, se nos dio una función exponencial, que luego evaluamos para una entrada dada. A veces nos dan información acerca de una función exponencial sin conocer la función explícitamente. Debemos utilizar la información para escribir primero la forma de la función y luego determinar las constantes
y
y evaluar la función.
### Aplicar la fórmula del interés compuesto
Los instrumentos de ahorro en los que las ganancias se reinvierten continuamente, como los fondos de inversión y las cuentas de jubilación, utilizan el interés compuesto. El término compuesto se refiere a los intereses devengados no solo sobre el valor original, sino sobre el valor acumulado de la cuenta.
La tasa anual equivalente (TAE) de una cuenta, también llamada tasa nominal, es el tipo de interés anual que devenga una cuenta de inversión. El término nominal se utiliza cuando la capitalización se produce un número de veces distinto de una vez al año. De hecho, cuando se capitalizan los intereses más de una vez al año, ¡el tipo de interés efectivo acaba siendo mayor que el nominal! Se trata de una poderosa herramienta para invertir.
Podemos calcular el interés compuesto con la fórmula del interés compuesto, que es una función exponencial de las variables tiempo
capital
TAE
y el número de periodos de capitalización en un año
Por ejemplo, observe la , que muestra el resultado de invertir 1.000 dólares al 10 % durante un año. Observe cómo el valor de la cuenta aumenta a medida que aumenta la frecuencia de la capitalización.
### Evaluar funciones con base e
Como hemos visto anteriormente, el importe ganado en una cuenta aumenta a medida que aumenta la frecuencia de capitalización. La muestra que el aumento de la capitalización anual a la semestral es mayor que el aumento de la mensual a la diaria. Esto podría llevarnos a preguntarnos si este patrón continuará.
Examine el valor de 1 dólar invertido al 100 % de interés durante 1 año, capitalizado a diversas frecuencias, que figuran en la .
Estos valores parecen acercarse a un límite a medida que
aumenta sin límites. De hecho, como
aumenta cada vez más, la expresión
se acerca a un número utilizado con tanta frecuencia en matemáticas que hasta tiene su propio nombre: la letra
Este valor es un número irracional, lo que significa que su expansión decimal se eterniza sin repetirse. A continuación, se muestra su aproximación con seis decimales.
### Investigar el crecimiento continuo
Hasta ahora hemos trabajado con bases racionales para funciones exponenciales. Sin embargo, en la mayoría de los fenómenos del mundo real, se utiliza e como base de las funciones exponenciales. Los modelos exponenciales que utilizan
como base se denominan modelos de crecimiento o decaimiento continuo. Vemos estos modelos en las finanzas, la informática y la mayoría de las ciencias, como la física, la toxicología y la dinámica de fluidos.
### Ecuaciones clave
### Conceptos clave
1. La función exponencial se define como aquella con una constante positiva distinta de
elevado a un exponente variable. Vea el .
2. Una función se evalúa al resolver en un valor específico. Vea el y el .
3. Se puede encontrar un modelo exponencial cuando se conocen la tasa de crecimiento y el valor inicial. Vea el .
4. Se puede encontrar un modelo exponencial cuando se conocen los dos puntos de datos del modelo. Vea el .
5. Se puede encontrar un modelo exponencial cuando se utilizan dos puntos de datos del gráfico del modelo. Vea el .
6. Se puede encontrar un modelo exponencial cuando se utilizan dos puntos de datos del gráfico y una calculadora. Vea el .
7. El valor de una cuenta en cualquier momento
puede calcularse mediante la fórmula del interés compuesto cuando se conocen el importe de capital, el tipo de interés anual y los periodos de capitalización. Vea el .
8. La inversión inicial de una cuenta puede hallarse con la fórmula del interés compuesto cuando se conocen el valor de la cuenta, el tipo de interés anual, los periodos de capitalización y la duración de la cuenta. Vea el .
9. El número
es una constante matemática que se utiliza a menudo como base de los modelos de crecimiento y decaimiento exponencial en el mundo real. Su aproximación decimal es
10. Las calculadoras científicas y gráficas tienen la clave
o
para calcular las potencias de
Vea el .
11. Los modelos de crecimiento o decaimiento continuo son modelos exponenciales que utilizan
como base. Los modelos de crecimiento y decaimiento continuo pueden encontrarse cuando se conocen el valor inicial y la tasa de crecimiento o decaimiento. Vea el y el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, identifique si el enunciado representa una función exponencial. Explique.
En los siguientes ejercicios, considere este escenario: Por cada año
la población de un bosque de árboles viene representada por la función
En un bosque vecino, la población del mismo tipo de árbol viene representada por la función
(Redondee las respuestas al número entero más cercano).
En los siguientes ejercicios, determine si la ecuación representa crecimiento exponencial, decaimiento exponencial o ninguno de los dos. Explique.
En los siguientes ejercicios, halle la fórmula de una función exponencial que pase por los dos puntos dados.
En los siguientes ejercicios, determine si la tabla puede representar una función lineal, exponencial o ninguna de las dos. Si resulta ser exponencial, halle una función que pase por los puntos.
En los siguientes ejercicios, utilice la fórmula del interés compuesto,
En los siguientes ejercicios, determine si la ecuación representa el crecimiento continuo, el decaimiento continuo o ninguno de los dos. Explique.
### Numéricos
En los siguientes ejercicios, evalúe cada función. Redondee las respuestas a cuatro decimales, si es necesario.
### En tecnología
En los siguientes ejercicios, utilice una calculadora gráfica para hallar la ecuación de una función exponencial dados los puntos en la curva.
### Extensiones
### Aplicaciones en el mundo real
|
# Funciones exponenciales y logarítmicas
## Gráficos de funciones exponenciales
### Objetivos de aprendizaje
1. Graficar funciones exponenciales (IA 10.2.1).
2. Graficar funciones (exponenciales) mediante transformaciones (CA 3.5.1-3.5.5).
### Objetivo 1: Graficar funciones exponenciales (IA 10.2.1).
### La práctica hace la perfección
### Objetivo 2: Graficar funciones (exponenciales) mediante transformaciones. (CA 3.5.1-3.5.5)
Desplazamientos verticales y horizontales: Dada una función , una nueva función donde es una constante, es un desplazamiento vertical de la función . Todos los valores de salida cambian en k unidades. Si k es positivo, el gráfico se desplazará hacia arriba. Si k es negativo, el gráfico se desplazará hacia abajo.
Dada una función , una nueva función , donde h es una constante, es un desplazamiento horizontal de la función . Si h es positivo, el gráfico se desplazará hacia la derecha. Si h es negativo, el gráfico se desplazará hacia la izquierda.
### La práctica hace la perfección
Graficar funciones (exponenciales) mediante transformaciones.
Como comentamos en la sección anterior, las funciones exponenciales se utilizan para muchas aplicaciones en el mundo real, como las finanzas, la medicina forense, la informática y la mayoría de las ciencias naturales. Trabajar con una ecuación que describe una situación en el mundo real nos brinda un método para hacer predicciones. Sin embargo, la mayoría de las veces la ecuación no es suficiente. Aprendemos mucho sobre las cosas al ver sus representaciones pictóricas, y es precisamente por tal motivo que graficar ecuaciones exponenciales es una herramienta poderosa. Nos da otra capa más de conocimiento para predecir acontecimientos futuros.
### Graficar funciones exponenciales
Antes de empezar a graficar, vale la pena repasar el comportamiento del crecimiento exponencial. Recordemos la tabla de valores de una función de la forma
cuya base es mayor que uno. Utilizaremos la función
Observe cómo cambian los valores de salida en la cuando la entrada aumenta en
Cada valor de salida es el producto de la salida anterior y la base,
Designamos la base
el cociente constante. De hecho, para cualquier función exponencial con la forma
es el cociente constante de la función. Esto significa que al aumentar la entrada en 1, el valor de la salida será el producto de la base y la salida anterior, independientemente del valor de
Observe en la tabla que
1. los valores de salida son positivos para todos los valores de
2. a medida que
aumenta, los valores de salida aumentan sin límite, y
3. a medida que
disminuye, los valores de salida se hacen más pequeños, para acercarse a cero.
La muestra la función de crecimiento exponencial
El dominio de
son todos números reales, el rango es
y la asíntota horizontal es
Para tener una idea del comportamiento del decaimiento exponencial, podemos crear una tabla de valores para una función de la forma
cuya base está entre cero y uno. Utilizaremos la función
Observe cómo cambian los valores de salida en la cuando la entrada aumenta en
De nuevo, debido a que la entrada se incrementa en 1, cada valor de salida es el producto de la salida anterior y la base, o la relación constante
Observe en la tabla que
1. los valores de salida son positivos para todos los valores de
2. a medida que
aumenta, los valores de salida se reducen, para acercarse a cero, y
3. a medida que
disminuye, los valores de salida crecen sin límite.
La muestra la función de decaimiento exponencial,
El dominio de
son todos números reales, el rango es
y la asíntota horizontal es
### Graficar transformaciones de funciones exponenciales
Las transformaciones de los gráficos exponenciales se comportan de forma similar a las de otras funciones. Al igual que con otras funciones matrices, podemos aplicar los cuatro tipos de transformaciones (desplazamiento, reflexión, estiramiento y compresión) a la función matriz
sin perder la forma. Por ejemplo, al igual que la función cuadrática mantiene su forma parabólica cuando se desplaza, refleja, estira o comprime, la función exponencial también mantiene su forma general, independientemente de las transformaciones aplicadas.
### Graficar un desplazamiento vertical
La primera transformación se produce cuando añadimos una constante
a la función matriz
que nos da un desplazamiento vertical de
unidades en la misma dirección que el signo. Por ejemplo, si empezamos por graficar una función matriz,
podemos entonces graficar dos desplazamientos verticales junto a ella, mediante
el desplazamiento hacia arriba,
y el desplazamiento hacia abajo,
Ambos desplazamientos verticales se muestran en la .
Observe los resultados del desplazamiento
verticalmente:
1. El dominio,
se mantiene sin cambios.
2. Cuando la función se desplaza hacia arriba
unidades a
3. Cuando la función se desplaza hacia abajo
unidades a
### Graficar un desplazamiento horizontal
La siguiente transformación se produce cuando añadimos una constante
a la entrada de la función matriz
lo que nos da un desplazamiento horizontal
unidades en la dirección opuesta al signo. Por ejemplo, si empezamos por graficar la función matriz
podemos entonces graficar dos desplazamientos horizontales junto a esta, mediante
el desplazamiento a la izquierda,
y el desplazamiento a la derecha,
Ambos desplazamientos horizontales se muestran en la .
Observe los resultados del desplazamiento
horizontalmente:
1. El dominio,
se mantiene sin cambios.
2. La asíntota,
se mantiene sin cambios.
3. La intersección en y se desplaza de tal manera que:
### Graficar un estiramiento o una compresión
Mientras que los desplazamientos horizontales y verticales implican la adición de constantes a la entrada o a la propia función, se produce estiramiento o compresión cuando multiplicamos la función matriz
por una constante
Por ejemplo, si empezamos por graficar la función matriz
podemos entonces graficar el estiramiento, mediante
para obtener
como se muestra a la izquierda en la , y la compresión, mediante
para obtener
como se muestra a la derecha en la .
### Graficar reflexiones
Además de desplazar, comprimir y estirar un gráfico, también podemos reflejarlo sobre el eje x o el eje y. Cuando multiplicamos la función matriz
entre
obtenemos una reflexión sobre el eje x. Cuando multiplicamos la entrada por
obtenemos una reflexión sobre el eje y. Por ejemplo, si empezamos por graficar la función matriz
podemos entonces graficar las dos reflexiones junto a esta. La reflexión sobre el eje x,
se muestra en el lado izquierdo de la , y la reflexión en torno al eje y
se muestra en el lado derecho de la .
### Resumir las traslaciones de la función exponencial
Ahora que hemos trabajado con cada tipo de traslación para la función exponencial, podemos resumirlas en la para llegar a la ecuación general de traslación de funciones exponenciales.
### Ecuaciones clave
### Conceptos clave
1. El gráfico de la función
tiene una intersección en y en
dominio
rango
y asíntota horizontal
Vea el .
2. Si los valores de
la función es creciente. La cola izquierda del gráfico se acercará a la asíntota
y la cola derecha aumentará sin límite.
3. Si los valores de
la función es decreciente. La cola izquierda del gráfico aumentará sin límite, y la cola derecha se acercará a la asíntota
4. La ecuación
representa el desplazamiento vertical de la función matriz
5. La ecuación
representa el desplazamiento horizontal de la función matriz
Vea el .
6. Las soluciones aproximadas de la ecuación
se pueden encontrar con una calculadora gráfica. Vea el .
7. La ecuación
donde
representa estiramiento vertical, si
o compresión, si
de la función matriz
Vea el .
8. Cuando la función matriz
se multiplica por
el resultado,
es una reflexión alrededor del eje x. Cuando la entrada se multiplica por
el resultado,
es una reflexión alrededor del eje y. Vea la .
9. Todas las traslaciones de la función exponencial se pueden resumir en la ecuación general
Vea la .
10. Utilizando la ecuación general
podemos escribir la ecuación de una función dada su descripción. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
### Gráficos
En los siguientes ejercicios, grafique la función y su reflexión alrededor del eje y en los mismos ejes, y obtenga la intersección en y.
En los siguientes ejercicios, grafique cada conjunto de funciones en los mismos ejes.
En los siguientes ejercicios, empareje cada función con una de los gráficos en la .
En los siguientes ejercicios, utilice los gráficos que se indican en la . Todos tienen la forma
En los siguientes ejercicios, grafique la función y su reflexión alrededor del eje x en los mismos ejes.
En los siguientes ejercicios, grafique la transformación de
Indique la asíntota horizontal, el dominio y el rango.
En los siguientes ejercicios, describa el comportamiento final de los gráficos de las funciones.
En los siguientes ejercicios, comience con el gráfico de
Luego escriba una función que resulte de la transformación dada.
En los siguientes ejercicios, cada gráfico es la transformación de
Escriba una ecuación que describa la transformación.
En los siguientes ejercicios, halle una ecuación exponencial para el gráfico.
### Numéricos
En los siguientes ejercicios, evalúe las funciones exponenciales para el valor indicado de
### En tecnología
En los siguientes ejercicios, utilice una calculadora gráfica para determinar las soluciones de la ecuación. Redondee a la milésima más cercana.
### Extensiones
|
# Funciones exponenciales y logarítmicas
## Funciones logarítmicas
### Objetivos de aprendizaje
1. Convertir de forma logarítmica a exponencial. (IA 10.3.1)
2. Evalúe funciones logarítmicas. (IA 10.3.2)
### Objetivo 1: Convertir de forma logarítmica a exponencial. (IA 10.3.1)
### La práctica hace la perfección
Dado que las ecuaciones y son equivalentes, podemos ir de un lado a otro entre estas. Este será a menudo el método para resolver algunas ecuaciones exponenciales y logarítmicas. Para ayudar con la conversión entre una y otra, veamos las ecuaciones con detenimiento. Observe las posiciones del exponente y la base.
Si recordamos que el logaritmo es el exponente, se facilita la conversión. Puede repetir: "la base al exponente nos da el número”.
### La práctica hace la perfección
Convierta entre forma exponencial y logarítmica.
Recuerde estas notaciones logarítmicas para completar lo siguiente: Logaritmo común Logaritmo natural
### Objetivo 2: Evaluar funciones logarítmicas (AI 10.3.2).
Podemos resolver y evaluar ecuaciones logarítmicas con la técnica de convertir la ecuación en su forma exponencial equivalente.
### La práctica hace la perfección
En 2010, un gran terremoto azotó Haití y causó estragos en más de 285.000 hogareshttp://earthquake.usgs.gov/earthquakes/eqinthenews/2010/us2010rja6/#summary. Consultado el 4 de marzo de 2013.. Un año después, otro terremoto más fuerte devastó Honshu, Japón, con destrucción y daños a más de 332.000 edificaciones,http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/#summary. Consultado el 4 de marzo de 2013. como las que se muestran en la . Aunque ambos infligieron daños considerables, el terremoto de 2011 fue 100 veces más fuerte que el de Haití. ¿Cómo lo sabemos? La magnitud de los movimientos telúricos se mide en lo que se conoce como la escala de Richter. El terremoto de Haití registró una magnitud de 7,0 en la escala de Richter,http://earthquake.usgs.gov/earthquakes/eqinthenews/2010/us2010rja6/. Consultado el 4 de marzo de 2013. mientras que el sismo en Japón registró una magnitud de 9,0.http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/#details. Consultado el 4 de marzo de 2013.
La escala de Richter es una escala logarítmica de base diez. En otras palabras, un sismo de magnitud 8 no es dos veces mayor que uno de magnitud 4. Es
veces más grande. En esta lección, investigaremos la naturaleza de la escala de Richter y la función de base diez de la que depende.
### Convertir de la forma logarítmica a la exponencial
Para analizar la magnitud de un movimiento telúrico o compararla con la de otro, debemos estar en capacidad de convertir entre la forma logarítmica y la exponencial. Por ejemplo, supongamos que la cantidad de energía que libera un terremoto es 500 veces mayor que la cantidad de energía que libera otro. Queremos calcular la diferencia en la magnitud. La ecuación que representa este problema es
donde
representa la diferencia de magnitud en la escala de Richter. ¿Cómo podríamos resolver
Todavía no hemos aprendido el método para resolver ecuaciones exponenciales. Ninguna de las herramientas algebraicas que se han analizado hasta ahora basta para resolver
Sabemos que
y
por lo que está claro que
deberá ser algún valor entre 2 y 3, ya que
aumenta. Podemos examinar un gráfico, como en la , para estimar mejor la solución.
Sin embargo, la estimación a partir de un gráfico es imprecisa. Para hallar una solución algebraica, debemos introducir una nueva función. Observe que el gráfico en la pasa la prueba de la línea horizontal. La función exponencial
es biunívoca, por lo que su inversa,
también es una función. Como ocurre con todas las funciones inversas, simplemente intercambiamos la
como
, a la vez que resolvemos para
con el fin de dar con la función inversa. Para representar
en función de
utilizamos una función logarítmica de la forma
La base
logaritmo de un número es el exponente por el que debemos elevar
para obtener esa cifra.
Leemos una expresión logarítmica como: "El logaritmo con base
de
es igual a
o, simplificado, la "base logarítmica
de
es
«”. También podemos enunciar: "
elevado a la potencia de
es
porque los logaritmos son exponentes. Por ejemplo, el logaritmo de base 2 de 32 es 5, porque 5 es el exponente que debemos aplicar a 2 para obtener 32. Dado que
podemos escribir
Lo leemos como “la base logarítmica 2 de 32 es 5".
Podemos expresar la relación entre la forma logarítmica y su correspondiente forma exponencial como sigue:
Tenga en cuenta que la base
es siempre positiva.
Dado que el logaritmo es una función, la manera más correcta de escribirlo es:
con paréntesis para denotar la evaluación de la función, al igual que haríamos con
Sin embargo, cuando la entrada es una sola variable o un número, es común ver los paréntesis eliminados y la expresión escrita sin paréntesis, como
Tenga en cuenta que muchas calculadoras requieren paréntesis alrededor de la
Podemos ilustrar la notación de los logaritmos de la siguiente manera:
Observe que, al comparar la función logarítmica y la función exponencial, la entrada y la salida se intercambian. Esto significa que
y de
son funciones inversas.
### Convertir de la forma exponencial a la forma logarítmica
Para convertir de exponentes a logaritmos, seguimos los mismos pasos, pero a la inversa. Identificamos la base
exponente
y salida
Entonces escribimos
### Evaluar logaritmos
Conocer los cuadrados, cubos y raíces de los números nos permite evaluar mentalmente muchos logaritmos. Por ejemplo, considere
Nos preguntamos: "¿A qué exponente hay que elevar
para obtener el 8?”. Dado que ya sabemos que
se deduce que
Ahora, considere resolver
y
mentalmente.
1. Preguntamos: "¿A qué exponente hay que elevar 7 para obtener 49?”. Sabemos que
Por lo tanto,
2. Preguntamos: "¿A qué exponente hay que elevar 3 para obtener 27?”. Sabemos que
Por lo tanto,
Incluso algunos logaritmos aparentemente más complicados pueden evaluarse sin necesidad de la calculadora. Por ejemplo, evaluemos
mentalmente.
1. Preguntamos: "¿A qué exponente hay que elevar
para obtener
“. Sabemos que
y
tal que
Por lo tanto,
### Usar logaritmos comunes
A veces podemos ver un logaritmo escrito sin base. En este caso, suponemos que la base es 10. En otras palabras, la expresión
significa
Llamamos logaritmo común a un logaritmo de base 10. Los logaritmos comunes se utilizan para medir la escala de Richter que se menciona al principio de la sección. Las escalas para medir el brillo de las estrellas y el pH de los ácidos y las bases también utilizan logaritmos comunes.
### Usar logaritmos naturales
La base más utilizada para los logaritmos es
Los logaritmos con base
son importantes en el cálculo y en algunas aplicaciones científicas; reciben el nombre de logaritmos naturales. El logaritmo con base
,
tiene su propia notación,
La mayoría de los valores de
se hallan únicamente con la calculadora. La mayor excepción es esa, porque el logaritmo de 1 es siempre 0 en cualquier base,
Para otros logaritmos naturales, podemos utilizar la tecla
, que se encuentra en la mayoría de las calculadoras científicas. También podemos hallar el logaritmo natural de cualquier potencia de
utilizando la propiedad inversa de los logaritmos.
### Ecuaciones clave
### Conceptos clave
1. La inversa de una función exponencial es una función logarítmica, y la inversa de una función logarítmica es una función exponencial.
2. Las ecuaciones logarítmicas se pueden escribir en una forma exponencial equivalente, utilizando la definición de logaritmo. Vea el .
3. Las ecuaciones exponenciales pueden escribirse en su forma logarítmica equivalente utilizando la definición de logaritmo. Vea el .
4. Las funciones logarítmicas con base
pueden evaluarse mentalmente utilizando el conocimiento previo de las potencias de
Vea el y el .
5. Los logaritmos comunes pueden evaluarse mentalmente utilizando los conocimientos previos de las potencias de
Vea el .
6. Cuando los logaritmos comunes no pueden evaluarse mentalmente, se utiliza la calculadora. Vea el .
7. Los problemas exponenciales del mundo real con base
pueden reescribirse como un logaritmo común y luego evaluarse con la calculadora. Vea el .
8. Los logaritmos naturales se pueden evaluar con la calculadora. .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, reescriba cada ecuación en forma exponencial.
En los siguientes ejercicios, reescriba cada ecuación en forma logarítmica.
En los siguientes ejercicios, resuelva para
al convertir la ecuación logarítmica en forma exponencial.
En los siguientes ejercicios, utilice la definición de logaritmos comunes y naturales para simplificar.
### Numéricos
En los siguientes ejercicios, evalúe la expresión logarítmica con base
sin utilizar la calculadora.
En los siguientes ejercicios, evalúe la expresión logarítmica común sin utilizar la calculadora.
En los siguientes ejercicios, evalúe la expresión logarítmica natural sin utilizar la calculadora.
### En tecnología
En los siguientes ejercicios, evalúe cada expresión con la calculadora. Redondee a la milésima más cercana.
### Extensiones
### Aplicaciones en el mundo real
|
# Funciones exponenciales y logarítmicas
## Gráficos de funciones logarítmicas
### Objetivos de aprendizaje
1. Hallar el dominio y el rango de una relación y una función. (IA 3.5.1)
2. Graficar funciones logarítmicas. (IA 10.3.3)
### Objetivo 1: Hallar el dominio y el rango de una relación y una función. (IA 3.5.1)
### La práctica hace la perfección
Hallar el dominio y el rango de una relación y una función.
### Objetivo 2: Graficar funciones logarítmicas. (IA 10.3.3)
Para graficar una función logarítmica , lo más fácil es convertir la ecuación en su forma exponencial, . Generalmente, cuando buscamos pares ordenados para el gráfico de una función, solemos elegir un valor x y luego determinar su correspondiente valor y. En este caso, puede resultarle más fácil elegir los valores de y, para luego determinar su correspondiente valor de x.
### La práctica hace la perfección
Graficar funciones logarítmicas
En Gráficos de funciones exponenciales vimos cómo la creación de una representación gráfica de un modelo exponencial nos da otra capa de conocimiento para predecir acontecimientos futuros. ¿De qué manera los gráficos logarítmicos nos permiten comprender las situaciones? Dado que toda función logarítmica es la función inversa de una función exponencial, podemos pensar en cada salida de un gráfico logarítmico como la entrada de la correspondiente ecuación exponencial inversa. En otras palabras, los logaritmos dan la causa de un efecto.
Para ilustrarlo, supongamos que invertimos
dólares en una cuenta que ofrece un tipo de interés anual de
calculada continuamente. Ya sabemos que el saldo de nuestra cuenta para cualquier año
se determina con la ecuación
Pero, ¿y si quisiéramos saber el año de cualquier saldo? Tendríamos que crear una nueva función correspondiente al intercambiar la entrada y la salida; por lo tanto, tendríamos que crear un modelo logarítmico para esta situación. Al graficar el modelo, podemos ver la salida (año) para cualquier entrada (saldo contable). Por ejemplo, ¿qué pasaría si quisiéramos saber cuántos años tardaríamos en duplicar nuestra inversión inicial? La muestra este punto en el gráfico logarítmico.
En esta sección hablaremos acerca de los valores para los que se define una función logarítmica, y luego nos centraremos en la creación de gráficos de la familia de funciones logarítmicas.
### Hallar el dominio de una función logarítmica
Antes de trabajar con los gráficos, echaremos un vistazo al dominio (el conjunto de valores de entrada) para el que se define la función logarítmica.
Recordemos que la función exponencial se define como
para cualquier número real
y constante
donde
1. El dominio de
es
2. El rango de
es
En la última sección aprendimos que la función logarítmica
es la inversa de la función exponencial
Entonces, como funciones inversas:
1. El dominio de
es el rango de
2. El rango de
es el dominio de
Las transformaciones de la función matriz
se comportan de forma similar a las de otras funciones. Al igual que con otras funciones matrices, podemos aplicar los cuatro tipos de transformaciones (desplazamiento, estiramiento, compresión y reflexión) a la función matriz sin perder la forma.
En Gráficos de funciones exponenciales vimos que ciertas transformaciones pueden cambiar el rango de
Del mismo modo, al aplicar transformaciones a la función matriz
podemos cambiar el dominio. Por lo tanto, al determinar el dominio de una función logarítmica, es importante recordar que el dominio consiste solo en números reales positivos. Es decir, el argumento de la función logarítmica deberá ser mayor que cero.
Por ejemplo, considere
Esta función se define para cualquier valor de
de manera que el argumento, en este caso
es mayor que cero. Para hallar el dominio, establecemos una inecuación y resolvemos para
En notación de intervalo, el dominio de
es
### Graficar funciones logarítmicas
Ahora que ya conocemos el conjunto de valores para los que se define una función logarítmica, pasemos a graficar funciones logarítmicas. La familia de funciones logarítmicas incluye la función matriz
junto con todas sus transformaciones: desplazamiento, estiramiento, compresión y reflexión.
Comenzamos con la función matriz
Ya que toda función logarítmica de esta forma es la inversa de una función exponencial con la forma
sus gráficos serán una reflexión el uno del otro a través de la línea
Para ilustrar esto, podemos observar la relación entre los valores de entrada y salida de
y su equivalente
en la .
Utilizando las entradas y salidas de la , podemos construir otra tabla para observar la relación entre los puntos de los gráficos de las funciones inversas
y
Vea la .
Como era de esperar, las coordenadas de la x y de la y se invierten para las funciones inversas. La muestra el gráfico de
y
Observe lo siguiente a partir del gráfico:
1.
tiene una intersección en y en
y
tiene una intersección en x en
2. El dominio de
es el mismo que el rango de
3. El rango de
es el mismo que el dominio de
### Graficar transformaciones de funciones logarítmicas
Como hemos mencionado al principio de la sección, las transformaciones de los gráficos logarítmicos se comportan de forma semejante a las de otras funciones matrices. Podemos desplazar, estirar, comprimir y reflejar la función matriz
sin perder la forma.
### Graficar un desplazamiento horizontal de f(x) = log(x)
Cuando una constante
se suma a la entrada de la función matriz
el resultado es un desplazamiento horizontal
unidades en la dirección opuesta al signo en
Para visualizar los desplazamientos horizontales, podemos observar el gráfico general de la función matriz
y para
junto al desplazamiento hacia la izquierda,
y el desplazamiento a la derecha,
Vea la .
### Graficar un desplazamiento vertical de y = log(x)
Cuando una constante
se suma a la función matriz
el resultado es un desplazamiento vertical
unidades en la dirección del signo en
Para visualizar los desplazamientos verticales, podemos observar el gráfico general de la función matriz
junto con el desplazamiento hacia arriba,
y el desplazamiento hacia abajo,
Vea la .
### Graficar estiramiento y compresión de y = log(x)
Cuando la función matriz
se multiplica por una constante
el resultado es un estiramiento vertical o compresión vertical del gráfico original. Para visualizar el estiramiento y la compresión, establecemos
y observe que el gráfico general de la función matriz
junto al estiramiento vertical,
y la compresión vertical,
Vea la .
### Graficar reflexiones de f(x) = log(x)
Cuando la función matriz
se multiplica por
el resultado es una reflexión alrededor del eje x. Cuando la entrada se multiplica por
el resultado es una reflexión alrededor del eje y. Para visualizar las reflexiones, restringimos
y observamos el gráfico general de la función matriz
junto a la reflexión alrededor del eje x,
y la reflexión en torno al eje y,
### Resumir las traslaciones de la función logarítmica
Ahora que hemos trabajado con cada tipo de traslación para la función logarítmica, podemos resumir cada una en la para llegar a la ecuación general de traslación de las funciones exponenciales.
### Ecuaciones clave
### Conceptos clave
1. Para hallar el dominio de una función logarítmica, establezca una inecuación que muestre el argumento mayor que cero, y resuelva para
Vea el y el
2. El gráfico de la función matriz
tiene una intersección en x en
dominio
rango
asíntota vertical
y
Vea el .
3. La ecuación
desplaza la función matriz
horizontalmente
Vea el .
4. La ecuación
desplaza la función matriz
verticalmente
Vea el .
5. Para cualquier constante
la ecuación
Vea el y el .
6. Cuando la función matriz
se multiplica por
el resultado es una reflexión alrededor del eje x. Cuando la entrada se multiplica por
el resultado es una reflexión alrededor del eje y.
Vea el .
7. Todas las traslaciones de la función logarítmica se pueden resumir en la ecuación general
Vea la .
8. Dada una ecuación con la forma general
podemos identificar la asíntota vertical
para la transformación. Vea el .
9. Utilizando la ecuación general
podemos escribir la ecuación de una función logarítmica dado su gráfico. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, indique el dominio y el rango de la función.
En los siguientes ejercicios, indique el dominio y la asíntota vertical de la función.
En los siguientes ejercicios, indique el dominio, la asíntota vertical y el comportamiento final de la función.
En los siguientes ejercicios, indique el dominio, el rango y las intersecciones en x y en y, si existen. Si no existen, escriba DNE.
### Gráficos
En los siguientes ejercicios, empareje cada función en la con la letra correspondiente a su gráfico.
En los siguientes ejercicios, empareje cada función en la con la letra correspondiente a su gráfico.
En los siguientes ejercicios, dibuje los gráficos de cada par de funciones en el mismo eje.
En los siguientes ejercicios, empareje cada función en la con la letra correspondiente a su gráfico.
En los siguientes ejercicios, dibuje el gráfico de la función indicada.
En los siguientes ejercicios, escriba una ecuación logarítmica correspondiente al gráfico mostrado.
### En tecnología
En los siguientes ejercicios, utilice una calculadora gráfica para hallar soluciones aproximadas a cada ecuación.
### Extensiones
|
# Funciones exponenciales y logarítmicas
## Propiedades logarítmicas
### Objetivos de aprendizaje
1. Simplifique expresiones con las propiedades de los exponentes. (IA 5.2.1)
2. Utilizar las propiedades de los logaritmos. (IA 10.4.1)
### Objetivo 1: Simplificar expresiones con las propiedades para los exponentes (AI 5.2.1)
### La propiedad del producto
Simplifique expresiones con las propiedades de los exponentes.
Para multiplicar potencias con la misma base necesitamos ________ exponentes
Esto nos lleva a la propiedad del producto
### La propiedad del cociente
Simplifique
Para dividir potencias con la misma base necesitamos __________ exponentes.
Esto nos lleva a la propiedad del cociente
### La propiedad de la potencia
Simplifique
Para elevar una potencia a otra potencia necesitamos __________ exponentes
Esto nos lleva a la propiedad de la potencia .
También utilizaremos estas otras propiedades:
### La práctica hace la perfección
Simplifique expresiones con las propiedades de los exponentes.
### Objetivo 2: Utilizar las propiedades de los logaritmos (AI 10.4.1).
### La práctica hace la perfección
En química, el pH se utiliza para medir la acidez o alcalinidad de una sustancia. La escala de pH va de 0 a 14. Las sustancias con un pH inferior a 7 se consideran ácidas, y las sustancias con un pH superior a 7 se consideran básicas. Nuestro organismo, por ejemplo, debe mantener un pH cercano a 7,35 para que las enzimas funcionen correctamente. Para hacerse una idea de lo que es ácido y lo que es básico, considere los siguientes niveles de pH de algunas sustancias comunes:
1. Ácido de batería: 0,8
2. Acidez estomacal: 2,7
3. Zumo de naranja: 3,3
4. Agua pura: 7 (a 25° C)
5. Sangre humana: 7,35
6. Coco fresco: 7,8
7. Hidróxido de sodio (lejía): 14
Para determinar si una solución es ácida o básica, buscamos su pH, que es una medida del número de iones de hidrógeno positivos activos en la solución. El pH se define mediante la siguiente fórmula, donde
es la concentración de iones de hidrógeno en la solución
La equivalencia de
y
es una de las propiedades del logaritmo que examinaremos en esta sección.
### Uso de la regla del producto para los logaritmos
Recuerde que las funciones logarítmicas y exponenciales se "deshacen" mutuamente. Esto significa que los logaritmos tienen propiedades similares a los exponentes. Aquí se dan algunas propiedades importantes de los logaritmos. En primer lugar, las siguientes propiedades son fáciles de comprobar.
Por ejemplo,
dado que
Y
dado que
A continuación, tenemos la propiedad inversa.
Por ejemplo, para evaluar
podemos reescribir el logaritmo como
y luego aplicar la propiedad inversa
para obtener
Para evaluar
podemos reescribir el logaritmo como
y luego aplicar la propiedad inversa
para obtener
Por último, tenemos la propiedad biunívoca.
Podemos utilizar la propiedad biunívoca para resolver la ecuación
para
Debido a que las bases son iguales, podemos aplicar la propiedad biunívoca al igualar los argumentos y resolver para
¿Qué pasa con la ecuación
La propiedad biunívoca no nos sirve en este caso. Antes de poder resolver una ecuación como esta, necesitamos un método para combinar los términos del lado izquierdo de la ecuación.
Recordemos que utilizamos la regla de multiplicación de exponentes para combinar el producto de potencias sumando exponentes:
Tenemos una propiedad similar para los logaritmos, denominada regla del producto de los logaritmos, la cual establece que el logaritmo de un producto es igual a una suma de logaritmos. Ya que los logaritmos son exponentes, y multiplicamos como bases, podemos sumar los exponentes. Utilizaremos la propiedad inversa para derivar la regla del producto, a continuación.
Dado un número real cualquiera
y números reales positivos
y
donde
mostraremos
Supongamos que
y
En forma exponencial, estas ecuaciones son
y
Se deduce que
Observe que la aplicación repetida de la regla del producto para los logaritmos nos permite simplificar el logaritmo del producto de cualquier número de factores. Por ejemplo, considere
Con la regla del producto para los logaritmos, podemos reescribir este logaritmo de un producto como la suma de los logaritmos de sus factores:
### Uso de la regla del cociente para los logaritmos
En los cocientes, tenemos una regla similar para los logaritmos. Recordemos que utilizamos la regla del cociente de exponentes para combinar el cociente de exponentes al restar:
La regla del cociente para los logaritmos establece que el logaritmo de un cociente es igual a una diferencia de logaritmos. Al igual que con la regla del producto, podemos utilizar la propiedad inversa para derivar la regla del cociente.
Dado un número real cualquiera
y números reales positivos
y
donde
mostraremos
Supongamos que
y
En forma exponencial, estas ecuaciones son
y
Se deduce que
Por ejemplo, para expandir
debemos expresar primero el cociente en términos mínimos. Al factorizar y cancelar obtenemos,
A continuación, aplicamos la regla del cociente al restar el logaritmo del denominador al del numerador. Luego aplicamos la regla del producto.
### Usar la regla de la potencia para los logaritmos
Hemos explorado la regla del producto y la regla del cociente. Ahora bien, ¿cómo podemos tomar el logaritmo de una potencia, como
Un método es el siguiente:
Observe que hemos utilizado la regla del producto para los logaritmos con el fin de hallar una solución para el ejemplo anterior. Al hacerlo, hemos derivado la regla de la potencia para los logaritmos, la cual establece que el logaritmo de una potencia es igual al exponente por el logaritmo de la base. Tenga en cuenta que, aunque la entrada de un logaritmo no se escriba como una potencia, podemos cambiarla por una potencia. Por ejemplo,
### Expandir expresiones logarítmicas
En conjunto, la regla del producto, la regla del cociente y la regla de la potencia suelen llamarse "leyes de los logaritmos". A veces aplicamos más de una regla para simplificar una expresión. Por ejemplo:
Podemos utilizar la regla de la potencia para expandir expresiones logarítmicas que incluyan exponentes negativos y fraccionarios. Aquí hay una prueba alternativa de la regla del cociente para los logaritmos, por el hecho de que un recíproco es una potencia negativa:
También podemos aplicar la regla del producto para expresar la suma o diferencia de logaritmos como el logaritmo de un producto.
Con la práctica, podemos mirar una expresión logarítmica y expandirla mentalmente, al escribir la respuesta final. Recordemos, sin embargo, que solo podemos hacerlo con productos, cocientes, potencias y raíces, nunca con sumas o restas dentro del argumento del logaritmo.
### Condensar expresiones logarítmicas
Podemos utilizar las reglas de los logaritmos que acabamos de aprender para condensar las sumas, las diferencias y los productos con la misma base en un solo logaritmo. Es importante recordar que los logaritmos deben tener la misma base para poder combinarse. Más adelante aprenderemos a cambiar la base de cualquier logaritmo antes de condensar.
### Usar la fórmula de cambio de base para los logaritmos
La mayoría de las calculadoras solo evalúan los logaritmos comunes y naturales. Para evaluar logaritmos con una base distinta de 10 o
utilizamos la fórmula de cambio de base, donde reescribimos el logaritmo como el cociente de logaritmos de cualquier otra base. Al utilizar la calculadora, los cambiaríamos a logaritmos comunes o naturales.
Para derivar la fórmula de cambio de base, utilizamos la propiedad biunívoca y la regla de la potencia para los logaritmos.
Dados cualesquiera números reales positivos
y
donde
como de
demostramos
Supongamos que
Potenciando ambos lados con base
, llegamos a una forma exponencial, a saber
Se deduce que
Por ejemplo, para evaluar
con una calculadora, primero debemos reescribir la expresión como el cociente de logaritmos comunes o naturales. Utilizaremos el logaritmo común.
### Ecuaciones clave
### Conceptos clave
1. Podemos utilizar la regla del producto de los logaritmos para reescribir el logaritmo de un producto como la suma de logaritmos. Vea el .
2. Podemos utilizar la regla del cociente de los logaritmos para reescribir el logaritmo de un cociente como la diferencia de logaritmos. Vea el .
3. Podemos utilizar la regla de la potencia para los logaritmos con el objeto de reescribir el logaritmo de una potencia como el producto del exponente y el logaritmo de su base. Vea el , el y el .
4. Podemos utilizar la regla del producto, la regla del cociente y la regla de la potencia juntas para combinar o expandir un logaritmo con una entrada compleja. Vea el , el y el .
5. Las reglas de los logaritmos también se pueden utilizar para condensar sumas, diferencias y productos con la misma base como un solo logaritmo. Vea el , el , el y el .
6. Podemos convertir un logaritmo con cualquier base en un cociente de logaritmos con cualquier otra base mediante la fórmula de cambio de base. Vea el .
7. La fórmula de cambio de base se utiliza a menudo para reescribir un logaritmo con una base distinta de 10 y
como el cociente de los logaritmos naturales o comunes. De esta manera se puede utilizar la calculadora para evaluar. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, expanda cada logaritmo lo máximo posible. Reescriba cada expresión como suma, diferencia o producto de logaritmos.
En los siguientes ejercicios, condense a un solo logaritmo si es posible.
En los siguientes ejercicios, utilice las propiedades de los logaritmos para expandir cada uno lo máximo posible. Reescriba cada expresión como suma, diferencia o producto de logaritmos.
En los siguientes ejercicios, condense cada expresión a un solo logaritmo utilizando las propiedades de los logaritmos.
En los siguientes ejercicios, reescriba cada expresión como un cociente equivalente de logaritmos con la base indicada.
En los siguientes ejercicios, supongamos
y
Utilice la fórmula de cambio de base junto con las propiedades de los logaritmos para reescribir cada expresión en términos de
y
Muestre los pasos para resolver.
### Numéricos
En los siguientes ejercicios, utilice las propiedades de los logaritmos para evaluar sin usar la calculadora.
En los siguientes ejercicios, utilice la fórmula de cambio de base para evaluar cada expresión como cociente de logaritmos naturales. Utilice la calculadora para aproximar cada uno de ellos a cinco decimales.
### Extensiones
|
# Funciones exponenciales y logarítmicas
## Ecuaciones exponenciales y logarítmicas
### Objetivos de aprendizaje
1. Resolver ecuaciones exponenciales. (IA 10.2.2)
2. Resolver ecuaciones logarítmicas. (IA 10.3.4)
### Objetivo 1: Resolver ecuaciones exponenciales. (IA 10.2.2)
Las ecuaciones que incluyen una expresión exponencial se denominan ecuaciones exponenciales. Hay dos tipos de ecuaciones exponenciales: las que tienen la base común en cada lado y las que no tienen base común.
Tipo 1: Posible base común en cada lado: Utilice las propiedades de los exponentes para reescribir cada lado con una base común. Utilice la propiedad base-exponente para igualar los exponentes y resolver para x.
Tipo 2: No hay base común posible: Utilice las propiedades de los exponentes para reescribir cada lado en términos de una expresión exponencial. Tome el logaritmo o ln de cada lado y utilice la regla de la potencia para bajar la potencia. Resuelva la ecuación restante para x.
### La práctica hace la perfección
Resuelva. Halle la respuesta exacta y luego aproxímela con tres decimales.
### Objetivo 2: Resolver ecuaciones logarítmicas. (IA 10.3.4)
Hay dos tipos de ecuaciones logarítmicas: las que tienen términos logarítmicos en un solo lado de la ecuación o las que tienen términos logarítmicos en cada lado de la ecuación. Ya que el dominio de las funciones logarítmicas consiste únicamente en números positivos, compruebe bien las soluciones.
Tipo 1: Términos logarítmicos en un lado de la ecuación: Utilice las propiedades de los logaritmos para reescribir un lado con un solo término logarítmico. Convierta a notación exponencial y resuelva para x.
Si los valores de entonces .
Tipo 2: Términos logarítmicos en ambos lados de la ecuación: En primer lugar, utilice las propiedades del logaritmo para reescribir cada lado en términos de una única expresión logarítmica, si es necesario. Utilice la propiedad biunívoca de la igualdad logarítmica para que los argumentos sean iguales entre sí. Resuelva la ecuación resultante para x.
### La práctica hace la perfección
No olvide comprobar sus soluciones.
En 1859, un terrateniente australiano llamado Thomas Austin liberó 24 conejos en la naturaleza para su caza. Debido a que Australia tenía pocos depredadores y abundante comida, la población de conejos se disparó. En menos de diez años, la población de conejos se contaba por millones.
El crecimiento demográfico descontrolado, como en el caso de los conejos silvestres de Australia, puede modelarse con funciones exponenciales. Las ecuaciones resultantes de esas funciones exponenciales pueden resolverse para analizar y hacer predicciones sobre el crecimiento exponencial. En esta sección, aprenderemos técnicas para resolver funciones exponenciales.
### Usar bases semejantes para resolver ecuaciones exponenciales
La primera técnica implica dos funciones con bases similares. Recordemos que la propiedad biunívoca de las funciones exponenciales nos señala que, para cualesquiera números reales
y
donde
si y solo si
En otras palabras, cuando una ecuación exponencial tiene la misma base en cada lado, los exponentes deberán ser iguales. Esto también se aplica cuando los exponentes son expresiones algebraicas. Por lo tanto, podemos resolver muchas ecuaciones exponenciales con las reglas de los exponentes para reescribir cada lado como una potencia con la misma base. A continuación, utilizamos el hecho de que las funciones exponenciales son biunívocas para igualar los exponentes y resolver la incógnita.
Por ejemplo, considere la ecuación
Para resolver
utilizamos la propiedad de división de los exponentes con el objeto de reescribir el lado derecho, de manera que ambos lados tengan la base común,
A continuación, aplicamos la propiedad biunívoca de los exponentes al igualarlos y resolver para
:
### Reescribir las ecuaciones para que todas las potencias tengan la misma base
A veces la base común de una ecuación exponencial no es explícita. En estos casos, simplemente reescribimos los términos de la ecuación como potencias con base común y resolvemos con la propiedad biunívoca.
Por ejemplo, considere la ecuación
Podemos reescribir ambos lados de esta ecuación como potencia de
Entonces aplicamos las reglas de los exponentes, junto con la propiedad biunívoca, para resolver
### Resolver ecuaciones exponenciales mediante logaritmos
A veces los términos de una ecuación exponencial no pueden reescribirse con una base común. En estos casos, resolvemos al tomar el logaritmo de cada lado. Recordemos que, dado que
equivale a
podemos aplicar logaritmos con la misma base en ambos lados de la ecuación exponencial.
### Ecuaciones que contienen e
Un tipo común de ecuaciones exponenciales son las de base
Esta constante se repite una y otra vez en la naturaleza, en las matemáticas, en la ciencia, en la ingeniería y en las finanzas. Cuando tenemos una ecuación con una base
en cualquier lado, podemos utilizar el logaritmo natural para resolverla.
### Soluciones extrañas
A veces, los métodos utilizados para resolver una ecuación introducen una solución extraña, que es una solución correcta desde el punto de vista algebraico pero que no satisface las condiciones de la ecuación original. Una de estas situaciones surge al resolver cuando se toma el logaritmo en ambos lados de la ecuación. En estos casos, recuerde que el argumento del logaritmo deberá ser positivo. Si el número que evaluamos en una función de logaritmo es negativo, no hay salida.
### Usar la definición de un logaritmo para resolver ecuaciones logarítmicas
Ya hemos visto que toda ecuación logarítmica
es equivalente a la ecuación exponencial
Podemos utilizar este hecho, junto con las reglas de los logaritmos, para resolver ecuaciones logarítmicas donde el argumento sea una expresión algebraica.
Por ejemplo, considere la ecuación
Para resolver esta ecuación, podemos utilizar las reglas de los logaritmos con el objeto de reescribir el lado izquierdo en forma compacta y luego aplicar la definición de logaritmos para resolver
### Usar la propiedad biunívoca de los logaritmos para resolver ecuaciones logarítmicas
Al igual que con las ecuaciones exponenciales, podemos utilizar la propiedad biunívoca para resolver ecuaciones logarítmicas. La propiedad biunívoca de las funciones logarítmicas nos señala que, para cualquier número real
y cualquier número real positivo
donde
Por ejemplo,
Por lo tanto, si
entonces podemos resolver para
y obtenemos
Para comprobarlo, podemos sustituir
en la ecuación original:
En otras palabras, cuando una ecuación logarítmica tiene la misma base en cada lado, los argumentos deberán ser iguales. Esto también se aplica cuando los argumentos son expresiones algebraicas. Por lo tanto, cuando se da una ecuación con logaritmos de la misma base en cada lado, podemos utilizar las reglas de los logaritmos para reescribir cada lado como un único logaritmo. A continuación, utilizamos el hecho de que las funciones logarítmicas son biunívocas para igualar los argumentos y resolver la incógnita.
Por ejemplo, considere la ecuación
Para resolver esta ecuación, podemos utilizar las reglas de los logaritmos con el objeto de reescribir el lado izquierdo como un solo logaritmo, y luego aplicar la propiedad biunívoca para resolver
Para comprobar el resultado, sustituya
en
### Resolver problemas aplicados mediante ecuaciones exponenciales y logarítmicas
En las secciones anteriores, hemos aprendido las propiedades y las reglas de las funciones exponenciales y logarítmicas. Hemos visto que cualquier función exponencial puede escribirse como una función logarítmica y viceversa. Hemos utilizado los exponentes para resolver ecuaciones logarítmicas y los logaritmos para resolver ecuaciones exponenciales. Ahora estamos preparados para combinar nuestras habilidades para resolver ecuaciones que modelen situaciones del mundo real, tanto si la incógnita está en un exponente como en el argumento de un logaritmo.
Una de estas aplicaciones se encuentra en la ciencia, al calcular el tiempo que tarda en decaer la mitad del material inestable de la muestra de una sustancia radiactiva, lo que se denomina su semivida. La enumera la semivida de varias de las sustancias radiactivas más comunes.
Podemos ver lo mucho que varían las semividas de estas sustancias. Conocer la vida media de una sustancia nos permite calcular la cantidad que queda después de un tiempo determinado. Podemos emplear la fórmula para el decaimiento radiactivo:
donde
1.
es la cantidad inicial presente
2.
es la semivida de la sustancia
3.
es el tiempo en el que se estudia la sustancia
4.
es la cantidad de la sustancia presente después del tiempo
### Ecuaciones clave
### Conceptos clave
1. Podemos resolver muchas ecuaciones exponenciales con las reglas de los exponentes para reescribir cada lado como una potencia con la misma base. A continuación, utilizamos el hecho de que las funciones exponenciales son biunívocas para igualar los exponentes y resolver la incógnita.
2. Cuando se nos da una ecuación exponencial en la que las bases se muestran explícitamente iguales, igualamos los exponentes y resolvemos la incógnita. Vea el .
3. Cuando se nos da una ecuación exponencial en la que las bases no se muestran explícitamente iguales, reescribimos cada lado de la ecuación como potencias de la misma base, luego igualamos los exponentes y resolvemos la incógnita. Vea el , el y el .
4. Cuando una ecuación exponencial no pueda reescribirse con una base común, resuélvela al tomar el logaritmo de cada lado. Vea el .
5. Podemos resolver ecuaciones exponenciales con base
al aplicar el logaritmo natural de ambos lados porque las funciones exponenciales y logarítmicas son inversas entre sí. Vea el y el .
6. Después de resolver una ecuación exponencial, compruebe cada solución en la ecuación original para detectar y eliminar cualquier solución extraña. Vea el .
7. Cuando se da una ecuación de la forma
donde
es una expresión algebraica, podemos utilizar la definición de logaritmo para reescribir la ecuación como la ecuación exponencial equivalente
y resolver la incógnita. Vea el y el .
8. También podemos utilizar la representación gráfica para resolver ecuaciones con la forma
Graficamos ambas ecuaciones
y de
en el mismo plano de coordenadas e identificamos la solución como el valor de x del punto de intersección. Vea el .
9. Cuando se da una ecuación de la forma
donde
y
son expresiones algebraicas, podemos utilizar la propiedad biunívoca de los logaritmos para resolver la ecuación
para la incógnita. Vea el .
10. Al combinar las habilidades aprendidas en esta sección y en las anteriores, podemos resolver ecuaciones que modelen situaciones del mundo real, tanto si la incógnita está en un exponente como en el argumento de un logaritmo. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, utilice bases semejantes para resolver la ecuación exponencial.
En los siguientes ejercicios, utilice logaritmos para resolver.
En los siguientes ejercicios, utilice la definición de logaritmo para reescribir la ecuación como exponencial.
En los siguientes ejercicios, utilice la definición de logaritmo para resolver la ecuación.
En los siguientes ejercicios, utilice la propiedad biunívoca de los logaritmos para resolver.
En los siguientes ejercicios, resuelva cada ecuación para
### Gráficos
En los siguientes ejercicios, resuelva la ecuación para
si hay una solución. A continuación, grafique ambos lados de la ecuación y preste atención al punto de intersección (si existe) para verificar la solución.
En los siguientes ejercicios, resuelva el valor indicado y grafique la situación mostrando el punto de solución.
### En tecnología
En los siguientes ejercicios, resuelva cada ecuación al reescribir la expresión exponencial con el logaritmo indicado. A continuación, utilice la calculadora para estimar la variable a 3 decimales.
En los siguientes ejercicios, utilice una calculadora para resolver la ecuación. A menos que se indique lo contrario, redondee todas las respuestas a la diezmilésima más cercana.
### Extensiones
|
# Funciones exponenciales y logarítmicas
## Modelos exponenciales y logarítmicos
### Objetivos de aprendizaje
1. Utilizar modelos exponenciales en aplicaciones. (IA 10.2.3)
2. Utilizar modelos logarítmicos en aplicaciones. (IA 10.3.5)
### Objetivo 1: Utilizar modelos exponenciales en aplicaciones. (IA 10.2.3)
### Usar modelos exponenciales
Las funciones exponenciales modelan muchas situaciones. Si tiene una cuenta de ahorros, habrá experimentado el uso de una función exponencial. Hay dos fórmulas que se utilizan para determinar el saldo de la cuenta cuando se devengan los intereses. Si se invierte un capital, P, a un tipo de interés, r, durante t años, el nuevo saldo, A, dependerá de la frecuencia con que se capitalicen los intereses.
### Crecimiento y decaimiento exponencial
Otros temas que se modelan mediante funciones exponenciales son el crecimiento y el decaimiento. Ambos utilizan también la fórmula que empleamos para el crecimiento del dinero. Para el crecimiento y el decaimiento, generalmente utilizamos como la cantidad original en lugar de llamarla el capital. Vemos que el crecimiento exponencial tiene una tasa de crecimiento positiva y el decaimiento exponencial tiene una tasa de crecimiento negativa.
### La práctica hace la perfección
### Objetivo 2: Utilizar modelos logarítmicos en aplicaciones. (IA 10.3.5)
### Nivel de decibelios del sonido
Hay muchas aplicaciones que se modelan mediante ecuaciones logarítmicas. Primero veremos la ecuación logarítmica que da el nivel de decibelios (dB) del sonido. Los decibelios oscilan entre 0, que apenas es audible, y 160, que puede romper un tímpano. El 10-12 de la fórmula representa la intensidad del sonido apenas audible.
La magnitud de un terremoto se mide mediante una escala logarítmica, denominada escala de Richter. El modelo es donde es la intensidad de la onda de choque. Este modelo mide la intensidad de los terremotos.
### La práctica hace la perfección
Utilizar modelos logarítmicos en aplicaciones.
Ya hemos explorado algunas aplicaciones básicas de las funciones exponenciales y logarítmicas. En esta sección, profundizamos en algunas aplicaciones importantes, incluso los isótopos radiactivos y la ley de enfriamiento de Newton.
### Modelar el crecimiento y el decaimiento exponencial
En las aplicaciones del mundo real, necesitamos modelar el comportamiento de una función. En el modelado matemático, elegimos una función general conocida con propiedades que sugieren que modelará el fenómeno del mundo real que deseamos analizar. En el caso de un crecimiento rápido, podemos elegir la función de crecimiento exponencial:
donde es igual al valor en el tiempo cero, es la constante de Euler, y es una constante positiva que determina la tasa (porcentaje) de crecimiento. Podemos utilizar la función de crecimiento exponencial en las aplicaciones que implican el tiempo de duplicación, el tiempo que tarda una cantidad en duplicarse. Fenómenos como la fauna, las inversiones financieras, las muestras biológicas y los recursos naturales pueden exhibir un crecimiento basado en un tiempo de duplicación. Sin embargo, en algunas aplicaciones, como veremos cuando hablemos de la ecuación logística, el modelo logístico a veces se ajusta mejor a los datos que el modelo exponencial.
Por otro lado, si una cantidad cae rápidamente hacia cero, sin llegar nunca a cero, entonces probablemente deberíamos elegir el modelo de decaimiento exponencial. De nuevo, tenemos la forma donde es el valor inicial, y es la constante de Euler. Ahora es una constante negativa que determina la tasa de decaimiento. Podemos utilizar el modelo de decaimiento exponencial cuando calculamos la semivida, o el tiempo que tarda una sustancia en decaer exponencialmente hasta la mitad de su cantidad original. Utilizamos la semivida en las aplicaciones relacionadas con los isótopos radiactivos.
A la hora de elegir una función que sirva de modelo matemático, a menudo utilizamos puntos de datos recogidos mediante una cuidadosa observación y medición para construir puntos en un gráfico y esperamos poder reconocer su forma. Los gráficos de crecimiento y decaimiento exponencial tienen una forma distintiva, como podemos ver en la y la . Es importante recordar que, aunque partes de cada uno de los dos gráficos parecen estar en el eje x, en realidad están a una distancia mínima por encima del eje x.
El crecimiento y el decaimiento exponencial suelen implicar números muy grandes o muy pequeños. Para describir estas cifras, solemos utilizar órdenes de magnitud. El orden de magnitud es la potencia de diez, cuando el número se expresa en notación científica, con un dígito a la izquierda del decimal. Por ejemplo, la distancia a la estrella más cercana, Próxima Centauri, medida en kilómetros, es de 40.113.497.200.000 kilómetros. Expresado en notación científica, esto es Así, podríamos describir esta cifra como de orden de magnitud
### Semivida
Ahora pasemos al decaimiento exponencial. Uno de los términos más comunes que se asocian al decaimiento exponencial, como ya se ha indicado arriba, es la semivida, el tiempo que tarda una cantidad que decae exponencialmente en disminuir hasta la mitad de su cantidad original. Cada isótopo radiactivo tiene una semivida, y el proceso que describe el decaimiento exponencial de un isótopo se denomina decaimiento radiactivo.
Para hallar la semivida de una función que describe el decaimiento exponencial, resuelva la siguiente ecuación:
Vemos que la semivida depende solo de la constante y no en la cantidad inicial
La fórmula se deriva de la siguiente manera
Dado que el tiempo, es positivo, debe, como es de esperar, ser negativo. Esto nos da la fórmula de la semivida
### Datación por radiocarbono
La fórmula del decaimiento radiactivo es importante en la datación por radiocarbono, que se utiliza para calcular la fecha aproximada de la muerte de una planta o de un animal. La datación por radiocarbono fue descubierta en 1949 por Willard Libby, que ganó el Premio Nobel por su descubrimiento. Compare la diferencia entre el cociente de dos isótopos de carbono en un artefacto orgánico o fósil con la proporción de esos dos isótopos en el aire. Se cree que tiene una precisión de alrededor del 1 % de error para las plantas o animales que murieron en los últimos 60.000 años.
El carbono 14 es un isótopo radiactivo del carbono que tiene una semivida de 5.730 años. Se encuentra en pequeñas cantidades en el dióxido de carbono del aire que respiramos. La mayor parte del carbono de la Tierra es carbono 12, que tiene un peso atómico de 12 y no es radiactivo. Los científicos han determinado el cociente entre el carbono 14 y el carbono 12 en el aire durante los últimos 60.000 años, mediante el empleo de anillos de árboles y otras muestras orgánicas de fechas conocidas, aunque la relación ha cambiado ligeramente a lo largo de los siglos.
Mientras una planta o un animal esté vivo, la proporción de los dos isótopos del carbono en su cuerpo se acerca a la proporción en la atmósfera. Cuando muere, el carbono 14 de su cuerpo se descompone y no se reemplaza. Al comparar la proporción entre el carbono 14 y el carbono 12 en una muestra en descomposición con la proporción conocida en la atmósfera, se puede calcular aproximadamente la fecha en que murió la planta o el animal.
Dado que la semivida del carbono 14 es de 5.730 años, la fórmula para la cantidad restante después de años es
donde
Esta fórmula se deriva de la siguiente manera:
Para calcular la edad de un objeto, resolvemos esta ecuación para
Por necesidad, dejamos de lado aquí los muchos detalles que un científico tiene en cuenta al realizar la datación por carbono 14, y solo nos fijamos en la fórmula básica. La proporción entre el carbono 14 y el carbono 12 en la atmósfera es de aproximadamente 0,0000000001%. Supongamos que es la proporción entre el carbono 14 y el carbono 12 en el artefacto orgánico o fósil sujeto a la datación, determinada por un método que recibe el nombre de centelleo líquido. A partir de la ecuación sabemos que la relación entre el porcentaje de carbono-14 en el objeto que estamos datando y la cantidad inicial de carbono-14 en el objeto cuando se formó es Resolvemos esta ecuación para para obtener
### Calcular el tiempo de duplicación
Para las cantidades en decaimiento, determinamos el tiempo que tarda en decaer la mitad de una sustancia. En el caso de las cantidades crecientes, es posible que queramos averiguar el tiempo que tarda una cantidad en duplicarse. Como ya lo hemos mencionado, el tiempo que tarda una cantidad en duplicarse recibe el nombre de tiempo de duplicación.
Dada la ecuación básica de crecimiento exponencial
el tiempo de duplicación se puede calcular al resolver para cuando la cantidad original se ha duplicado, es decir, al resolver
La fórmula se deriva de la siguiente manera:
Así, el tiempo de duplicación es
### Utilizar la ley de enfriamiento de Newton
El decaimiento exponencial también puede aplicarse a la temperatura. Cuando un objeto caliente se deja en el aire circundante, que está a una temperatura más baja, la temperatura del objeto disminuirá exponencialmente, para nivelarse a la temperatura del aire circundante. En un gráfico de la función de temperatura, la nivelación corresponderá a una asíntota horizontal a la temperatura del aire circulante. A menos que la temperatura ambiente sea cero, esto corresponderá a un desplazamiento vertical de la función genérica de decaimiento exponencial. Esta traslación nos lleva a la ley del enfriamiento de Newton, la fórmula científica de la temperatura en función del tiempo cuando la temperatura de un objeto se iguala a la temperatura ambiente
Esta fórmula se deriva de la siguiente manera:
### Uso de modelos de crecimiento logístico
El crecimiento exponencial no puede continuar para siempre. Los modelos exponenciales, aunque pueden ser útiles a corto plazo, tienden a desmoronarse cuanto más tiempo se prolongan. Piense en una aspirante a escritor que escribe una sola línea el primer día y se propone duplicar el número de líneas que escribe cada día durante un mes. Antes de que acabe el mes, deberá escribir más de 17.000 millones de líneas, es decir, 500 millones de páginas. No es práctico, por no decir imposible, que alguien escriba tanto en tan poco tiempo. Con el tiempo, deberá aplicarse un modelo exponencial que se aproxime a algún valor límite, y entonces el crecimiento se ve obligado a ralentizarse. Por esta razón, a menudo es mejor utilizar un modelo con un límite superior, en lugar de un modelo de crecimiento exponencial, aunque el modelo de crecimiento exponencial sigue siendo útil a corto plazo, antes de acercarse al valor límite.
El modelo de crecimiento logístico es aproximadamente exponencial al principio, pero tiene una tasa de crecimiento reducida a medida que la producción se acerca al límite superior del modelo, denominada capacidad de carga. Para las constantes
y
el crecimiento logístico de una población en el tiempo
viene representado por el modelo
El gráfico en la muestra la evolución de la tasa de crecimiento con el paso del tiempo. El gráfico aumenta de izquierda a derecha, pero la tasa de crecimiento aumenta únicamente hasta que alcanza su punto máximo, momento en el que disminuye.
### Elegir un modelo adecuado para los datos
Ahora, que hemos hablado de varios modelos matemáticos, tenemos que aprender a elegir el modelo adecuado para los datos brutos de los que disponemos. Son muchos los factores que influyen en la elección de un modelo matemático, entre ellos la experiencia, las leyes científicas y los patrones de los propios datos. No todos los datos pueden describirse mediante funciones elementales. A veces, se elige una función que se aproxima a los datos en un intervalo determinado. Por ejemplo, supongamos que se recogen datos sobre el número de viviendas compradas en Estados Unidos entre los años 1960 y 2013. Tras representar estos datos en un gráfico de dispersión, observamos que la forma de los datos de los años 2000 a 2013 sigue una curva logarítmica. Podríamos restringir el intervalo de 2000 a 2010, aplicar el análisis de regresión mediante un modelo logarítmico y utilizarlo para predecir el número de compradores de viviendas para el año 2015.
Tres tipos de funciones que suelen ser útiles en los modelos matemáticos son las lineales, las exponenciales y las logarítmicas. Si los datos se encuentran en una línea recta, o parecen encontrarse aproximadamente a lo largo de una línea recta, un modelo lineal sería lo mejor. Si los datos no son lineales, se suele considerar un modelo exponencial o logarítmico, aunque también se pueden considerar otros modelos, como los cuadráticos.
Al momento de elegir entre un modelo exponencial y uno logarítmico, nos fijamos en la forma en que se curvan los datos. Esto se denomina concavidad. Si trazamos una línea entre dos puntos de datos, y todos (o la mayoría) de los datos entre esos dos puntos se encuentran por encima de esa línea, decimos que la curva es cóncava hacia abajo. Podemos pensar que es un cuenco que se dobla hacia abajo y que, por tanto, no puede retener el agua. Si todos (o la mayoría) de los datos entre esos dos puntos están por debajo de la línea, decimos que la curva es cóncava hacia arriba. En este caso, podemos pensar en un cuenco que se dobla hacia arriba y que, por ende, puede contener agua. Una curva exponencial, ya sea ascendente o descendente, ya sea que represente el crecimiento o el decaimiento, siempre es cóncava hacia arriba y se aleja de su asíntota horizontal. Una curva logarítmica siempre es cóncava respecto a su asíntota vertical. En el caso de los datos positivos, que es el más común, la curva exponencial siempre es cóncava hacia arriba, a la vez que la curva logarítmica siempre es cóncava hacia abajo.
Una curva logística cambia la concavidad. Comienza por ser cóncava hacia arriba y luego pasa a ser cóncava hacia abajo, más allá de un punto determinado, denominado punto de inflexión.
Después de usar el gráfico para elegir un tipo de función como modelo, sustituimos los puntos y resolvemos para hallar los parámetros. Reducimos el error de redondeo al elegir puntos lo más alejados posible.
### Expresar un modelo exponencial con base
Aunque se pueden utilizar potencias y logaritmos de cualquier base en el modelado, las dos bases más comunes son
y
En ciencia y matemáticas, la base
se prefiere a menudo. Podemos utilizar las leyes de los exponentes y de los logaritmos para cambiar cualquier base a base
### Ecuaciones clave
### Conceptos clave
1. La función exponencial básica es
Si
tenemos un crecimiento exponencial; si
tenemos un decaimiento exponencial.
2. También podemos escribir esta fórmula en términos de crecimiento continuo como
donde
es el valor inicial. Si los valores de
es positivo, entonces tenemos un crecimiento exponencial cuando
y el decaimiento exponencial cuando
Vea el .
3. En general, resolvemos los problemas que implican crecimiento o decaimiento exponencial en dos pasos. En primer lugar, establecemos un modelo y lo utilizamos para calcular los parámetros. A continuación, utilizamos la fórmula con estos parámetros para predecir el crecimiento y el decaimiento. Vea el .
4. Podemos calcular la edad,
de un artefacto orgánico al medir la cantidad,
de carbono 14 que queda en el artefacto y utilizar la fórmula
para resolver para
Vea el .
5. Dado el tiempo de duplicación o el tiempo medio de una sustancia, podemos hallar una función que represente su crecimiento o decaimiento exponencial. Vea el .
6. Podemos utilizar la ley de enfriamiento de Newton para calcular el tiempo que tardará un objeto en enfriarse hasta alcanzar una temperatura deseada, o para calcular qué temperatura tendrá un objeto después de un tiempo determinado. Vea el .
7. Podemos utilizar las funciones de crecimiento logístico para modelar situaciones del mundo real en las que la tasa de crecimiento cambia con el tiempo, como el crecimiento demográfico, la propagación de enfermedades y la difusión de rumores. Vea el .
8. Podemos utilizar los datos del mundo real, recabados a lo largo del tiempo, para observar las tendencias. El conocimiento de los gráficos lineales, exponenciales, logarítmicos y logísticos permite elaborar los modelos que mejor se ajusten a nuestros datos. Vea el .
9. Cualquier función exponencial con la forma
puede reescribirse como una función exponencial equivalente con la forma
donde
Vea el .
### Ejercicios de la sección
### Verbales
### Numéricos
En los siguientes ejercicios, utilice el modelo de crecimiento logístico
### En tecnología
En los siguientes ejercicios, introduzca los datos de cada tabla en una calculadora gráfica y grafique los diagramas de dispersión resultantes. Determine si los datos de la tabla pueden representar una función lineal, exponencial o logarítmica.
En los siguientes ejercicios, utilice una calculadora gráfica y este escenario: la población de una piscifactoría en
años se modela mediante la ecuación
### Extensiones
### Aplicaciones en el mundo real
En los siguientes ejercicios, utilice este escenario: Un médico prescribe 125 miligramos de un fármaco que decae aproximadamente 30 % cada hora.
En los siguientes ejercicios, utilice este escenario: Se inyectan a un tumor
gramos de yodo 125, que tiene una tasa de decaimiento de
por día.
En los siguientes ejercicios, utilice este escenario: Un biólogo registró un recuento de
bacterias presentes en un cultivo después de 5 minutos y 1.000 bacterias presentes después de 20 minutos.
En los siguientes ejercicios, utilice este escenario: Una olla de sopa caliente con una temperatura interna de
se sacó de la estufa para enfriar a
en una habitación. Después de quince minutos, la temperatura interna de la sopa era
En los siguientes ejercicios, utilice este escenario: Un pavo se saca del horno con una temperatura interna de
y se deja enfriar a
en una habitación. Después de media hora, la temperatura interna del pavo es
En los siguientes ejercicios, halle el valor del número que aparece en cada escala logarítmica. Redondee todas las respuestas a la milésima más cercana.
En los siguientes ejercicios, utilice este escenario: La ecuación
modela el número de personas de una ciudad que han escuchado un rumor al cabo de t días.
En el siguiente ejercicio, elija la opción correcta. |
# Funciones exponenciales y logarítmicas
## Ajustar modelos exponenciales a los datos
### Objetivos de aprendizaje
1. Dibujar e interpretar diagramas de dispersión (lineales, exponenciales, logarítmicos). (CA 4.3.1)
2. Ajustar una ecuación de regresión a un conjunto de datos y utilizar el modelo lineal (o exponencial) para hacer predicciones. (CA 4.3.4)
### Objetivo 1: Dibujar e interpretar diagramas de dispersión (lineales, exponenciales, logarítmicos). (CA 4.3.1)
Un diagrama de dispersión es un gráfico de puntos trazados que indica una relación entre las variables de un conjunto de datos.
### La práctica hace la perfección
Dibujar e interpretar diagramas de dispersión (lineales, exponenciales, logarítmicos).
### Objetivo 2: Ajustar una ecuación de regresión a un conjunto de datos y utilizar el modelo lineal (o exponencial) para hacer predicciones. (CA 4.3.4)
Podemos hallar una función lineal que se ajuste a los datos del problema anterior al “meterle el ojo” a una línea que parezca ajustarse. Sin embargo, aunque la estimación de una línea funciona relativamente bien, la tecnología puede ayudarnos a encontrar una línea que se ajuste a los datos de la forma más perfecta posible.
Esta línea se denomina línea de regresión por mínimos cuadrados o modelo de regresión lineal.
La línea de regresión es aquella que más se aproxima a los datos en el diagrama de dispersión, lo que significa que es el mejor ajuste para los datos.
Ajustar una ecuación de regresión a un conjunto de datos y utilizar el modelo lineal (o exponencial) para hacer predicciones.
### La práctica hace la perfección
Ajustar una ecuación de regresión a un conjunto de datos y utilizar el modelo lineal (o exponencial) para hacer predicciones.
En las secciones anteriores de este capítulo, se nos ha dado una función explícitamente para graficar o evaluar, o se nos ha dado un conjunto de puntos que se garantiza que se encuentran en la curva. Luego utilizamos el álgebra para hallar la ecuación que se ajusta a los puntos exactamente. En esta sección, utilizamos una técnica de modelado, denominada análisis de regresión, para hallar una curva que modele los datos recogidos en las observaciones del mundo real. Con el análisis de regresión, no esperamos que todos los puntos se sitúen perfectamente en la curva. La idea es hallar el modelo que mejor se ajuste a los datos. A continuación, utilizamos el modelo para hacer predicciones sobre acontecimientos futuros.
No se deje confundir por la palabra modelo. En matemáticas, a menudo utilizamos los términos función, ecuación y modelo indistintamente, aunque cada uno tenga su propia definición formal. El término modelo suele utilizarse para indicar que la ecuación o función se aproxima a una situación del mundo real.
En esta sección nos concentraremos en tres tipos de modelos de regresión: exponencial, logarítmica y logística. Haber trabajado ya con cada una de estas funciones nos da una ventaja. Conocer sus definiciones formales, el comportamiento de sus gráficos y algunas de sus aplicaciones en el mundo real nos brinda la oportunidad de profundizar en su comprensión. A medida que se presenta cada modelo de regresión, se incluyen las características clave y las definiciones de su función asociada para su revisión. Dedique un momento a repensar cada una de estas funciones, a reflexionar sobre el trabajo que hemos realizado hasta ahora y a explorar las formas en que se utiliza la regresión para modelar fenómenos del mundo real.
### Construir un modelo exponencial a partir de datos
Como hemos aprendido, hay multitud de situaciones que pueden modelarse mediante funciones exponenciales, como el crecimiento de las inversiones, el decaimiento radiactivo, los cambios de presión atmosférica y las temperaturas de un objeto que se enfría. ¿Qué tienen en común estos fenómenos? Por un lado, todos los modelos aumentan o disminuyen con el paso del tiempo. Sin embargo, eso no es todo. Es la manera en que los datos aumentan o disminuyen lo que nos ayuda a determinar si es mejor modelar con una ecuación exponencial. Conocer el comportamiento de las funciones exponenciales en general nos permite reconocer cuándo utilizar la regresión exponencial, así que repasemos el crecimiento y el decaimiento exponencial.
Recordemos que las funciones exponenciales tienen la forma
o
Al realizar el análisis de regresión, utilizamos la forma más común en las utilidades gráficas,
Dedique un momento a reflexionar sobre las características que ya hemos aprendido acerca de la función exponencial
(suponiendo que
1.
deberá ser mayor que cero y no igual a uno.
2. El valor inicial del modelo es
Como parte de los resultados, su calculadora mostrará un número conocido como el coeficiente de correlación, etiquetado por la variable
o
(Es posible que tenga que cambiar la configuración de la calculadora para que se muestren). Los valores son una indicación de la "bondad de ajuste" de la ecuación de regresión a los datos. Lo más habitual es utilizar el valor de
en vez de
pero cuanto más se acerque cualquiera de los dos valores a 1, mejor se aproximará la ecuación de regresión a los datos.
### Construir un modelo logarítmico a partir de datos
Al igual que con las funciones exponenciales, hay muchas aplicaciones en el mundo real para las funciones logarítmicas: la intensidad del sonido, el nivel de pH de las soluciones, los rendimientos de las reacciones químicas, la producción de bienes y el crecimiento de los bebés. Al igual que con los modelos exponenciales, los datos modelados por funciones logarítmicas son siempre crecientes o siempre decrecientes con el paso del tiempo. De nuevo, es la manera en que aumentan o disminuyen lo que nos permite determinar si un modelo logarítmico es el mejor.
Recordemos que las funciones logarítmicas aumentan o disminuyen rápidamente al principio, pero luego desaceleran constantemente con el paso del tiempo. Al reflexionar sobre las características que ya hemos aprendido con respecto a esta función, podemos analizar mejor las situaciones del mundo real que reflejan este tipo de crecimiento o decaimiento. Al realizar el análisis de regresión logarítmica, utilizamos la forma de la función logarítmica más común en las herramientas gráficas,
Para esta función
1. Todos los valores de entrada,
deberán ser mayor que cero.
2. El punto
está en el gráfico del modelo.
3. Si los valores de
el modelo es creciente. El crecimiento aumenta rápidamente al principio y luego desacelera constantemente con el paso del tiempo.
4. Si los valores de
el modelo es decreciente. El decaimiento se produce rápidamente al principio y luego desacelera constantemente con el paso del tiempo.
### Construir un modelo logístico a partir de datos
Al igual que el crecimiento exponencial y logarítmico, el crecimiento logístico aumenta con el paso del tiempo. Una de las diferencias más notables con los modelos de crecimiento logístico es que, a partir de cierto punto, el crecimiento desacelera de forma constante y la función se aproxima a un límite superior, o valor límite. Por ello, la regresión logística es lo mejor para modelar fenómenos en los que existen límites de expansión, como la disponibilidad de espacio vital o de nutrientes.
Cabe señalar que las funciones logísticas en realidad modelan el crecimiento exponencial con recursos limitados. Hay muchos ejemplos de este tipo de crecimiento en situaciones del mundo real, como el crecimiento demográfico y la propagación de enfermedades, los rumores e incluso las manchas en la tela. Al realizar el análisis de regresión logística, utilizamos la forma más común en las herramientas gráficas:
Recordemos que:
1.
es el valor inicial del modelo.
2. cuando
el modelo aumenta rápidamente al principio, hasta alcanzar su punto de máxima tasa de crecimiento,
En ese punto, el crecimiento desacelera de forma constante y la función se vuelve asintótica al límite superior
3.
es el valor límite, a veces llamado capacidad de carga, del modelo.
### Conceptos clave
1. La regresión exponencial se utiliza para modelar situaciones en las que el crecimiento comienza lentamente y luego se acelera rápidamente sin límite, o en las que el decaimiento comienza rápidamente y luego desacelera para acercarse cada vez más a cero.
2. Utilizamos el comando "ExpReg" en una herramienta gráfica para ajustar una función de la forma
a un conjunto de puntos de datos. Vea el .
3. La regresión logarítmica se utiliza para modelar situaciones en las que el crecimiento o el decaimiento se aceleran rápidamente al principio y luego desaceleran con el paso del tiempo.
4. Utilizamos el comando "LnReg" en una herramienta gráfica para ajustar una función de la forma
a un conjunto de puntos de datos. Vea el .
5. La regresión logística se utiliza para modelar situaciones en las que el crecimiento se acelera rápidamente al principio y luego desacelera de forma constante a medida que la función se acerca a un límite superior.
6. Utilizamos el comando "Logistic" en una herramienta gráfica para ajustar una función de la forma
a un conjunto de puntos de datos. Vea el .
### Ejercicios de la sección
### Verbales
### Gráficos
En los siguientes ejercicios, haga coincidir la función de mejor ajuste dada con el correspondiente diagrama de dispersión desde la hasta la . Responda con la letra que se encuentra debajo del gráfico correspondiente.
### Numéricos
### En tecnología
En los siguientes ejercicios, utilice este escenario: La población
en un estanque de carpas koi sobre
meses se modela mediante la función
En los siguientes ejercicios, utilice este escenario: La población
en un hábitat de una especie de lobos en peligro de extinción se modela mediante la función
donde
se da en años.
En los siguientes ejercicios, consulte la .
En los siguientes ejercicios, consulte la .
En los siguientes ejercicios, consulte la .
En los siguientes ejercicios, consulte la .
En los siguientes ejercicios, consulte la .
En los siguientes ejercicios, consulte la .
### Extensiones
### Ejercicios de repaso del capítulo
### Funciones exponenciales
### Gráficos de funciones exponenciales
### Funciones logarítmicas
### Gráficos de funciones logarítmicas
### Propiedades logarítmicas
### Ecuaciones exponenciales y logarítmicas
### Modelos exponenciales y logarítmicos
En los siguientes ejercicios, utilice este escenario: Un médico prescribe
miligramos de un fármaco que decae en un
cada hora.
En los siguientes ejercicios, utilice este escenario: Una sopa con una temperatura interna de
°F se sacó de la estufa para enfriar a una temperatura ambiente de
. Después de quince minutos, la temperatura interna de la sopa era
En los siguientes ejercicios, utilice este escenario: La ecuación
modela el número de personas de una escuela que han escuchado un rumor después de
días.
En los siguientes ejercicios, introduzca los datos de cada tabla en una calculadora gráfica y grafique los diagramas de dispersión resultantes. Determine si los datos de la tabla representan probablemente una función lineal, exponencial o logarítmica.
### Ajuste de modelos exponenciales a los datos
En los siguientes ejercicios, utilice una herramienta gráfica para crear un diagrama de dispersión de los datos en la tabla. Observe la forma del diagrama de dispersión para determinar si los datos se describen mejor mediante un modelo exponencial, logarítmico o logístico. A continuación, utilice la función de regresión adecuada para hallar una ecuación que modele los datos. Cuando sea necesario, redondee los valores a cinco decimales.
### Prueba de práctica
En los siguientes ejercicios, utilice una herramienta gráfica para crear un diagrama de dispersión de los datos en la tabla. Observe la forma del diagrama de dispersión para determinar si los datos se describen mejor mediante un modelo exponencial, logarítmico o logístico. A continuación, utilice la función de regresión adecuada para hallar una ecuación que modele los datos. Cuando sea necesario, redondee los valores a cinco decimales. |
# Funciones trigonométricas
## Introducción
La vida está llena de fenómenos que se repiten a intervalos regulares. Cada día, por ejemplo, las mareas suben y bajan en respuesta a la atracción gravitacional de la luna.Hamacher, D. W., Tapim, A., Passi, S. y Barsa, J. (2018). Y como consecuencia del propio movimiento de la luna, las mareas se producen con distinta intensidad. A lo largo de la historia, muchos pueblos indígenas utilizaron esta regularidad para construir relatos culturales y dirigir actividades clave, como la agricultura, la caza y la pesca. Los aborígenes del área del estrecho de Torres (el extremo norte) de Australia utilizaban los picos de las mareas para determinar los mejores momentos para pescar. Sus ancianos explican que las fuertes mareas de primavera agitan los sedimentos y oscurecen la visión de los peces haciéndolos más proclives a atrapar los señuelos, lo que genera una mayor pesca.
En matemáticas, la función que repite sus valores a intervalos regulares se conoce como función periódica. Los gráficos de estas funciones revelan una forma general que refleja un patrón que se repite. Esto significa que el gráfico de la función tiene la misma salida exactamente en el mismo lugar en cada ciclo. Esto se traduce en que todos los ciclos de la función tienen exactamente la misma longitud. Así, si conocemos todos los detalles de un ciclo completo de una función periódica verdadera, entonces conocemos el estado de las salidas de la función en todo momento: futuro y pasado. En este capítulo, investigaremos varios ejemplos de funciones periódicas. |
# Funciones trigonométricas
## Ángulos
Un golfista se balancea para golpear una bola por encima de una trampa de arena y llegar al green. Un piloto de aerolínea maniobra un avión hacia una pista estrecha. Un diseñador de vestidos crea la última moda. ¿Qué tienen todos ellos en común? Todos ellos trabajan con ángulos, al igual que todos nosotros en un momento u otro. A veces es necesario medir los ángulos con exactitud mediante instrumentos. Otras veces los estimamos o juzgamos a ojo. En cualquier caso, el ángulo adecuado puede marcar la diferencia entre el éxito y el fracaso en muchas empresas. En esta sección, examinaremos las propiedades de los ángulos.
### Dibujar ángulos en posición estándar
Para definir correctamente un ángulo, primero hay que definir una raya. La raya consiste en un punto en una línea y todos los puntos que se extienden en una dirección desde ese punto. El primer punto se denomina punto final de la raya. Podemos referirnos a una raya concreta al indicar su punto final y cualquier otro punto en esta. La raya en la puede denominarse EF, o indicarse en forma de símbolo
Un ángulo es la unión de dos rayas que tienen un punto final común. El punto final se denomina vértice, mientras que las dos rayas son los lados del ángulo. El ángulo en la se forma a partir de
y
Los ángulos pueden nombrarse al utilizar un punto en cada raya y el vértice, como el ángulo DEF, o en forma de símbolo
Las letras griegas se utilizan a menudo como variables para la medida de un ángulo. La es una lista de letras griegas que se utilizan para representar ángulos. Además, un ejemplo de ángulo se muestra en la .
La creación de ángulos es un proceso dinámico. Empezamos con dos rayas superpuestas. Dejamos una fija y rotamos la otra. La raya fija es el lado inicial, y la raya rotada es el lado terminal. Para identificar los diferentes lados, indicamos la rotación con un pequeño arco y una flecha cerca del vértice como en la .
Como hemos comentado al principio de la sección, las aplicaciones de los ángulos son múltiples. Sin embargo, para poder utilizarlos correctamente, debemos estar en la capacidad de medirlos. La medida de un ángulo es la cantidad de rotación desde el lado inicial hasta el lado terminal. Probablemente, la unidad de medida de ángulos más conocida es el grado. Un grado es
de una rotación circular, por lo que una rotación circular completa contiene 360 grados. Un ángulo medido en grados debería incluir siempre la unidad "grados" después del número, o incluir el símbolo de grado º. Por ejemplo, 90 grados = 90º.
Para formalizar nuestro trabajo, empezaremos dibujando ángulos en un plano de coordenadas de la x y de la y. Los ángulos pueden aparecer en cualquier posición del plano de coordenadas. Sin embargo, a efectos de comparación, la convención es ilustrarlos en la misma posición siempre que sea posible. Un ángulo está en posición estándar si su vértice está situado en el origen, y su lado inicial se extiende a lo largo del eje positivo x. Vea la .
Si el ángulo se mide en sentido contrario a las agujas del reloj desde el lado inicial hasta el lado terminal, se dice que es positivo. Si el ángulo se mide en el sentido de las agujas del reloj, se dice que es negativo.
Al dibujar un ángulo en posición estándar siempre comienza de la misma manera: se dibuja el lado inicial a lo largo del eje positivo x. Para situar el lado terminal del ángulo, debemos calcular la fracción de una rotación completa que representa el ángulo. Lo hacemos al dividir la medida del ángulo en grados entre 360º. Por ejemplo, para dibujar un ángulo de 90º, calculamos que
Por lo tanto, el lado terminal estará a una cuarta parte del círculo, en sentido contrario a las agujas del reloj desde el eje positivo x. Para dibujar un ángulo de 360º, calculamos que
Por lo tanto, el lado terminal dará una vuelta completa alrededor del círculo, en sentido contrario a las agujas del reloj desde el eje positivo x. En este caso, el lado inicial y el lado terminal se superponen. Vea la .
Como definimos un ángulo en posición estándar por su lado inicial, tenemos un tipo especial de ángulo, cuyo lado terminal se encuentra en un eje, un ángulo cuadrangular. Este tipo de ángulo puede tener una medida de 0°, 90°, 180°, 270° o 360°. Vea la .
### Convertir entre grados y radianes
Dividir un círculo en 360 partes es una elección arbitraria, aunque crea la conocida medida de grados. Podemos elegir otras formas para dividir un círculo. Para calcular otra unidad, piense en el proceso de dibujar un círculo. Imagine que se detiene antes de completar el círculo. La parte que ha dibujado se denomina arco. Un arco puede ser una porción de un círculo completo, un círculo completo o más de un círculo completo, representado por más de una rotación completa. La longitud del arco alrededor de un círculo entero se denomina la circunferencia de ese círculo.
La circunferencia de un círculo es
Si dividimos ambos lados de esta ecuación entre
creamos el cociente entre la circunferencia y el radio, que siempre es
independientemente de la longitud del radio. Así que la circunferencia de cualquier círculo es
veces la longitud del radio. Esto significa que si tomáramos una cuerda tan larga como el radio y la utilizáramos para medir longitudes consecutivas alrededor de la circunferencia, habría espacio para seis longitudes de cuerda completas y un poco más de un cuarto de la séptima, como se muestra en la .
Esto nos lleva a nuestra nueva medida de ángulo. Un radián es la medida de un ángulo central de un círculo que interseca un arco de longitud igual al radio de dicho círculo. Un ángulo central es un ángulo formado en el centro de un círculo por dos radios. Dado que la circunferencia total es igual a
veces el radio, una rotación circular completa es
radianes. Así que
Vea la . Observe que, cuando se describe un ángulo sin una unidad específica, se refiere a la medida del radián. Por ejemplo, una medida de ángulo de 3 indica 3 radianes. De hecho, la medida del radián es adimensional, ya que es el cociente de una longitud (circunferencia) dividido entre la longitud (radio) y las unidades de longitud se cancelan.
### Relacionar las longitudes de los arcos con los radios
La longitud de arco
es la longitud de la curva a lo largo del arco. Al igual que la circunferencia completa de un círculo siempre tiene una relación constante con el radio, la longitud de arco producida por un ángulo cualquiera también tiene una relación constante con el radio, independientemente de su longitud.
Este cociente, denominado medición de radián, es el mismo, independientemente del radio del círculo (solo depende del ángulo). Esta propiedad nos permite definir la medida de cualquier ángulo como el cociente de la longitud de arco
al radio
Vea la .
Si los valores de
entonces
Para profundizar en esta idea, consideremos dos círculos, uno con radio 2 y otro con radio 3. Recordemos que la circunferencia de un círculo es
donde
es el radio. El círculo más pequeño tiene entonces la circunferencia
y el más grande tiene circunferencia
Ahora trazamos un ángulo de 45° en los dos círculos, como en la .
Observe lo que ocurre si calculamos el cociente de la longitud del arco dividido entre el radio del círculo.
Dado que ambos ratios son
las medidas de los ángulos de ambos círculos son las mismas, aunque la longitud del arco y el radio sean diferentes.
### Usar radianes
Dado que la medición de radián es el cociente de dos longitudes, es una medida sin unidades. Por ejemplo, en la , supongamos que el radio fuera de 2 pulgadas y la distancia a lo largo del arco fuera también de 2 pulgadas. Cuando calculamos la medida del radián del ángulo, las "pulgadas" se cancelan, y tenemos un resultado sin unidades. Por lo tanto, no es necesario escribir la etiqueta "radianes" después de una medición de radián, y si vemos un ángulo que no está etiquetado con "grados" o el símbolo de grado, podemos asumir que es una medición de radián.
Considerando el caso más básico, el círculo unitario (un círculo de radio 1), sabemos que 1 rotación equivale a 360 grados, 360°. También podemos seguir una rotación alrededor de un círculo al calcular la circunferencia,
y para el círculo unitario
Estas dos formas diferentes de girar alrededor de un círculo nos dan una manera de convertir de grados a radianes.
### Identificar ángulos especiales, medidos en radianes
Además de conocer las medidas en grados y radianes de un cuarto de revolución, media revolución y revolución completa, hay otros ángulos que se encuentran con frecuencia en la revolución de un círculo con los que deberíamos estar familiarizados. Es habitual encontrar múltiplos de 30, 45, 60 y 90 grados. Estos valores se muestran en la . Será muy útil memorizar estos ángulos cuando estudiamos las propiedades asociadas a ellos.
Ahora, podemos enumerar los valores de los radianes con respecto a las medidas comunes de un círculo correspondientes a las que se enumeran en la , y que se muestran en la . Verifique cada una de estas medidas.
### Convertir radianes y grados
Dado que tanto los grados como los radianes miden ángulos, tenemos que ser capaces de convertirlos. Podemos hacerlo fácilmente utilizando una proporción.
Esta proporción muestra que la medida del ángulo
en grados dividido entre 180 es igual a la medida del ángulo
en radianes dividido entre
Dicho de otra manera, los grados son a 180 como los radianes son a
### Calcular ángulos coterminales
La conversión entre grados y radianes puede facilitar el trabajo con ángulos en algunas aplicaciones. Para otras aplicaciones, quizá necesitemos otro tipo de conversión. Los ángulos negativos y los ángulos superiores a una revolución completa son más difíciles de trabajar que los que están en el rango de 0° a 360°, o de 0 a
Sería conveniente sustituir esos ángulos fuera de rango por un ángulo correspondiente dentro del rango de una sola revolución.
Es posible que más de un ángulo tenga el mismo lado terminal. Observe la . El ángulo de 140° es un ángulo positivo, medido en sentido contrario a las agujas del reloj. El ángulo de -220° es un ángulo negativo, medido en el sentido de las agujas del reloj. No obstante, ambos ángulos tienen el mismo lado terminal. Si dos ángulos en posición estándar tienen el mismo lado terminal, son ángulos coterminales. Todo ángulo mayor que 360° o menor que 0° es coterminal con un ángulo entre 0° y 360°, y a menudo es más conveniente hallar el ángulo coterminal dentro del rango de 0° a 360° que trabajar con un ángulo que esté fuera de ese rango.
Cualquier ángulo tiene infinitos ángulos coterminales porque cada vez que sumamos 360° a ese ángulo, o le restamos 360°, el valor resultante tiene un lado terminal en el mismo lugar. Por ejemplo, 100° y 460° son coterminales por esta razón, al igual que -260°. Reconocer que cualquier ángulo tiene infinitos ángulos coterminales explica la forma repetitiva en los gráficos de las funciones trigonométricas.
El ángulo de referencia de un ángulo es la medida del menor ángulo agudo positivo
formado por el lado terminal del ángulo
y el eje horizontal. Por lo tanto, los ángulos de referencia positivos tienen lados terminales que se encuentran en el primer cuadrante y pueden utilizarse como modelos de ángulos en otros cuadrantes. Observe en la los ejemplos de ángulos de referencia para ángulos en diferentes cuadrantes.
### Calcular ángulos coterminales, medidos en radianes
Podemos calcular los ángulos coterminales medidos en radianes de la misma manera que lo hemos hecho mediante el empleo de grados. En ambos casos, calculamos los ángulos coterminales al sumar o restar una o más rotaciones completas.
### Determinar la longitud de un arco
Recordemos que la medición de radián
de un ángulo se definió como el cociente de la longitud de arco
de un arco circular al radio
del círculo,
A partir de esta relación, podemos calcular la longitud de arco a lo largo de un círculo, dado un ángulo.
### Calcular el área de un sector de un círculo
Además de la longitud de arco, también podemos utilizar los ángulos para hallar el área de un sector de un círculo. Un sector es una región de un círculo delimitado por dos radios y el arco intersecado, como una porción de pizza o pastel. Recordemos que el área de un círculo de radio
se puede hallar con la fórmula
Si los dos radios forman un ángulo de
medido en radianes, entonces
es la relación entre la medida del ángulo y la medida de una rotación completa y es también, por tanto, la relación entre el área del sector y el área del círculo. Así, el área de un sector es la fracción
multiplicado por toda la superficie. (Recuerde siempre que esta fórmula solo procede si
está en radianes).
### Utilizar la velocidad lineal y angular para describir el movimiento en una trayectoria circular
Además de calcular el área de un sector, podemos utilizar los ángulos para describir la velocidad de un objeto en movimiento. Un objeto que viaja en una trayectoria circular tiene dos tipos de velocidad. La velocidad lineal es la velocidad a lo largo de una trayectoria recta y se determina por la distancia que recorre (su desplazamiento) en un intervalo determinado. Por ejemplo, si una rueda con un radio de 5 pulgadas gira una vez por segundo, un punto en el borde de la rueda se mueve una distancia igual a la circunferencia, o
pulgadas, cada segundo. Así que la velocidad lineal del punto es
in/s. La ecuación de la velocidad lineal es la siguiente, donde
es la velocidad lineal,
es el desplazamiento, y
es el tiempo.
La velocidad angular es el resultado del movimiento circular y se determina por el ángulo por el que gira un punto en un intervalo determinado. En otras palabras, la velocidad angular es la rotación angular por unidad de tiempo. Así, por ejemplo, si un engranaje realiza una rotación completa cada 4 segundos, podemos calcular su velocidad angular como
90 grados por segundo. La velocidad angular puede indicarse en radianes por segundo, rotaciones por minuto o grados por hora, por ejemplo. La ecuación de la velocidad angular es la siguiente, donde
(leído como omega) es la velocidad angular,
es el ángulo recorrido, y
es el tiempo.
Al combinar la definición de velocidad angular con la ecuación de la longitud de arco,
hallamos una relación entre las velocidades angulares y lineales. La ecuación de la velocidad angular puede resolverse para
lo que arroja
Sustituyendo esto en la ecuación de la longitud de arco se obtiene:
Sustituyendo esto en la ecuación de la velocidad lineal se obtiene:
Las ruedas hidráulicas se utilizan desde hace miles de años para transferir la potencia del agua que fluye a otros dispositivos. La siguiente imagen muestra el diseño de la rueda hidráulica romana del siglo III en Hierápolis, una ciudad de la actual Turquía. El agua hacía girar la rueda, que a su vez hacía girar una manivela conectada a dos sierras utilizadas para cortar bloques. Estos elementos de diseño se utilizaron en aplicaciones de ruedas hidráulicas en todo el mundo, e incluso facilitaron el principio subyacente de la máquina de vapor, inventada unos 1.500 años más tarde.
### Ecuaciones clave
### Conceptos clave
1. Un ángulo se forma a partir de la unión de dos rayas, al mantener fijo el lado inicial y rotar el lado terminal. La cantidad de rotación determina la medida del ángulo.
2. Un ángulo está en posición estándar si su vértice está en el origen y su lado inicial se encuentra a lo largo del eje positivo x. Un ángulo positivo se mide en sentido contrario a las agujas del reloj desde el lado inicial y un ángulo negativo se mide en sentido de las agujas del reloj.
3. Para dibujar un ángulo en posición estándar, dibuje el lado inicial a lo largo del eje positivo x y luego coloque el lado terminal de acuerdo con la fracción de una rotación completa que el ángulo representa. Vea el .
4. Además de en grados, la medida de un ángulo puede describirse en radianes. Vea el .
5. Para convertir entre grados y radianes, utilice la proporción
Vea el y el .
6. Dos ángulos que tienen el mismo lado terminal reciben el nombre de ángulos coterminales.
7. Podemos hallar ángulos coterminales si sumamos o restamos 360° o
Vea el y el .
8. Los ángulos coterminales se pueden hallar mediante el empleo de radianes, al igual que se hace con los grados. Vea el .
9. La longitud de un arco de círculo es una fracción de la circunferencia del círculo completo. Vea el .
10. El área del sector es una fracción del área del círculo completo. Vea el .
11. Un objeto que se mueve en una trayectoria circular tiene tanto velocidad lineal como angular.
12. La velocidad angular de un objeto que se desplaza en una trayectoria circular es la medida del ángulo por el que gira en una unidad de tiempo. Vea el .
13. La velocidad lineal de un objeto que recorre una trayectoria circular es la distancia que recorre en una unidad de tiempo. Vea el .
### Ejercicios de la sección
### Verbales
### Gráficos
En los siguientes ejercicios, dibuje un ángulo en posición estándar con la medida dada.
En los siguientes ejercicios, consulte la . Redondee a dos decimales.
En los siguientes ejercicios, consulte la . Redondee a dos decimales.
### Algebraicos
En los siguientes ejercicios, convierta los ángulos en radianes a grados.
En los siguientes ejercicios, convierta los ángulos en grados a radianes.
En los siguientes ejercicios, utilice la información dada para determinar la longitud de un arco de un círculo. Redondee a dos decimales.
En los siguientes ejercicios, utilice la información dada para calcular el área del sector. Redondee a cuatro decimales.
En los siguientes ejercicios, calcule el ángulo entre 0° y 360° que es coterminal al ángulo dado.
En los siguientes ejercicios, calcule el ángulo entre 0 y
en radianes que es coterminal al ángulo dado.
### Aplicaciones en el mundo real
### Extensiones
|
# Funciones trigonométricas
## Círculo unitario: funciones seno y coseno
¿Busca emociones? Entonces considere un paseo en el Ain Dubai, la rueda de la fortuna más alta del mundo. Ubicada en Dubai, la ciudad más poblada y el centro financiero y turístico de los Emiratos Árabes Unidos, la rueda de la fortuna se eleva a 820 pies, unas 1,5 décimas de milla. Descrita como una rueda de observación, los pasajeros disfrutan de unas vistas espectaculares del Burj Khalifa (el edificio más alto del mundo) y de Palm Jumeirah (un archipiélago construido por el hombre que alberga más de 10.000 personas y 20 complejos turísticos) mientras viajan desde el suelo hasta la cima y vuelven a bajar en un patrón repetitivo. En esta sección, examinaremos este tipo de movimiento giratorio alrededor de un círculo. Para ello, tenemos que definir primero el tipo de círculo y, a continuación, situar ese círculo en un sistema de coordenadas. Entonces podemos hablar del movimiento circular en términos de los pares de coordenadas.
### Hallar los valores de la función para el seno y el coseno
Para definir nuestras funciones trigonométricas, empezamos por dibujar un círculo unitario, un círculo centrado en el origen con radio 1, como se muestra en la . El ángulo (en radianes) que
interseca forma un arco de longitud
Si utilizamos la fórmula
y en el entendido de que
vemos que, para un círculo unitario,
Recordemos que los ejes de la x y de la y dividen el plano de coordenadas en cuatro cuartos llamados cuadrantes. Marcamos estos cuadrantes para imitar la dirección que barrería un ángulo positivo. Los cuatro cuadrantes se denominan I, II, III y IV.
Para cualquier ángulo
podemos marcar la intersección del lado terminal y el círculo unitario por sus coordenadas,
Las coordenadas de la
como
serán las salidas de las funciones trigonométricas
y
respectivamente. Esto significa que
y
### Definir las funciones seno y coseno
Ahora, que tenemos marcado nuestro círculo unitario, podemos aprender cómo las coordenadas
se relacionan con la longitud del arco y el ángulo. La función seno relaciona un número real
con la coordenada de la y en el punto donde el ángulo correspondiente interseca el círculo unitario. Más precisamente, el seno de un ángulo
es igual al valor y del punto final en el círculo unitario de un arco de longitud
En la , el seno es igual a
Al igual que en todas las funciones, la función seno tiene una entrada y una salida. Su entrada es la medida del ángulo; su salida es la coordenada de la y en el punto correspondiente en el círculo unitario.
La función coseno de un ángulo
equivale al valor x del punto final en el círculo unitario de un arco de longitud
En la , el coseno es igual a
En el entendido de que el seno y el coseno son funciones, no es necesario escribirlas siempre con paréntesis:
es lo mismo que
y
es lo mismo que
Igualmente,
es una notación abreviada de uso común para
Tenga en cuenta que muchas calculadoras y computadoras no reconocen la notación abreviada. En caso de duda, utilice los paréntesis adicionales cuando introduzca los cálculos en una calculadora o una computadora.
### Hallar el seno y coseno de los ángulos en un eje
En los ángulos cuadrangulares, el punto correspondiente en el círculo unitario cae en el eje x o en el eje y. En ese caso, podemos calcular fácilmente el coseno y el seno a partir de los valores de
como
### La identidad pitagórica
Ahora que podemos definir el seno y el coseno, aprenderemos cómo se relacionan entre sí y con el círculo unitario. Recordemos que la ecuación del círculo unitario es
Dado que
y
podemos sustituir por
como
para obtener
Esta ecuación,
se conoce como la identidad pitagórica. Vea la .
Podemos utilizar la identidad pitagórica para hallar el coseno de un ángulo si conocemos el seno, y viceversa. Sin embargo, ya que la ecuación arroja dos soluciones, necesitamos conocer más acerca del ángulo para elegir la solución con el signo correcto. Si conocemos el cuadrante donde se encuentra el ángulo, podemos elegir fácilmente la solución correcta.
### Hallar el seno y el coseno de los ángulos especiales
Ya hemos aprendido algunas propiedades de los ángulos especiales, tales como la conversión de radianes a grados. También podemos calcular el seno y el coseno de los ángulos especiales con la identidad pitagórica y nuestro conocimiento acerca de los triángulos.
### Hallar el seno y el coseno de los ángulos de 45°
En primer lugar, examinaremos los ángulos de
o
como se muestra en la . Un triángulo de
es isósceles, por lo que las coordenadas de la x y de la y en el punto correspondiente en el círculo son las mismas. Ya que los valores de x y de y son iguales, los valores del seno y del coseno también serán iguales.
A
, que es de 45 grados, el radio del círculo unitario biseca el primer ángulo cuadrangular. Esto significa que el radio se encuentra a lo largo de la línea
Un círculo unitario tiene un radio igual a 1. Así, el triángulo rectángulo formado bajo la línea
tiene lados
como
y un radio = 1. Vea la
A partir del teorema de Pitágoras obtenemos
Al sustituir
obtenemos
Al combinar términos similares obtenemos
Asimismo, al resolver para
obtenemos
En el cuadrante I,
En
o 45 grados,
Si entonces racionalizamos los denominadores, obtenemos
Por lo tanto, las coordenadas
de un punto en un círculo de radio
en un ángulo de
son
### Hallar el seno y el coseno de los ángulos de 30º y 60º
A continuación, hallaremos el coseno y el seno en un ángulo de
o
. En primer lugar, dibujaremos un triángulo dentro de un círculo con un lado en un ángulo de
y otro lado en un ángulo de
como se muestra en la . Si los dos triángulos rectángulos resultantes se combinan en un triángulo grande, observe que los tres ángulos de este triángulo mayor serán
como se muestra en la .
Debido a que todos los ángulos son iguales, los lados también son iguales. La línea vertical tiene longitud
y debido a que los lados son todos iguales, también podemos concluir que
o
Dado que
,
Además, ya que
en nuestro círculo unitario,
Con la identidad pitagórica podemos calcular el valor del coseno.
Las coordenadas
para el punto en un círculo con radio
en un ángulo de
son
En
(60°), el radio del círculo unitario, 1, sirve como hipotenusa de un triángulo rectángulo de 30-60-90 grados,
como se muestra en la . El ángulo
tiene medida
En el punto
dibujamos un ángulo
con medida de
Sabemos que los ángulos de un triángulo suman
por lo que la medida del ángulo
también es
Ahora tenemos un triángulo equilátero. Ya que cada lado del triángulo equilátero
tiene la misma longitud, y sabemos que un lado es el radio del círculo unitario, todos los lados deberán tener longitud 1.
La medida del ángulo
es 30°. Entonces, si es doble, el ángulo
es de 60°.
es la bisectriz perpendicular de
por lo que corta
por la mitad. Esto significa que
es
del radio, o
Observe que
es la coordenada de la x en el punto
que se encuentra en la intersección del ángulo de 60° con el círculo unitario. Esto nos da un triángulo
con hipotenusa de 1 y lado
de longitud
A partir del teorema de Pitágoras, obtenemos
Sustituyendo
obtenemos
Resuelva para
obtenemos
Dado que
tiene el lado terminal en el cuadrante I, donde la coordenada de la y es positiva, elegimos
el valor positivo.
A
(60°), las coordenadas
para el punto en un círculo con radio
en un ángulo de
son
para que hallemos el seno y el coseno.
Ahora hemos determinado los valores del coseno y del seno para todos los ángulos más comunes en el primer cuadrante del círculo unitario. La resume estos valores.
La muestra los ángulos comunes en el primer cuadrante del círculo unitario.
### Usar una calculadora para hallar el seno y el coseno
Para hallar el coseno y el seno de otros ángulos que no sean los ángulos especiales, recurrimos a la computadora o a la calculadora. Tenga en cuenta: La mayoría de las calculadoras pueden ponerse en modo "grados" o "radianes", lo que le indica las unidades del valor de entrada. Cuando evaluamos
en la calculadora, esta lo evaluará como el coseno de 30 grados si está en modo "grados", o el coseno de 30 radianes si está en modo "radianes".
### Identificar el dominio y rango de las funciones seno y coseno
Ahora que podemos hallar el seno y el coseno de un ángulo, tenemos que hablar del dominio y el rango. ¿Cuál es el dominio de las funciones seno y coseno? Es decir, ¿cuáles son los números mínimos y máximos que pueden ser entradas de las funciones? Debido a que los ángulos menores que 0 y los mayores que
pueden seguir graficándose en el círculo unitario y tener valores reales de
y
no hay límite inferior o superior a los ángulos que pueden introducirse en las funciones de seno y coseno. La entrada de las funciones de seno y coseno es la rotación desde el eje positivo x, y puede ser cualquier número real.
¿Cuál es el rango de las funciones seno y coseno? ¿Cuáles son los valores mínimo y máximo posibles de su salida? Podemos ver las respuestas al examinar el círculo unitario, como se muestra en la . Los límites de la coordenada de la x son
Los límites de la coordenada de la y también son
Por lo tanto, el rango de las funciones seno y coseno es
### Hallar ángulos de referencia
Hemos hablado acerca de hallar el seno y el coseno de los ángulos en el primer cuadrante, pero ¿qué pasa si nuestro ángulo está en otro cuadrante? Para cualquier ángulo dado en el primer cuadrante, hay un ángulo en el segundo cuadrante con el mismo valor del seno. Dado que el valor del seno es la coordenada de la y en el círculo unitario, el otro ángulo con el mismo seno compartirá el mismo valor y, pero tendrá el valor x opuesto. Por lo tanto, su valor del coseno será el opuesto al valor del coseno del primer ángulo.
Asimismo, habrá un ángulo en el cuarto cuadrante con el mismo coseno que el ángulo original. El ángulo con el mismo coseno compartirá el mismo valor x, pero tendrá el valor y opuesto. Por lo tanto, su valor del seno será el opuesto al valor del seno del ángulo original.
Como se muestra en la , el ángulo
tiene el mismo valor del seno que el ángulo
los valores del coseno son opuestos. El ángulo
tiene el mismo valor del coseno que el ángulo
los valores del seno son opuestos.
Recordemos que el ángulo de referencia es el ángulo agudo,
formado por el lado terminal del ángulo
y el eje horizontal. El ángulo de referencia es siempre un ángulo entre
y
o
y
radianes. Como podemos observar en la , para cualquier ángulo en los cuadrantes II, III o IV, hay un ángulo de referencia en el cuadrante I.
### Usar ángulos de referencia
Ahora tomemos un momento para reconsiderar la rueda de la fortuna que se mencionó al principio de esta sección. Supongamos que un pasajero toma una fotografía mientras la rueda de la fortuna está detenida a veinte pies sobre el nivel del suelo. A continuación, el pasajero rota tres cuartas partes del círculo. ¿Cuál es la nueva elevación del pasajero? Para responder a preguntas como esta, tenemos que evaluar las funciones seno o coseno en ángulos mayores de 90 grados o en un ángulo negativo. Los ángulos de referencia permiten evaluar las funciones trigonométricas para ángulos fuera del primer cuadrante. También se utilizan para hallar las coordenadas
para esos ángulos. Utilizaremos el ángulo de referencia del ángulo de rotación combinado con el cuadrante en el que se encuentra el lado terminal del ángulo.
### Usar ángulos de referencia para evaluar funciones trigonométricas
Podemos hallar el coseno y el seno de cualquier ángulo en cualquier cuadrante si conocemos el coseno o el seno de su ángulo de referencia. Los valores absolutos del coseno y del seno de un ángulo son los mismos que los del ángulo de referencia. El signo depende del cuadrante del ángulo original. El coseno será positivo o negativo, dependiendo del signo de los valores de x en ese cuadrante. El seno será positivo o negativo, dependiendo del signo de los valores de y en ese cuadrante.
### Usar ángulos de referencia para hallar coordenadas
Ahora que hemos aprendido a calcular los valores del coseno y del seno para los ángulos especiales del primer cuadrante, podemos utilizar la simetría y los ángulos de referencia para completar los valores del coseno y del seno en el resto de los ángulos especiales del círculo unitario. Se muestran en la . Tómese su tiempo para aprender las coordenadas
de todos los ángulos mayores en el primer cuadrante.
Además de aprender los valores de los ángulos especiales, podemos utilizar los ángulos de referencia para hallar coordenadas
en cualquier punto del círculo unitario, con lo que sabemos de los ángulos de referencia junto con las identidades
Primero, hallamos el ángulo de referencia correspondiente al ángulo dado. A continuación, tomamos los valores del seno y del coseno del ángulo de referencia y les atribuimos los signos correspondientes a los valores de y y de x del cuadrante.
### Ecuaciones clave
### Conceptos clave
1. La búsqueda de los valores de las funciones del seno y del coseno comienza al dibujar un circulo unitario, centrado en el origen y con un radio de 1 unidad.
2. Utilizando el círculo unitario, el seno de un ángulo
es igual al valor y del punto final en el círculo unitario de un arco de longitud
mientras que el coseno de un ángulo
es igual al valor x del punto final. Vea el .
3. Los valores del seno y del coseno se determinan más directamente cuando el punto correspondiente del círculo unitario cae sobre un eje. Vea el .
4. Cuando se conoce el seno o el coseno, podemos utilizar la identidad pitagórica para hallar el otro. La identidad pitagórica también sirve para determinar el seno y coseno de ángulos especiales. Vea el .
5. Las calculadoras y los programas de gráficos son útiles para hallar el seno y el coseno si se conoce el procedimiento adecuado para introducir la información. Vea el .
6. El dominio de las funciones seno y coseno son todos los números reales.
7. El rango de las funciones seno y coseno es
8. El seno y el coseno de un ángulo tienen el mismo valor absoluto que el seno y el coseno de su ángulo de referencia.
9. Los signos del seno y del coseno se determinan a partir de los valores de x y de y en el cuadrante del ángulo original.
10. El ángulo de referencia es el ángulo de tamaño,
formado por el lado terminal del ángulo
y el eje horizontal. Vea el .
11. Los ángulos de referencia pueden utilizarse para hallar el seno y el coseno del ángulo original. Vea el .
12. Los ángulos de referencia también se pueden utilizar para hallar las coordenadas de un punto en un círculo. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, utilice el signo dado de las funciones seno y coseno para hallar el cuadrante en el que se asienta el punto terminal determinado por .
En los siguientes ejercicios, halle el valor exacto de cada función trigonométrica.
### Numéricos
En los siguientes ejercicios, indique el ángulo de referencia para el ángulo dado.
En los siguientes ejercicios, halle el ángulo de referencia, el cuadrante del lado terminal y el seno y coseno de cada ángulo. Si el ángulo no es uno de los ángulos especiales del círculo unitario, utilice la calculadora y redondee a tres decimales.
En los siguientes ejercicios, halle el valor solicitado.
### Gráficos
En los siguientes ejercicios, utilice el punto dado en el circulo unitario para hallar el valor del seno y el coseno de
### En tecnología
En los siguientes ejercicios, utilice una calculadora gráfica para evaluar.
### Extensiones
En los siguientes ejercicios, evalúe.
### Aplicaciones en el mundo real
En los siguientes ejercicios, utilice este escenario: Un niño se sube a un carrusel que tarda un minuto en dar una vuelta. El niño entra en el punto
es decir, en la posición hacia el norte. Supongamos que el carrusel gira en sentido contrario a las agujas del reloj. |
# Funciones trigonométricas
## Las otras funciones trigonométricas
Una rampa para sillas de ruedas que cumpla las normas de la Ley de Estadounidenses con Discapacidades debe formar un ángulo con el suelo cuya tangente sea
o menos, independientemente de su longitud. Una tangente representa un cociente, por lo que esto significa que por cada 1 pulgada de subida, la rampa deberá tener 12 pulgadas de recorrido. Las funciones trigonométricas nos permiten especificar las formas y proporciones de los objetos, independientemente de las dimensiones exactas. Ya hemos definido las funciones seno y coseno de un ángulo. Aunque el seno y el coseno son las funciones trigonométricas más utilizadas, existen otras cuatro. Juntas forman el conjunto de las seis funciones trigonométricas. En esta sección, investigaremos las funciones restantes.
### Hallar los valores exactos de las funciones trigonométricas secante, cosecante, tangente y cotangente
Para definir el resto de las funciones, volveremos a dibujar un círculo unitario con un punto
correspondiente a un ángulo de
como se muestra en la . Al igual que con el seno y el coseno, podemos utilizar las coordenadas
para hallar las otras funciones.
La primera función que definiremos es la tangente. La tangente de un ángulo es el cociente entre el valor de y, y el valor de x del punto correspondiente del círculo unitario. En la , la tangente del ángulo
es igual a
Debido a que el valor de y es igual al seno de
y el valor de x es igual al coseno de
la tangente del ángulo
también puede definirse como
La función tangente se abrevia como
Las tres funciones restantes pueden expresarse como recíprocas de las funciones que ya hemos definido.
1. La función secante es la recíproca de la función coseno. En la , la secante del ángulo
es igual a
La función secante se abrevia como
2. La función cotangente es la recíproca de la función tangente. En la , la cotangente del ángulo
es igual a
La función cotangente se abrevia como
3. La función cosecante es la recíproca de la función seno. En la , la cosecante del ángulo
es igual a
La función cosecante se abrevia como
Ya que conocemos los valores del seno y del coseno para los ángulos comunes del primer cuadrante, también podemos calcular los demás valores de la función para esos ángulos al establecer
igual al coseno, así como
igual al seno y luego usar las definiciones de tangente, secante, cosecante y cotangente. Los resultados se indican en la .
### Usar ángulos de referencia para evaluar la tangente, la secante, la cosecante y la cotangente
Podemos evaluar funciones trigonométricas de ángulos fuera del primer cuadrante utilizando ángulos de referencia, como ya lo hemos hecho con las funciones seno y coseno. El procedimiento es el mismo: Halle el ángulo de referencia formado por el lado terminal del ángulo dado con el eje horizontal. Los valores de la función trigonométrica para el ángulo original serán los mismos que los del ángulo de referencia, excepto el signo positivo o negativo, que viene determinado por los valores de x y de y en el cuadrante original. La muestra qué funciones son positivas en qué cuadrante.
Para recordar cuáles de las seis funciones trigonométricas son positivas en cada cuadrante, podemos utilizar la frase nemotécnica: “A Smart Trig Class” (Una clase de trigonometría inteligente). Cada una de las cuatro palabras de la frase corresponde a uno de los cuatro cuadrantes, empezando por el cuadrante I y girando en sentido contrario a las agujas del reloj. En el cuadrante I, que es "A", “ll” (todas las) seis funciones trigonométricas son positivas. En el cuadrante II, "Smart”, solo el eno y su función recíproca, la cosecante, son positivos. En el cuadrante III, "Trig”, solo la angente y su función recíproca, cotangente, son positivas. Por último, en el cuadrante IV, "Class,” (clase) solo el oseno y su función recíproca, la secante, son positivos.
### Usar funciones trigonométricas pares e impares
Para utilizar libremente nuestras seis funciones trigonométricas con entradas de ángulos positivos y negativos, debemos examinar cómo trata cada función una entrada negativa. Resulta que hay una diferencia importante entre las funciones en este respecto.
Considere la función
que se muestra en la . El gráfico de la función es simétrico con respecto al eje y. A lo largo de la curva, dos puntos cualesquiera con valores de x opuestos tienen el mismo valor de función. Esto coincide con el resultado del cálculo:
y así sucesivamente. Así que
es una función par, una función tal que dos entradas que son opuestas tienen la misma salida. Esto significa que
Consideremos ahora la función
que se muestra en la . El gráfico no es simétrico con respecto al eje y. A lo largo del gráfico, dos puntos cualesquiera con valores de x opuestos también tienen valores de y opuestos. Así que
es una función impar, una función tal que dos entradas que son opuestas tienen salidas que también son opuestas. Esto significa que
Podemos comprobar si una función trigonométrica es par o impar al dibujar un círculo unitario con un ángulo positivo y otro negativo, como en la . El seno del ángulo positivo es
El seno del ángulo negativo es -y. La función seno, entonces, es una función impar. Podemos probar cada una de las seis funciones trigonométricas de esta manera. Los resultados se indican en la .
### Reconocer y utilizar las identidades fundamentales
Hemos explorado una serie de propiedades de las funciones trigonométricas. Ahora, podemos llevar las relaciones un paso más allá y derivar algunas identidades fundamentales. Las identidades son enunciados verdaderos para todos los valores de la entrada sobre la que se definen. Normalmente, las identidades se derivan de definiciones y relaciones que ya conocemos. Por ejemplo, la identidad pitagórica, que aprendimos antes, se deriva del teorema de Pitágoras y de las definiciones de seno y coseno.
### Formas alternativas de la identidad pitagórica
Podemos utilizar estas identidades fundamentales para derivar formas alternativas de la identidad pitagórica,
Una forma se obtiene al dividir ambos lados entre
La otra forma se obtiene al dividir ambos lados entre
Como hemos comentado al inicio del capítulo, la función que repite sus valores en intervalos regulares se conoce como función periódica. Las funciones trigonométricas son periódicas. Para las cuatro funciones trigonométricas, seno, coseno, cosecante y secante, la revolución de un círculo o
dará lugar a las mismas salidas para estas funciones. Igualmente, para la tangente y la cotangente, solo media revolución dará lugar a las mismas salidas.
Otras funciones también pueden ser periódicas. Por ejemplo, la duración de los meses se repite cada cuatro años. Si los valores de
representa el tiempo de duración, medido en años, y
representa el número de días en el mes de febrero, entonces
Este patrón se repite una y otra vez a lo largo del tiempo. En otras palabras, cada cuatro años, es seguro que febrero tenga el mismo número de días que tenía 4 años antes. El 4 es el menor número positivo que satisface esta condición y se denomina periodo. Un periodo es el intervalo más corto en el que una función realiza un ciclo completo; en este ejemplo, el período es 4 y representa el tiempo que tardamos en estar seguros de que febrero tendrá el mismo número de días.
### Evaluar funciones trigonométricas con la calculadora
Hemos aprendido a evaluar las seis funciones trigonométricas para los ángulos comunes del primer cuadrante y a utilizarlas como ángulos de referencia para los ángulos de otros cuadrantes. Para evaluar las funciones trigonométricas de otros ángulos, utilizamos una calculadora científica o gráfica o un programa informático. Si la calculadora tiene un modo de grados y un modo de radianes, confirme que haya elegido el modo correcto antes de realizar un cálculo.
Evaluar una función tangente con una calculadora científica en lugar de una calculadora gráfica o un sistema de álgebra computacional es como evaluar un seno o un coseno: Introduzca el valor y pulse la tecla TAN. Para las funciones recíprocas, es posible que no haya determinadas teclas dedicadas que indiquen CSC, SEC o COT. En ese caso, la función deberá evaluarse como el recíproco del seno, del coseno o de la tangente.
Si necesitamos trabajar con grados y nuestra calculadora o programa informático no tienen modo de grados, podemos introducir los grados multiplicados por el factor de conversión
para convertir los grados en radianes. Para hallar la secante de
podríamos pulsar
o
### Ecuaciones clave
### Conceptos clave
1. La tangente de un ángulo es el cociente del valor de y con el valor de x del punto correspondiente en el círculo unitario.
2. La secante, la cotangente y la cosecante son recíprocas de otras funciones. La secante es la recíproca de la función coseno, la cotangente es la recíproca de la función tangente y la cosecante es la recíproca de la función seno.
3. Las seis funciones trigonométricas se determinan a partir de un punto en el círculo unitario. Vea el .
4. Las funciones trigonométricas también se determinan a partir de un ángulo. Vea el .
5. Las funciones trigonométricas de los ángulos fuera del primer cuadrante se determinan con ángulos de referencia. Vea el .
6. Se dice que una función es par si
e impar si
7. El coseno y la secante son pares; el seno, la tangente, la cosecante y la cotangente son impares.
8. Las propiedades pares e impares se utilizan para evaluar funciones trigonométricas. Vea el .
9. La identidad pitagórica permite hallar el coseno a partir del seno o el seno a partir del coseno.
10. Las identidades se utilizan para evaluar funciones trigonométricas. Vea el y el .
11. Las identidades fundamentales, como la identidad pitagórica, pueden manipularse algebraicamente para producir nuevas identidades. Vea el .
12. Las funciones trigonométricas se repiten a intervalos regulares.
13. El periodo
de una función repetitiva
es el intervalo más pequeño, tal que
para cualquier valor de
14. Los valores de las funciones trigonométricas de los ángulos especiales se determinan mediante un análisis matemático.
15. Para evaluar las funciones trigonométricas de otros ángulos, podemos utilizar una calculadora o un programa informático. Vea el .
### Ejercicios de la sección
### Verbales
### Algebraicos
En los siguientes ejercicios, halle el valor exacto de cada expresión.
En los siguientes ejercicios, utilice los ángulos de referencia para evaluar la expresión.
### Gráficos
En los siguientes ejercicios, utilice el ángulo en el círculo unitario para calcular el valor de cada una de las seis funciones trigonométricas.
### En tecnología
En los siguientes ejercicios, utilice una calculadora gráfica para evaluar.
### Extensiones
En los siguientes ejercicios, utilice las identidades para evaluar la expresión.
En los siguientes ejercicios, utilice las identidades para simplificar la expresión.
### Aplicaciones en el mundo real
|
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