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Remy Hair:
Remy Hair is a very popular type of hair used for hair extensions, but what is it?
One thing to note is that Remy Hair is not always virgin hair. (More about that later)
Once hair has been colored or chemically processed in any way short of removing the cuticles (Cuticle: The outside horny layers are composed of transparent, overlapping, protective scale-like cells, towards the hair ends. The cuticle protects the inner structure of the hair. Chemical relaxers, hair color and permanent wave solution enter the hair cortex raising the scales on the cuticle) it is referred to as Remy.
Good quality Remy Hair can be categorized in the 'premium' segment, as far as hair quality is concerned. Remy Hair has its cuticle intact and running in the same direction "unidirectional cuticle" to prevent tangling. The cuticles protect the hair from damage and give the hair its natural look.
Remy Hair is usually categorized into two types:
Remy Hair Single Drawn: This type of Remy Hair is taken out directly from the scalp by shaving the head. Care is taken to remove the very short hair, with the longer hair, found in different hair length, giving a pony-tail like appearance.
Remy Hair Double Drawn: This type of hair is the finest quality with the same wave length in a piece. The hairs are arranged with equal lengths. There should not be any short hair in a piece.
- Then the hair is further classified into grades, referred to as Quality A, B and C.
Quality A: These are an expensive type of weft hair made up of Indian Virgin Remy hair. This type is unidirectional and characterized by double drawn hair, where the whole weave is made up of hairs of the same length.
Quality B: This type is again made up of special double drawn hair, virgin Remy Hair, and is unidirectional. The length of hairs though may vary by up to 1-2 inches.
Quality C: This is the finest quality of weft hair. The cuticles are intact and are unidirectional. The entire weave contains hairs of different length.
It is important to note that Remy Hair is processed hair. This process could range from simply conditioned and hydrated, to coloured and chemically altered.


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Microsoft's free video editing software for use on Windows Vista
Windows Vista / Windows 10 / Windows 8.1 / Windows 7 / Windows 10
Microsoft Corporation
Windows Movie Maker Vista is a version of the popular Movie Maker program designed by Windows for computers running Vista. If you have a Windows 7 or Vista operating system, this program comes already installed and as part of the Windows Live Essentials package. Computers running a newer version of Windows can download a copy separately.
This is a nice program for beginners and those who want to make some basic videos at home. It works with most formats of videos and photos and allows you to change the format you use before exporting videos. The program is very easy to use too and is suitable for both adults and kids.
You have the option of searching your computer to find the video that you want to edit, but you can also use Movie Maker to capture a new video. The Edit Movie option lets you select from different video effects to give your work a professional look. It comes loaded with a number of transition effects for transitioning between different videos or photos.
With this program, you can even add your own credits to the end or title credits at the beginning to let others know that you created the video on your own. Though you can use Movie Maker with just one video, you also have the option of editing together videos to make one longer piece.
If you aren't familiar with video editing, you'll love that this program comes with some video tips for beginnings. Those tips teach you how to save your work and how to share it with others. You'll also learn how to edit shorter videos together and how to capture new videos. This section also includes practical information on adding transitions and special effects as well as credits.
The options menu includes a feature that lets you add your name as the author to each video that you make, which is helpful when uploading content to the web because it stops others from taking credit for your hard work. You can also set an auto save feature and tell the program how often you want it to save your work. This prevents you from losing a video during a power failure or a computer crash. You can also tell the program to open your most recent project each time that you launch it.
Windows Movie Maker for Vista and similar operating systems is one of the top programs for beginners who want to edit videos. It doesn't come with all the advanced features and fancy settings that others do, but it will help you create great videos with effects, transitions and even credits.
This is one of the most simple, reliable and accessible video editing software programs on the planet, and it is totally free to use and enjoy. The latest version enables users greater control of caption as well as audio editing, and it is also faster and more stable than before.
There are some really expensive video editing software programs out there today, and Windows has designed this particular program to offer a totally free and relatively comparable alternative to consider. It enables users to cut and splice video clips through a drag-and-drop interface, add captions, titles and credits while also being able to integrate several visual effects.
Users simply have to insert the video clips into the editor, and the software will convert and process them into almost any format imaginable once the project is ready for production. It also comes with a large number of presets that automatically optimize videos for popular websites such as YouTube and Facebook.
The good news is that this program is really easy to install and use because it is a Microsoft product. The bad news is that it does not include a lot of little extras that are common in more comprehensive video editing programs. Users can edit audio volume but inserting various tracks into the videos is not as easy.
It is also difficult to create complex effects, and there are only a handful that are available with the stock program. Watermarking features are lackluster, and the only way to edit videos is by cutting and pasting. The interface is also very different from professional editing tools as well.
This is a great utility for simple to intermediate editing projects, and it is very user-friendly. Anyone can get up and running with little or no experience, and the user interface is very easy to understand.
Completely free
Easy to use
Comprehensive but basic
Can produce videos in several formats
Only a few stock effects are available
Limited editing features
Great Presentation Companion to PowerPoint!
Powerful tool used to make top-notch presentations
Collection of features that let you turn photos into stunning slideshows
Create high quality moving visuals for logos and texts
Great Presentation Companion to PowerPoint!
Prezi desktop
Powerful tool used to make top-notch presentations
Wondershare DVD Slideshow Builder
Collection of features that let you turn photos into stunning slideshows
Aurora 3D Animation Maker
Create high quality moving visuals for logos and texts

subset: commoncrawl


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Label: Escape Music 2012
Review by Kimmo Toivonen
Uk's Redline may be signed to a label that's mostly known for its' more melodic output, but don't mistake them for an AOR band. Nope, their sound is closer to heavy metal, maybe not by today's standards but in 1985 they would have been called a Heavy Metal band.
After listening the first few songs, I wasn't particulary impressed. Tracks like "Battle Cry" and "King Of The Mountain" are what I'd call "basic hard rock", competently played and sung but uninteresting with not much in the way of melodies. One has to wait until track four to hear any backing vocals, which makes the first tracks sound a bit dry.
A cool riff kicks off track number five, "Twisting The Knife", and it feels like I had put on another album! There's backing vocals, there's melodies and hooks! Not to mention a very appealing "mid-eighties US metal" vibe - I'm thinking of such bands as Icon, King Kobra, Dokken...
The dramatic semi-ballad "Cold Silence" benefits of the string arrangement created by one Jimmy Lea of Slade fame and gets "a thumbs up", even though I still think it could've used a stronger chorus hook. The 80'ies them continues with "High Price To Pay" which has the kind of sequencer effect that ZZ Top favoured on their mega-albums back then. Kinda cool, but the chorus is a bit of letdown again.
The album's standout for me is definitely "Edge Of Falling", which beats the current Dokken line-up in their own game - cool guitars, great hook, fine vocal performance. This song sounds more like vintage Dokken than anything that Don Dokken has released lately, yet it doesn't rip off any of their songs directly. Well, that "Why Baby Why" line does sound familiar, but let's call it a tribute!
"Some Kinda Mean" is a good song too with sharp riffing from the axe duo of A.D. and Steve Petty, while the band's potential live anthem "We Came To Rock" closes the album on a positive note.
After the not-so-good start this album turned out to be a decent one after all. A special mention must go to the production team, the album sounds great, even though backing vocals are used way too sparingly on the first few songs. Speaking of vocals, Kez Taylor must be mentioned as well, his solid performance elevates the weaker tracks to a higher level. And now that I've started to name the band members, Mark Biddiscombe (drums) and Steve Hill (bass) is the rhythm section, solid as a rock...
For the next album, I hope that the band cherishes their melodic side and writes some killer chorus hooks. But still, this is a decent start.


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Psychopsis Mendenhall 'Hildos' in bloom
Orchids of the "Psychopsis" genus are aptly called the "Butterfly Orchids." They bloom with large singular flowers on tall arching stems, which really do look like some exotic insect in flight.
Psychopsis Mendenhall 'Hildos'
I posted about my Psychopsis Mendenhall 'Hildos' forming a bud back in early December. The orchid was in spike when I purchased it last June, meaning that the flower spike took over 7 months to mature. Fortunately, these orchids are known to reflower off the same spike for many years, so the subsequent waits should not be this long.
The flower opened about two weeks ago, and is still going strong. The bloom is 5 inches tall and 4 inches wide--a little less than the 6" I've seen reported elsewhere online. The flower is colored orange on yellow. I was expecting a redder orange, as seen in photo here. There does seem to be variation in the depth of the color, which may be caused by differences in growing conditions. I did not notice any scent.
Psychopsis Mendenhall 'Hildos'
One outstanding feature of the bloom is that the flower is very three-dimensional. The petals flex backwards, and the 'skirt' curls into a circle, creating a challenge for a would-be-photographer. None of these pictures look quite right if I were to compare them against the original, and I think the problem lies with the fact that the photos flatten the flower.
I also really liked the many textures on the flower. The lip is shiny like hard plastic. The skirt has an iridescent quality to it. Meanwhile the two lateral petals have a more velvety texture. All around, a very interesting flower!
New roots on Psychopsis Mendenhall 'Hildos'
Surprisingly, the orchid itself has thrived during the 3 weeks I was away. Its pot was on the bottom of the terrarium, submerged in about 2 inches of water, which created a constant source of moisture for the orchid via capillary action. I think semihydroponic culture is based on a similar premise. The media was moist when I came back home, and I found many fresh green roots growing throughout the pot. This makes a great improvement over the root rot last October.
Some more photos just for fun:
Psychopsis Mendenhall 'Hildos' lip closeup
Psychopsis Mendenhall 'Hildos' skirt closeup
Psychopsis Mendenhall 'Hildos' head on view


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But defending is not just about reacting when you've lost the ball, but being proactive when you're in possession.
More after the break
"Everybody assumes that defending is all about when the opposition's got the ball. It isn't – it's about getting your right positions when you've got the ball," says Taylor.
In this video Taylor maps out the defensive positions a team needs to take up to protect against a counter attack.
The Freeradio Grass Roots Football Show is the biggest grass roots football event in Europe. For more information on this year's event at the Birmingham NEC on May 25-27 visit www.grassrootsfootball.co.uk
Also see:
Defending corners: The essentials
Last 5 mins and you need a goal
Graham Taylor: playing the long ball
Graham Taylor: coping with criticism


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Energy is Key to Smarter Cities Energy is an important parameter of a smart city. In order to meet sustainability goals and ensure long-term resiliency, city planners are looking for solutions to reduce greenhouse gas emissions, optimize local resources, enhance economic resiliency and strengthen critical energy infrastructure. On April 19th, the Open Innovation Club will host … Continue reading
Category Archives: Smart City
The Future of Urban Mobility
Urban population and density is growing. Current transportation infrastructure cannot support an increase in vehicles on the road, hence the importance of improving public transit options and the efficiency of current vehicles in circulation. Mobility as-a-Service The car of the future is connected, with direct access to the internet and interactions with other connected objects … Continue reading
The Economics of Sharing: Airbnb breaks all records in the Paris Region
Paris is now the most popular city in the world on Airbnb. And France is the second largest market for the short-term housing rental website. Spotlight on the success story of this global leader of the sharing economy. Just a few figures suffice to measure the extraordinary success of California startup Airbnb since its Paris … Continue reading
Smart Cities And Smart Energy Conferences in the U.S. in 2016
Technology and connectivity is transforming our daily lives, particularly cities and energy. The way we live, move, work and play in urban settings is changing on a daily basis, and the way energy is generated, delivered and consumed is also evolving. Whether you are an entrepreneur, a startup, a large corporation, an academic or just … Continue reading
"Startup City" and the Importance of Public-Private Partnerships for the Future of Urban Livability and Mobility
(Photo: Cover of Startup City) I recently attended a talk by Gabe Klein on his new book "Startup City: Inspiring Private & Pubic Entrepreneurship, Getting Projects Done and Having Fun". Technology and automation have led to new business models and allowed innovative solutions to emerge, which have changed consumption habits and behavior of citizens … Continue reading
Two Inria technologies rewarded at the IPSO Challenge 2015 in San Jose
The Designer of Things conference took place last week in San Jose. This was the opportunity for designers and developers on the cutting edge of future tech space to collaborate, learn, exchange ideas and forward the conversation about wearable tech, 3D printing and IoT. During the conference, 10 semi-finalists for the 2015 IPSO CHALLENGE showcased … Continue reading
The City of the Future is Smart, Connected and Collaborative
According to the Smart Cities Council, a smart city gathers data from smart devices and sensors embedded in its roadways, power grids, buildings and other assets. It shares that data via a smart communications system that is typically a combination of wired and wireless. It then uses smart software to create valuable information and digitally enhanced services. For a city to be … Continue reading


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We find many customers like to share their experiences with others so they can benefit from these unique all natural products.
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Folks, I am worried for the future of America. We all know that the only things we have going for us as a nation are our competitive sports, especially football. I mean, who doesn't love watching grown men hug each other and roll around on the ground in an effort to make sure the right person gets the balls?
Well, folks, all of that is in danger now! On Sunday, a former defensive end for Missouri who was considered one of the best players of 2013, Michael Sam, announced that he was gay. Sam is considered to be one of the top draft picks – we cannot allow this to happen!
America, football is sacred. There is nothing 'gay' about it. I mean, what is more masculine than a bunch of dudes in hot pants bending over in front of each in order to pass a ball between their legs? Or how about the masculine, pro-hetero tradition of showering together? If we let gay men on the team, how will we know that congratulatory slap on the ass for a play well-done doesn't have ulterior motives?
Think about it – football doesn't need controversy! It has a reputation for hiring men who are above reproach, like: OJ Simpson, Michael Vick, Benjamin Roethlis-howeveryouspellhisname, that one guy from the Giants who shot himself in the leg, or that guy from Cleveland who assaulted a member of law enforcement at the Ft. Lauderdale airport.
Those guys are model citizens! We can't risk bringing a player onboard who could demoralize and stigmatize the entire League! By having an openly gay player, you risk the world finding out that gay men are capable of doing the exact same things as straight men! If Sam continued to play as well for the pros as he did in college, then the NFL could be forced to hire more gay men to play the game. This would be a travesty because gay men have a reputation for being pro-feminist, compassionate, anti-misogynist, and friendly people – there is no room for any of that in professional football!
Sports are supposed to be angry and violent! Allowing happy people to play risks diluting it and then before you know it, all we are watching is a contact sport that consists of playful slapping and random giggles – kind of like the Lingerie League…wait, the Lingerie League is amazing to watch..is it getting hot in here?
But I digress, the worst part is, if more gay men are playing football, then more gay men may start watching football. This might mean male cheerleaders in skimpy outfits shouting for to the crowd that they "are going to take it to the end." That is horrifying, right?
To top it all off, other players don't want it! I mean, this isn't the Flintstones – no one wants to "have a gay 'ole time." Remember when Chris Culliver of the 49ers said, he "wouldn't play with a gay teammate?" That's because he would rather get his rocks off with his straight buddies who don't openly show that they enjoy it! Plus, look at how Sam's college peers reacted in August of last year to his announcement to them that he was gay, they went on to be 12-2 for the season. They were so demoralized that they lost two games!
America, we have to stop this now. First it was military service, then it was marriage…and before long, the LGBT community will expect the equal rights they should have had along! And then, who knows what will happen? Will women will demand to have equal rights, too? And will we wake up to find that they are playing in the NFL!
After all, this is America…if we wanted everyone to be treated the same regardless of race, creed, sexuality, or religion…we would move to Canada.


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Dear fellow T-Is and professionals
Please find the enclosed report titled "ThE OmInOuS Parallels" concerning The United States and Worlds Silent Holocaust that discusses the issues of government harassment against U.S. Citizen's using a combination of Military Grade Electronic and Psychological Torture to subjugate and destroy people's lives both within the United States and abroad.
For emphasis, there has never been nor is there now any sane justification for this type of torture within a civilized society, more especially a democratic one. And before anyone insinuates that I'm anti government or a radical I am not. The record will show that I've been a successful and ethical businessperson, and have proven myself in both the U.S. armed forces and academia.
That being said part of the T-I's torture is that we are always classified as being crazy; moreover, when the subject of mind control and this type of harassment is brought up it's always discarded and considered a myth.First, let's make clear of who's really crazy and THEY are those person's who HIDE behind their top secret clearance that allows them to destroys innocent lives all the while claiming that it's in the best interest of our National Security, should they get caught in their crime. [Continued]
[click on the above title to download this entire document in .doc format]
===snipped===>"And Ye Shall Know The Truth And The Truth Shall Set You Free"
WAKE UP AMERICA....ITs OUR COUNTRY!!!
Love "Light" and Energy_Don
Proxy: http://tools.rosinstrument.com/cgi-bin/fpc.pl


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Sweet, supportive, loving, incredible Brave Girls….you know that all around you and all around the world Brave Girls just like you are struggling. They don't show it, but inside they feel it. What if you knew? What if you could see into their hearts? What if she was your sister or your daughter or your mom. Today our question is…
What would you tell a Brave Girl who has lost her hope?
Remember…she is real. What would you tell her if you had a quiet minute together? Leave a comment and tell her…she'll find it.


text:
Download EBOOK Boy in Darkness PDF for free
Category: Children's Books
The author of the book: Mervyn Peake
Format files: PDF, EPUB, TXT, DOCX
The size of the: 916 KB
Language: English
Edition: Hodder Children's Books
Date of issue: 1 June 1999
Description of the book "Boy in Darkness":Titus escapes for adventure, but tired and suffering from lack of food and water, he is captured by Hyena and Goat - a mysterious pair who hate each other. But both realize he will be the perfect sacrifice for Lamb who has waited many years for a mortal on which to use his diabolical art.
Reviews of the Boy in DarknessUntil now regarding the guide we've got Boy in Darkness comments users are yet to but quit their particular overview of the sport, or otherwise not read it however. Nevertheless, for those who have previously look at this ebook and you really are willing to produce their own discoveries well ask you to spend your time to leave an overview on our site (we are able to distribute both equally bad and the good reviews). Basically, "freedom involving speech" Most of us completely helped. Your comments to book Boy in Darkness : additional visitors can come to a decision in regards to book. Such help could make all of us more U . s .!
Mervyn PeakeSad to say, at the moment we don't possess any specifics of this performer Mervyn Peake. Nevertheless, we would appreciate for those who have almost any specifics of this, and so are ready to offer this. Send that to all of us! We've got the many look at, of course, if all the details are generally real, we are going to distribute on our web site. It is crucial for us that each one real in relation to Mervyn Peake. Most of us thank you upfront to be willing to head over to fulfill all of us!
Download EBOOK Boy in Darkness for free
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text:
Friends of the Bride 7"
Since the DiS community have been so supportive of the initial steps in my latest musical venture, you can be first to know the details of the release of our first 7" single ("Want In?" c/w "Cut Down On My Friends"). It's a limited edition of 300 and each is hand-numbered.
It'll be out on 6 NOV (But you can pre-order somehow or other when I sort out the myspace)
It'll be £1.99, free P+P (UK only)
Thanks for reading!
Best wishes,
have me one of these.
NAh mate
you're having at least 40. I don't want to have a garage full of these in two years time like with the fog band single. Need to shift some units.
you are my merch crew
I thought we weren't going to talk about this?
My initial reply was just to save this thread from embarassingly dropping off the front page with zero replies.
I want one
Give us it?
and for France ?
Do you take euros ?
Will you play in Paris someday ?
Why does it rain ?
Err not sure, Lyle,,,,
Will let you know...
Anyway I put an ad on the myspace now. Seems to be working ok.
ive not had my fog band single yet
so that's two bits of vinyl heading my way isn't it????
I hope
you'll let me know...
i get a free one
I'll have one but I won't be able to catch either of your gigs
thanks to rubbishy things like being in Brighton and another country. :-(


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Proceedings from ICME-10
Review of Math Investigations
After reading about the curriculum on the web, I find it quite interesting. The curriculum was developed in the 1990s, and it was developed with support from the National Science Foundation. From their website, I learn that the Investigations in Number, Data, and Space (which is the official name of the curriculum, it appears) was designed to:
- Support students to make sense of mathematics and learn that they can be mathematical thinkers.
- Focus on computational fluency with whole numbers as a major goal of the elementary grades.
- Provide substantive work in important areas of mathematics—rational numbers, geometry, measurement, data, and early algebra—and connections among them.
- Emphasize reasoning about mathematical ideas.
- Communicate mathematics content and pedagogy to teachers.
- Engage the range of learners in understanding mathematics.
For me as a researcher, I think it is interesting to see how much resistance these "reform curriculum" efforts encounter, and it reminds me of something I read in The teaching gap. Teaching of mathematics appears to be some kind of cultural entity, and I think Stigler and Hiebert used the notion: "cultural scripts". In order to implement a new curriculum, it is often necessary to change some of these cultural scripts, and that appears to be a rather cumbersome endeavor...
P.S. If any of you has some references to research, articles, etc. that relates to the above mentioned curriculum papers, please let me know!
New TMME monograph
- How can modelling activities be used to foster interdisciplinary projects in the school and university setting?
- How can the intricate connections between mathematics and physics be used to design and research interdisciplinary activities in schools and the university?
- How can research within the ethnomathematics domain of mathematics education be linked to critical mathematics education and interdisciplinary projects involving mathematics, art and culture?
- How can the push for mathematical and statistical literacy be connected to other subjects in the school curricula and emphasized via interdisciplinary activities?
- What are concrete examples of classroom experiments with empirical data that demonstrate new and unusual connections/relations between mathematics, arts and the sciences with implications for pedagogy?
- What is the role of technology and new ICT interfaces in linking communities of learners in interdisciplinary activities involving problem solving? The book is an important contribution to the literature on educational initiatives in interdisciplinary education increasing vital for emerging professions of the 21st century.
Women of mathematics
Though women earn nearly half of the mathematics baccalaureate degrees in the United States, they make up a much smaller percentage of those pursuing advanced degrees in mathematics and those entering mathematics-related careers. Through semi-structured interviews, this study took a qualitative look at the beliefs held by five undergraduate women mathematics students about themselves and about mathematicians. The findings of this study suggest that these women held stereotypical beliefs about mathematicians, describing them to be exceptionally intelligent, obsessed with mathematics, and socially inept. Furthermore, each of these women held the firm belief that they do not exhibit at least one of these traits, the first one being unattainable and the latter two being undesirable. The results of this study suggest that although many women are earning undergraduate degrees in mathematics, their beliefs about mathematicians may be preventing them from identifying as one and choosing to pursue mathematical careers.
Realistic Mathematics Education in Indonesia
This paper reports an experimental study on the development of exemplary curriculum materials for the teaching of fractions in Indonesian primary schools. The study's context is the current reform movement adopting realistic mathematics education (RME) theory, known as Pendidikan Matematika Realistik Indonesia (PMRI), and it looked at the role of design research in supporting the dissemination of PMRI. The study was carried out in two cycles of teaching experiments in two primary schools. The findings of the design research signified the importance of collaboration between mathematics educators and teachers in developing RME curriculum materials. The availability of RME curriculum materials is an important component in the success of the PMRI movement, particularly in supporting students and teachers in activity-based mathematics learning. Most of the students and teachers in the two schools positively appraised teaching and learning with the developed materials. Since the teachers were actively involved in developing the materials, they felt a sense of ownership and recognised that their students' classroom experiences of the materials helped them avoid standard difficulties. That appears to be a particular benefit of the bottom-up approach characteristic of the PMRI movement.
Future teachers' competence to plan a lesson
The study "Mathematics Teaching in the 21st Century (MT21)" focuses beyond others on the measurement of teachers' general pedagogical knowledge (GPK). GPK is regarded as a latent construct embedded in a larger theory of teachers' professional competence. It is laid out how GPK was defined and operationalized. As part of an international comparison GPK was measured with several complex vignettes. In the present paper, the results of future mathematics teachers' knowledge from four countries (Germany, South Korea, Taiwan, and the US) with very different teacher-education systems are presented. Significant and relevant differences between the four countries as well as between future teachers at the beginning and at the end of teacher education were found. The results are discussed with reference to cultural discourses about teacher education.
Cognitive styles
This paper reports the outcomes of an empirical study undertaken to investigate the effect of students' cognitive styles on achievement in measurement tasks in a dynamic geometry learning environment, and to explore the ability of dynamic geometry learning in accommodating different cognitive styles and enhancing students' learning. A total of 49 6th grade students were tested using the VICS and the extended CSA-WA tests (Peterson, Verbal imagery cognitive styles and extended cognitive style analysis-wholistic analytic test—Administration guide. New Zealand: Peterson, 2005) for cognitive styles. The same students were also administered a pre-test and a post-test involving 20 measurement tasks. All students were taught a unit in measurement (area of triangles and parallelograms) with the use of dynamic geometry, after a pre-test. As expected, the dynamic geometry software seems to accommodate different cognitive styles and enhances students' learning. However, contrary to expectations, verbalisers and wholist/verbalisers gained more in their measurement achievement in the environment of dynamic geometry than students who had a tendency towards other cognitive styles. The results are discussed in terms of the nature of the measurement tasks administered to the students.
Embodied design
Design-based research studies are conducted as iterative implementation-analysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even when resulting in empirically effective educational products, remains under-conceptualized as long as researchers cannot be explicit about their craft and specifically how data analyses inform design decisions. Consequentially, design decisions may appear arbitrary, design methodology is insufficiently documented for broad dissemination, and design practice is inadequately conversant with learning-sciences perspectives. One reason for this apparent under-theorizing, I propose, is that designers do not have appropriate constructs to formulate and reflect on their own intuitive responses to students' observed interactions with the media under development. Recent socio-cultural explication of epistemic artifacts as semiotic means for mathematical learners to objectify presymbolic notions (e.g., Radford, Mathematical Thinking and Learning 5(1): 37–70, 2003) may offer design-based researchers intellectual perspectives and analytic tools for theorizing design improvements as responses to participants' compromised attempts to build and communicate meaning with available media. By explaining these media as potential semiotic means for students to objectify their emerging understandings of mathematical ideas, designers, reciprocally, create semiotic means to objectify their own intuitive design decisions, as they build and improve these media. Examining three case studies of undergraduate students reasoning about a simple probability situation (binomial), I demonstrate how the semiotic approach illuminates the process and content of student reasoning and, so doing, explicates and possibly enhances design-based research methodology.
Teachers' perspectives on authentic mathematics
We investigate experienced high school geometry teachers' perspectives on "authentic mathematics" and the much-criticized two-column proof form. A videotaped episode was shown to 26 teachers gathered in five focus groups. In the episode, a teacher allows a student doing a proof to assume a statement is true without immediately justifying it, provided he return to complete the argument later. Prompted by this episode, the teachers in our focus groups revealed two apparently contradictory dispositions regarding the use of the two-column proof form in the classroom. For some, the two-column form is understood to prohibit a move like that shown in the video. But for others, the form is seen as a resource enabling such a move. These contradictory responses are warranted in competing but complementary notions, grounded on the corpus of teacher responses, that teachers hold about the nature of authentic mathematical activity when proving.
New roles for mathematics
A new concept, compulsory multi-disciplinary courses, was introduced in upper secondary school curriculum as a central part of a recent reform. This paper reports from a case study of such a triple/four-disciplinary project in mathematics, physics, chemistry and 'general study preparation' performed under the reform by a team of experienced teachers. The aim of the case study was to inquire how the teachers met the demands of the introduction of this new concept and, to look for signs of new relations established by the students between mathematics and other subjects, as a result of the multi-disciplinary teaching. The study revealed examples of good practice in planning and teaching. In addition, it served to illuminate interesting aspects of how students perceived the school subject mathematics and its relations to other subjects and to common sense.
YESS-4, Day 7
At the last day of YESS-4, Ferdinando Arzarello is going to deliver the main lecture. The topic for his talk is "Tools for analyzing learning processes in mathematics". He starts off with a discussion of problems concerning What, Why, How and Goals:
- What is necessary to observe in the classroom? (What)
- Which theoretical frames are suitable to answer the What-problem? (Why)
- How to observe all that is necessary? and How to interpret the observed data according to the assumed frame? (How)
- How to improve consequent didactical practices in the classroom? (Goal)
YESS-4, Day 5
At the 5th day of the YERME Summer School, Günter Törner is going to deliver the main lecture. His topic is "theory versus practice", and you can learn more from the paper that is published on the YESS-4 website.
Törner has published a multitude of papers and books in mathematics (algebra, geometry and discrete mathematics) as well as mathematics education. Several of them are available on his website, so take a look at the links I just gave you!
YESS-4, Day 4
The main lecture today at YESS-4 is held by Laurinda Brown. The theme of her main paper is: "Observing systems - how do we see what we see?". She aims at discussing issues concerning observations, and she points at the necessity of including discussions of theoretical, methodological and philosophical issues.
For more information, you should read her CERME-4 article and an article from Educational Studies in Mathematics. Both are published on the YESS-4 website.
YESS-4, Day 3
The main lecture at Day 3 of the YERME Summer School is held by Jean-Baptiste Lagrange. His talk will be concerning research about technology in mathematics education. Lagrange is going to look at different technologies with certain theoretical concerns:
- programming with the reification theories,
- microworlds with situated cognition,
- spreadsheets and computer symbolic systems with the instrumental and anthropological approaches,
- today fast developing web based technologies with the need for new approaches.
New book from Springer
In the new times of globalisation, international academic contacts and collaborations are ever increasing. They are taking many forms, from international conferences and publications, student and academic exchange, cross cultural research projects, curriculum development to professional development activities and affect every aspect of academic life from teaching, research to service. This book aims to:
- Develop theoretical frameworks of the phenomena of internationalisation and globalisation and identify related ethical, moral, political and economic issues facing mathematics and science educators.
- Provide a venue for the publication of results of international comparisons on cultural differences and similarities rather than merely on achievement and outcomes.
- Provide a forum for critical discussion of the various models and forms of international projects and collaborations.
- Provide a representation of the different voices and interests from around the world rather than consensus on issues.
YESS-4, Day 2
The main lecture at day 2 of the YERME Summer School will be held by Guershon Harel from University of California, San Diego. Harel's talk will address two main issues in mathematics education:
- What is the mathematics that we should teach in school?
- How should we teach it?
Use of examples in elementary mathematics
This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers' choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness.
YERME Summer School
This week, the 4th version of YERME Summer School (YESS-4) is organized in Turkey. The venue for the summer school is Karadeniz Technical University in Trabzon, near the Black Sea. KTU is a public research university with 30.000 students. There are about 40 master and PhD-students in mathematics education.
The summer school has a very interesting program, and although I am not able to attend it myself, I will try and cover it in my blog.
YESS-4 features a panel of distinguished experts, who will deliver the main lectures:
- Prof.Dr. Guershon Harel, University of California (USA)
- Prof.Dr. Linda Brown, University of Bristol (England)
- Prof.Dr. Jean-Baptiste Lagrange, IUFM De Reims Paris VII University (France)
- Prof.Dr. Günter Törner, Universität Duisburg-Essen Standort (Germany)
- Prof.Dr. Ferdinando Arzarello, Università di Torino (Italy)
The opening talk will be held this afternoon by Barbara Jaworski.
JMTE, August 2008
- Researchers and their roles in teacher education, by Konrad Krainer
- Investigating changes in prospective teachers' views of a 'good teacher' while engaging in computerized project-based learning, by Ilana Lavy and Atara Shriki
- Teaching experiments and professional development, by Anderson Hassel Norton and Andrea McCloskey
- Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving, by Andreas J. Stylianides and Deborah L. Ball
- Expanding the instructional triangle: conceptualizing mathematics teacher development, by Kelli Nipper and Paola Sztajn
Showing you're working
To help students view mathematics in a more favourable light, a number of former pupils were contacted and asked to give details of how they use mathematics in their daily lives. This information was gathered through an online questionnaire or visits to the school to talk to pupils—a booklet of responses was also given to students. Attitudinally pre- and post-testing students suggested that this initiative helped address pupils' concerns regarding the purpose of classroom mathematics. The diversity of professions also helped dispel many myths about the usefulness of mathematics. Subsequently, the project has proven to be a catalyst for a range of cross-curricular projects and events inspired by the former pupils' case studies, all of which serve to continue to address the initial aims of the project regarding pupil perception of the subject, in the light of both workplace and everyday life.
Mathematical belief change
Grootenboer provides a nice overview of previous research in this area, and that alone is reason enough to read this article. In addition, the study he reports is very interesting. Unlike many other studies of teachers' beliefs, Grootenboer has conducted a naturalistic study (in his own classroom), and he collected data from different sources: observation, interviews and assignments. If, like me, you are interested in teachers' beliefs in mathematics education, you should definitely read this article! Here is the abstract:
The development and influence of beliefs in teacher education has been a topic of increasing interest for researchers in recent years. This study explores the responses of a group of prospective primary teachers to attempts to facilitate belief change as part of their initial teacher education programme in mathematics. The students' responses seemed to fall into three categories: non-engagement; building a new set of beliefs and; reforming existing beliefs. In this article the participants' responses are outlined and illustrated with stories from three individuals. This study suggests that belief reform is complex and fraught with ethical dilemmas. Certainly there is a need for further research in this area, particularly given the pervasive influence of beliefs on teaching practice.
Learning mathematics for teaching
Here is the abstract:
Student teaching (guided teaching by a prospective teacher under the supervision of an experienced "cooperating" teacher) provides an important opportunity for prospective teachers to increase their understanding of mathematics in and for teaching. The interactions between a student teacher and cooperating teacher provide an obvious mechanism for such learning to occur. We report here on data that is part of a larger study of eight student teacher/cooperating teacher pairs, and the core themes that emerged from their conversations. We focus on two pairs for whom the core conversational themes represent disparate approaches to mathematics in and for teaching. One pair, Blake and Mr. B., focused on controlling student behavior and rarely talked about mathematics for teaching. The other pair, Tara and Mr. T., focused on having students actively participating in the lesson and on mathematics from the students' point of view. These contrasting experiences suggest that student teaching can have a profound effect on prospective teachers' understanding of mathematics in and for teaching.
Why do gestures matter?
The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed "sensuous cognition." The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal "material" conception of thinking. The very texture of thinking, it is suggested, cannot be reduced to that of impalpable ideas; it is instead made up of speech, gestures, and our actual actions with cultural artifacts (signs, objects, etc.). As illustrated through an example from a Grade 10 mathematics lesson, thinking does not occur solely in the head but also in and through a sophisticated semiotic coordination of speech, body, gestures, symbols and tools.Luis Radford is a distinguished scholar, and he has published a large number of important articles over the years. If you want to read more about his work, you should visit his list of publications. Most of his articles are freely available in pdf-format!
Exploring gender factors
Students' mathematical achievement in Iceland, as reported in PISA 2003, showed significant and (by comparison) unusual gender differences in mathematics: Iceland was the only country in which the mathematics gender gap favored girls. When data were broken down and analyzed, the Icelandic gender gap appeared statistically significant only in the rural areas of Iceland, suggesting a question about differences in rural and urban educational communities. In the 2007 qualitative research study reported in this paper, the authors interviewed 19 students from rural and urban Iceland who participated in PISA 2003 in order to investigate these differences and to identify factors that contributed to gender differences in mathematics learning. Students were asked to talk about their mathematical experiences, their thoughts about the PISA results, and their ideas about the reasons behind the PISA 2003 results. The data were transcribed, coded, and analyzed using techniques from analytic induction in order to build themes and to present both male and female student perspectives on the Icelandic anomaly. Strikingly, youth in the interviews focused on social and societal factors concerning education in general rather then on their mathematics education.
Gestures and conceptual integration
Spontaneous gesture produced in conjunction with speech is considered as both a source of data about mathematical thinking, and as an integral modality in communication and cognition. The analysis draws on a corpus of more than 200 gestures collected during 3 h of interviews with prospective elementary school teachers on the topic of fractions. The analysis examines how gestures express meaning, utilizing the framework of cognitive linguistics to argue that gestures are both composed of, and provide inputs to, conceptual blends for mathematical ideas, and a standard typology drawn from gesture studies is extended to address the function of gestures within mathematics more appropriately.A key idea in the article is that mathematics is seen as "an embodied, socially constructed human product", and gestures therefore might provide a relevant contribution to the mathematical thinking and communication. Edwards provides a nice explanation for the role of research on gestures:
(...) gesture constitutes a particular modality of embodied cognition, and, along with oral speech, written inscriptions, drawings and graphing, it can serve as a window on how learners think and talk about mathematics.The article provides a good overview of the theoretical framework for this area of research, and the study itself is also interesting. The participants (all women) were twelve volunteers from a course for prospective elementary school teachers, and the course was taught by Edwards herself. The participants were interviewed in pair, and the interview sessions were videotaped. The gestures that were caught on videotape were classified by McNeill's scheme.
Construction of moral discourses
This qualitative study examines the way three American young adolescent girls who come from different class and racial backgrounds construct their social and academic identities in the context of their traditional mathematics classroom. The overall analysis shows an interesting dynamic among each participant's class and racial background, their social/academic identity and its collective foundation, the types of ideologies they repudiate and subscribe to, the implicit and explicit strategies they adopt in order to support the legitimacy of their own position, and the ways they manifest their position and identity in their use of language referring to their mathematics classroom. Detailed analysis of their use of particular terms, such as "I," "we," "they," and "should/shouldn't" elucidates that each participant has a unique view of her mathematics classroom, developing a different type of collective identity associated with a particular group of students. Most importantly, this study reveals that the girls actively construct a social and ideological web that helps them articulate their ethical and moral standpoint to support their positions. Throughout the complicated appropriation process of their own identity and ideological standpoint, the three girls made different choices of actions in mathematics learning, which in turn led them to a different math track the following year largely constraining their possibility of access to higher level mathematical knowledge in the subsequent schooling process.
RME, September 2008
- How persuaded are you? A typology of responses Authors: Matthew Inglis; Juan Pablo Mejia-Ramos
- To be or to become: how dynamic geometry changes discourse Authors: Nathalie Sinclair; Violeta Yurita
- A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end Author: Ian Jones
- Paradoxes as a window to infinity Authors: Ami Mamolo; Rina Zazkis
- The effect of graphic calculators on Negev Arab pupils' learning of the concept of families of functions Author:Muhammad Abu-Naja
- The mathematical competence of adults returning to learning on a university
foundation programme: a selective comparison of performance with the
CSMS study Author: Mary Dodd
- Mathematics and dyslexics: classroom management skills and children's response to noise Author: Mari Palmer
- A synthesis of existing frameworks used to analyse mathematics curricula Author: Nusrat Fatima Rizvi
- Beginning elementary teachers' use of representations in mathematics teaching Author: Fay Turner
- Observing students' use of images through their gestures and gazes Author: Tracy Wylie
MTL, new issue
A new issue of Mathematical Thinking and Learning has been published:
> Mathematical Thinking and Learning: Volume 10 Issue 3 (http://www.informaworld.com/openurl?genre=issue&issn=1098-6065&volume=10&issue=3&uno_jumptype=alert&uno_alerttype=new_issue_alert,email
> ) is now available online at informaworld (http://
> www.informaworld.com).
> This new issue contains the following articles:
> Turnaround Students in High School Mathematics: Constructing
> Identities of Competence Through Mathematical Worlds, Pages 201 - 239
> Author: Ilana Seidel Horn
> Link: http://www.informaworld.com/openurl?genre=article&issn=1098-6065&volume=10&issue=3&spage=201&uno_jumptype=alert&uno_alerttype=new_issue_alert,email
> Toddlers' Spontaneous Attention to Number, Pages 240 - 270
> Authors: Arthur J. Baroody; Xia Li; Meng-lung Lai
> Link: http://www.informaworld.com/openurl?genre=article&issn=1098-6065&volume=10&issue=3&spage=240&uno_jumptype=alert&uno_alerttype=new_issue_alert,email
> The Interplay Between Gesture and Discourse as Mediating Devices in
> Collaborative Mathematical Reasoning:A Multimodal Approach, Pages
> 271 - 292
> Authors: Raymond Bjuland; Maria Luiza Cestari; Hans Erik Borgersen
> Link: http://www.informaworld.com/openurl?genre=article&issn=1098-6065&volume=10&issue=3&spage=271&uno_jumptype=alert&uno_alerttype=new_issue_alert,email
> A Modeling Perspective on the Teaching and Learning of Mathematical
> Problem Solving, Pages 293 - 304
> Authors: Nicholas G. Mousoulides; Constantinos Christou; Bharath
> Sriraman
> Link: http://www.informaworld.com/openurl?genre=article&issn=1098-6065&volume=10&issue=3&spage=293&uno_jumptype=alert&uno_alerttype=new_issue_alert,email
> A Critique on the Role of Social Justice Perspectives in Mathematics
> Education, Pages 305 - 312
> Author: Bettina Dahl
> Link: http://www.informaworld.com/openurl?genre=article&issn=1098-6065&volume=10&issue=3&spage=305&uno_jumptype=alert&uno_alerttype=new_issue_alert,email
Semiotics and subjectivity
In this response we address some of the significant issues that Tony Brown raised in his analysis and critique of the Special Issue of Educational Studies in Mathematics on "Semiotic perspectives in mathematics education" (Sáenz-Ludlow & Presmeg, Educational Studies in Mathematics 61(1–2), 2006). Among these issues are conceptualizations of subjectivity and the notion that particular readings of Peircean and Vygotskian semiotics may limit the ways that authors define key actors or elements in mathematics education, namely students, teachers and the nature of mathematics. To deepen the conversation, we comment on Brown's approach and explore the theoretical apparatus of Jacques Lacan that informs Brown's discourse. We show some of the intrinsic limitations of the Lacanian idea of subjectivity that permeates Brown's insightful analysis and conclude with a suggestion about some possible lines of research in mathematics education.
Stepping beyond high school mathematics
The Summer Explorations and Research Collaborations for High School Girls (SEARCH) Program, held annually since 2004 at Mount Holyoke College in the US, was created for talented high school girls to explore mathematics beyond that taught in high school. Our study, which focuses on factors that facilitate or inhibit the pursuit of higher level mathematics by girls, is centered on the 2006 SEARCH Program. We present a combination of qualitative and quantitative data drawn from student journals written during SEARCH, program evaluations written at the end of SEARCH, post-program interviews, and comparisons with two peer group samples. From this data we point to important factors, such as developing a mathematical voice, gaining a broader view of advanced mathematics, being challenged in a supportive atmosphere, and having a positive stance toward risk-taking, that may help to maintain the interest of talented girls in advanced mathematical studies.
Supporting mathematical literacy
Mathematical literacy implies the capacity to apply mathematical knowledge to various and context-related problems in a functional, flexible and practical way. Improving mathematical literacy requires a learning environment that stimulates students cognitively as well as allowing them to collect practical experiences through connections with the real world. In order to achieve this, students should be confronted with many different facets of reality. They should be given the opportunity to participate in carrying out experiments, to be exposed to verbal argumentative discussions and to be involved in model-building activities.
This leads to the idea of integrating science into maths education. Two sequences of lessons were developed and tried out at the University of Education Schwäbisch Gmünd integrating scientific topics and methods into maths lessons at German secondary schools. The results show that the scientific activities and their connection with reality led to well-based discussions. The connection between the phenomenon and the model remained remarkably close during the entire series of lessons. At present the sequences of lessons are integrated in the European ScienceMath project, a joint project between universities and schools in Denmark, Finland, Slovenia and Germany (see www.sciencemath.ph-gmuend.de).
A mathematician's lament
This month's column is devoted to an article called A Mathematician's Lament, written by Paul Lockhart in 2002. Paul is a mathematics teacher at Saint Ann's School in Brooklyn, New York. His article has been circulating through parts of the mathematics and math ed communities ever since, but he never published it. I came across it by accident a few months ago, and decided at once I wanted to give it wider exposure. I contacted Paul, and he agreed to have me publish his "lament" on MAA Online. It is, quite frankly, one of the best critiques of current K-12 mathematics education I have ever seen. Written by a first-class research mathematician who elected to devote his teaching career to K-!2 education.
Construction of mathematical meaning of motion graphs
This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpreting graphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of interaction: 2D freehand motion and 2D synthesized motion, designed by the composition of single variable function graphs. Our theoretical framework combines two perspectives: the embodied approach to the nature of mathematical thinking and the Vygotskian notion of semiotic mediation. The article describes in detail the actions, gestures, graph drawings, and verbal discourse of one pair of high school students and analyzes the social semiotic processes they experienced. Our analysis shows how the computerized artifacts and the students' gestures served as means of semiotic mediation. Specifically, they supported the interpretation and the production of motion graphs; they mediated the transition between an individual's meaning of mathematical signs and culturally accepted mathematical meaning; and they enable linking bodily actions with formal signs.The article gives a nice introduction to the theoretical foundations concerning the connections between bodily movement and semiotics. The study being described in the article was a learning experiment, and the use of illustrative photos and figures in the article makes it easy to understand the discussion of the different motions and pointing gestures that were used.
IJSME, September 2008
- Effects of advance organiser strategy during instruction on secondary school students' mathematics achievement in Kenya's Nakuru district, by Bernard N. Githua and Rachel Angela Nyabwa.
- Examining Reflective Thinking: A Study of Changes in Methods Students' Conceptions and Understandings of Inquiry Teaching, by Jing-Ru Wang and Sheau-Wen Lin
- Following Young Students' Understanding of Three Phenomena in which Transformations of Matter Occur, by Lena Löfgren and Gustav Helldén
- Secondary School Students' Construction and Use of Mathematical Models in Solving Word Problems, by Salvador Llinares and Ana Isabel Roig
- Cognitive Incoherence of Students Regarding the Establishment of Universality of Propositions through Experimentation/Measurement, by Mikio Miyazaki
- Differentials in Mathematics Achievement among Eighth-Grade Students in Malaysia, by Noor Azina Ismail and Halimah Awang
- Thai Grade 10 and 11 Students' Understanding of Stoichiometry and Related Concepts, by Chanyah Dahsah and Richard Kevin Coll
- The Inquiry Laboratory as a Source for Development of Metacognitive Skills, by Mira Kipnis and Avi Hofstein
The article by Llinares and Roig has a focus on students' problem solving, with a particular focus on word problems. Connections are made with research on mathematical modelling (e.g. the research of Danish colleague and editor of NOMAD, Morten Blomhøj), and the article gives a nice overview of research concerning problem solving and mathematical modelling. The study that is reported in the article is a survey/test where students were faced with five questions/problems. Llinares and Roig discuss the problem-solving strategies that were used to solve the three word problems in this test.
The article by Githua and Nyabwa provides insight into mathematics teaching in Kenya, and the article builds heavily on Ausubel's theory of advance organisers. The objectives of the reported study were to investigate whether or not there were statistical significant differences in mathematics achievement between students who had been taught using advance organisers or not, and they also wanted to investigate whether gender affected achievement when advance organisers were used.
Another interesting article was the one by Ismail and Awang, which provides more insight into factors that influenced the achievement of Malaysian students in the TIMSS 1999 student assessment.
New IJMEST articles
- A note on variance components model, by Anant M. Kshirsagar and R. Radhakrishnan
- An elementary proof of a converse mean-value theorem, by Ricardo Almeida
- Bionomic exploitation of a ratio-dependent predator-prey system, by Alakes Maiti, Bibek Patra and G.P. Samanta
ZDM, August 2008
- Introduction to the special issue on didactical and epistemological perspectives on mathematical proof, by Maria Alessandra Mariotti and Nicolas Balacheff
- Proofs as bearers of mathematical knowledge, by Gila Hanna and Ed Barbeau
- Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context, Man-Keung Siu
- Theorems that admit exceptions, including a remark on Toulmin, by Hans Niels Jahnke
- Truth versus validity in mathematical proof, by Viviane Durand-Guerrier
- Argumentation and algebraic proof, by Bettina Pedemonte
- Indirect proof: what is specific to this way of proving?, by Samuele Antonini and Maria Alessandra Mariotti
- Students' encounter with proof: the condition of transparency, by Kirsti Hemmi
- A method for revealing structures of argumentations in classroom proving processes, by Christine Knipping
- Strategies to foster students' competencies in constructing multi-steps geometric proofs: teaching experiments in Taiwan and Germany, by Aiso Heinze, Ying-Hao Cheng, Stefan Ufer, Fou-Lai Lin and Kristina Reiss
- Reasoning and proof in geometry: effects of a learning environment based on heuristic worked-out examples, by Kristina Maria Reiss, Aiso Heinze, Alexander Renkl and Christian Groß
- When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers, by Patricio Herbst and Takeshi Miyakawa
- DNR perspective on mathematics curriculum and instruction, Part I: focus on proving, by Guershon Harel
- The role of the researcher's epistemology in mathematics education: an essay on the case of proof, by Nicolas Balacheff
ESM, September 2008
- School mathematics and its everyday other? Revisiting Lave's 'Cognition in Practice', by Christian Greiffenhagen and Wes Sharrock
- Beyond 'blaming the victim' and 'standing in awe of noble savages': a response to "Revisiting Lave's 'cognition in practice'", by David W. Carraher
- The problem of the particular and its relation to the general in mathematics education, by Vicenç Font and Ángel Contreras
- Transitions among different symbolic generalizations by algebra beginners in a computer intensive environment, by Michal Tabach, Abraham Arcavi and Rina Hershkowitz
- Centenary birth anniversary of E. W. Beth (1908–1964), by Giorgio T. Bagni
Equity in mathematics education
Traditional models of gender equity incorporating deficit frameworks and creating norms based on male experiences have been challenged by models emphasizing the social construction of gender and positing that women may come to know things in different ways from men. This paper draws on the latter form of feminist theory while treating gender equity in mathematics as intimately interconnected with equity issues by social class and ethnicity. I integrate feminist and social justice literature in mathematics education and argue that to secure a transformative, sustainable impact on equity, we must treat mathematics as an integral component of a larger system producing educated citizens. I argue the need for a mathematics education with tri-fold support for mathematical literacy, critical literacy, and community literacy. Respectively, emphases are on mathematics, social critique, and community relations and actions. Currently, the integration of these three literacies is extremely limited in mathematics.
Exemplifying definitions
In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants' understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.
Mathematical paradoxes
This paper addresses the role of mathematical paradoxes in fostering polymathy among pre-service elementary teachers. The results of a 3-year study with 120 students are reported with implications for mathematics pre-service education as well as interdisciplinary education. A hermeneutic-phenomenological approach is used to recreate the emotions, voices and struggles of students as they tried to unravel Russell's paradox presented in its linguistic form. Based on the gathered evidence some arguments are made for the benefits and dangers in the use of paradoxes in mathematics pre-service education to foster polymathy, change beliefs, discover structures and open new avenues for interdisciplinary pedagogy.


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After releasing Shining Hearts and Shining Blade in almost two consecutive years, SEGA is announcing its latest work from the Shining Series Shining Ark (シャイニング・アーク) will be released in this winter on February 28, 2013 on PSP. For the new game, it will revolve around a young man Fried and a girl named Panis. Of course, we cannot fail to mention the voice actors and actresses of the series as Hiroshi Kamiya (神谷 浩史) and Houko Kuwashima (桑島 法子) will be playing the two protagonists respectively (and again).
From what we can see from the below plot, the story seems to be a bit similar to Shining Hearts, where folks are baking bread all the time, as well in the TV Anime this Spring. However, if you are a fan of the Shining series, you probably learned a long time ago that story is not what you care for, the beautiful illustrations and the wonderful voice cast are, and probably the fighting system. Also if you have watched the video below, you might notice a mysterious girl with a sickle in mask. With the opening of the game sung by Nana Mizuki, you can probably tell who that girl is. There is a main character showed up in both Shining Hearts and Shining Blade and her name is Sakuya. This is just a simple guess, not confirmed.
The Story
Fried, a resident of the island of Arcadia, finds a girl in danger and saves her. The girl named Panis then recovers thanks to his efforts, and his freshly-baked bread. Although Fried thought it would be very difficult to get the villagers to accept her, they eventually agree to let her in the village. Soon, Panis begins to show signs of mysterious powers: her singing voice can make plants grow and gather birds and fish around her. The villagers, seeing this, called her an "angel." However, there are those who come to the island who target the angel, and one day, on the night of the red moon, a large shadow appears to attack Panis. (via ANN)
Source: Famitsu, Official Website, ANN


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Three days of unrelenting drama ended in a blaze of red flares and glory when Mario Ancic beat Slovakia's Michal Mertinak 7-6, 6-3, 6-4 to claim a 3-2 victory for Croatia in the Davis Cup final on Sunday.
The 21-year-old sealed victory on his second match point and was promptly mobbed by his ecstatic team mates, including former Wimbledon champion Goran Ivanisevic and Ivan Ljubicic, the player who took them to the final virtually single-handed.
With hundreds of celebrating fans going berserk in the Sibamac Arena, Croatia captain Niki Pilic paid tribute to his team who became the first unseeded nation to win the trophy.
"The Davis Cup is one of the greatest competitions in the world and I'm so proud that my team is number one in 2005," said Pilic, who is the first captain to win the title with two different nations, having triumphed three times with Germany.
There is no doubt this one is the sweetest.
"Just because some nations are bigger, it doesn't mean they are better than we are," he added. "What's important is the feeling that with my own people we won it and for us it's an historic moment."
Ancic, who like Pilic is a native of Split, chose the perfect time to win his first live singles rubber of the year, coming to the rescue after Slovakia's Dominik Hrbaty had beaten Ljubicic in a five-set thriller to make it 2-2.
Sadly for Ljubicic, who woke up with a stiff neck and was sick during his 4-6, 6-3, 6-4, 3-6, 6-4 defeat, fell one win short of matching John McEnroe's 1982 feat of 12 straight victories in a Davis Cup year, although the team's debt to him is enormous.
"I took a chance, I decided to play," said the 26-year-old, who declared himself fit little more than an hour before he was due on court. "Then after the second set I went to the toilet to throw up."
Ljubicic looked shattered after his three hour 20 minute defeat by an inspired Hrbaty, but thanks to Ancic he could still celebrate the end of a stellar year.
"I think it's a fantastic win, this will never be forgotten, it will be written in the books forever," he said.
Ancic has lived in Ljubicic's shadow during the run to the final, but emerged to outclass world number 165 Mertinak, a 26-year-old better known for doubles.
Mertinak was only named to play the fifth rubber 15 minutes before it begun, Slovakia's captain Miloslav Mecir preferring him to the more experienced Karol Kucera.
Kucera had only been called up for Friday's first singles against Ljubicic after Slovak number two Karol Beck, who denied a doping rumour on Thursday, was ruled out with a bad knee.
Mertinak played a solid enough first set, but Ancic cruised through the tiebreak 7-1 and, apart from a brief wobble in the third set when he was broken, rarely looked in danger.
"It was 2-2, a must-win situation, there could be no excuses," said Ancic. "I think I stepped up in the tiebreak and from that moment I was in control."
Mecir was gracious in defeat.
"The best team won but all my players were fantastic," he said, adding that choosing between Mertinak and Kucera had been a tough call.
The atmosphere for the decisive rubber was electric, but nothing like as highly-charged as for Sunday's pulsating first singles.
Hrbaty had lost all five meetings with Ljubicic, but as he had done against Ancic on Friday to level the tie at 1-1, he produced tennis of the highest quality.
"In terms of mental pressure it was the most difficult match of my career," said the 27-year-old who threw all his rackets into the crowd after clawing Slovakia level.
He was outgunned early on, Ljubicic pumelling seven aces and countless searing winners to take the opener in 34 minutes.
Hrbaty launched a stunning counter-attack, however, that rocked an increasingly weary-looking Ljubicic back on his heels.
Hrbaty broke Ljubicic's mighty serve for the first time in the second game of the second set, then broke twice in the third set as the momentum shifted completely his way.
Ljubicic clawed one break back but Hrbaty hung on grimly to move two sets to one in front.
Ljubicic dug deep in a fourth set, then pounced for a decisive service break as Hrbaty went 0-40 down at 3-4. He closed out the set in ruthless fashion.
Hrbaty had the advantage of serving first in the fifth, forcing his opponent to serve to stay in the match at 4-5.
With the noise deafening, Ljubicic saved one match point with a backhand winner and another with a big first serve.
Hrbaty was relentless, however, and clinched victory when Ljubicic netted an attempted backhand pass.
His efforts proved in vain, though, as Ancic made sure it was Croatia, who became the 12th nation to have its name engraved on the famous old trophy.


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Why are ponytails on little girls and young women cute, but on women of a certain age (when worn in public somewhere besides the gym or while doing laundry) just a sign of giving up?
from Wikimedia Commons
Who knew the ponytail could be such a controversial hairstyle?
Of course some women could pull off a ponytail or any hairstyle.


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Top Tips:
WARNING: If you suspect an employee of foul play, it is a BAD idea to take a quick look through their e-mail outbox for proof. Doing so may irreparably damage the evidence and may make it inadmissible in court.
To avoid spoliation issues, it is critical that the source data is not altered when extracted from hard drives or other media.
It is vital to understand that digital forensics is not just about technology.
- Operating a computer for any reason changes and destroys evidence if it is not handled forensically!
- Business owners need to understand this growing risk and what to do if they think a current employee is up to wrongful activity.
- Don't Tamper With Evidence
- Preserve the Chain of Evidence
- Secure computers, mobile devices, USB devices and information system assets
- Conduct a proper and professional digital forensic imaging and an ECA investigation
- Don't rely on internal or external IT staff. Chances are they aren't handling data in a forensically sound manner
If the computer is ON – DO NOT TURN IT OFF
If the computer is OFF – DO NOT TURN IT ON
Quick response is critical: nothing is more important than in-person contact, especially when cyber investigations require a qualified first responder to a computer security incident.
It is essential to collect volatile information (information that is lost after a period of time or when a computer is turned off), to perform digital forensics and to establish proper chain-of-custody as soon as possible.
Attention to detail at this stage can decide the strength of any evidence to be used later. The legal system,and judges in particular, look favorably on organizations that bring in third-party digital forensic specialists from the outset.
Sedona Principles, 2nd Ed.
1. Electronically stored information is potentially discoverable under Fed. R.Civ. P. 34 or its state equivalents. Organizations must properly preserve electronically stored information that can reasonably be anticipated to be relevant to litigation.
2. When balancing the cost, burden, and need for electronically stored information,courts and parties should apply the proportionality standard embodied in Fed.R. Civ. P. 26(b)(2)(C) and its state equivalents, which require consideration of the technological feasibility and realistic costs of preserving, retrieving,reviewing, and producing electronically stored information, as well as the nature of the litigation and the amount in controversy.
3. Parties should confer early in discovery regarding the preservation and production of electronically stored information when these matters are at issue in the litigation and seek to agree on the scope of each party's rights and responsibilities.
4. Discovery requests for electronically stored information should be as clear as possible,while responses and objections to discovery should disclose the scope and limits of the production.
5. The obligation to preserve electronically stored information requires reasonable and good faith efforts to retain information that may be relevant to pending or threatened litigation. However, it is unreasonable to expect parties to take every conceivable step to preserve all potentially relevant electronically stored information.
6. Responding parties are best situated to evaluate the procedures, methodologies, and technologies appropriate for preserving and producing their own electronically stored information.
7. The requesting party has the burden on a motion to compel to show that the responding party's steps to preserve and produce relevant electronically stored information were inadequate.
8. The primary source of electronically stored information for production should be active data and information. Resort to disaster recovery backup tapes and other sources of electronically stored information that are not reasonably accessible requires the requesting party to demonstrate need and relevance that outweigh the costs and burdens of retrieving and processing the electronically stored information from such sources, including the disruption of business and information management activities.
9.Absent a showing of special need and relevance, a responding party should not be required to preserve, review, or produce deleted, shadowed, fragmented, or residual electronically stored information.
10. A responding party should follow reasonable procedures to protect privileges and objections in connection with the production of electronically stored information.
11. A responding party may satisfy its good faith obligation to preserve and produce relevant electronically stored information by using electronic tools and processes, such as data sampling, searching, or the use of selection criteria,to identify data reasonably likely to contain relevant information.
12.Absent party agreement or court order specifying the form or forms of production,production should be made in the form or forms in which the information is ordinarily maintained or in a reasonably usable form, taking into account the need to produce reasonably accessible metadata that will enable the receiving party to have the same ability to access, search, and display the information as the producing party where appropriate or necessary in light of the nature of the information and the needs of the case.
13.Absent a specific objection, party agreement or court order, the reasonable costs of retrieving and reviewing electronically stored information should be borne by the responding party, unless the information sought is not reasonably available to the responding party in the ordinary course of business. If the information sought is not reasonably available to the responding party in the ordinary course of business, then, absent special circumstances, the costs of retrieving and reviewing such electronic information may be shared by or shifted to the requesting party.
14.Sanctions, including spoliation findings, should be considered by the court only if it finds that there was a clear duty to preserve, a culpable failure to preserve and produce relevant electronically stored information, and reasonable probability that the loss of the evidence has materially prejudiced the adverse party.
Copyright©2007 The Sedona Conference®. All Rights Reserved. - Reprinted courtesy of The Sedona Conference®
Go to www.thesedonaconference.org to download a free copy of the complete document for your personal use only.


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If you're the kind of person who congratulates yourself when you actually understand a New Yorker cartoon with an obscure reference to a minor character in Moby Dick — regardless of whether or not you've ever been able to finish the book, although you pretend like you have (don't worry, I also fall into this category) — British cartoonist Tom Gauld's new collection, Baking with Kafka, was made just for you.
Unlike Gauld's last book, Mooncop, a graphic novel, Baking with Kafka is more like a compilation of graphic short stories — really short stories. The series of about 150 stand-alone, one-page comics imagines things like God getting in the way of the creativity of an artist illuminating a manuscript, or "Planning Neil Gaiman's 'Norse Mythology' Book Tour," where his assistant is a Viking.
Although the comics all exist separate from one another, many share an absurdist reality that uses historical references to poke fun at the present. Gauld's favorite topics include modern reading habits and the bureaucracy of the publishing industry, although visual art and #revolution also sneak in.
One of my favorites is in the first few pages. Its protagonist is a novel that's excited to have been assigned to a student, hoping it'll still be read despite the fact that the student has yet to open it, instead writing a term paper based solely on Wikipedia and the movie version. Gauld takes this same deadpan, characteristically British sense of humor to the museum: A "Planned Extension of the Art Gallery" has new wings dedicated to a "caviar silo," an "oligarch bunker," and a "limo tunnel."
Gauld's simple, almost cute drawing style stands in contrast to his comics' content, adding an extra dose of humor. The anthropomorphic books having identity crises in the face of new technology, the literally one-dimensional characters aspiring to develop in a badly written story, and even the "angry friends and relatives" fuming at the award-winning autobiographical novelist — a bearded fellow, probably Karl Ove Knausgård — are all drawn in the same manner.
Gauld's comments on 21st-century culture may be sadly true, but his jabs at politics are probably his most poignant. In "The Angry Mob," most of the people are either "not sure," "pretending to be angry," or "just like being in a mob." One of the last few comics is of a circular orange person at a museum, laughing at all the art about stupid green, purple, and blue people, but getting really angry at the depiction of an "orange nitwit." Get it? We didn't need to know a single thing about Moby Dick for that one.
Tom Gauld's Baking with Kafka is published by Drawn & Quarterly and available October 3. In October and November, Gauld will be touring bookstores in the UK, France, Texas, California, Washington, and Oregon.


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As every year does 2012 brought a lot of fun and crazy times!
So this year I bring you...
The Schwab Family
Top 10
of 2012
10. Dominic got his driver's license.
9. Connor played his first season of baseball.
8. Jeff got a new car.
7. Emma Kate started gymnastics.
6. Laura started reading again...as in books. From beginning to end!
5. Speaking of reading...Dominic read the WHOLE Bible.
4. We discovered some cool new vacation spots.
3. We just bought our last box of diapers. EVER!
2. Dom got a job.
1. The Lord revealed to us over and over His great love and many blessings.
Happy New Year!


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7: Neymar
The boy wonder has lived up to his billing thus far at Barcelona and, with the injury woes of Lionel Messi, has come into his own perhaps even sooner than fans expected him to.
At 21-years-of-age he quite literally has the world at his feet. Next year he can truly establish himself as one of the best players in the world- or will he crumble under the pressure of the World Cup on his own turf?