The Math Without Borders Home Study Companion series offers high school math video teaching courses presented by David Chandler on flash drives in MP4 format. Videos serve as companions to Paul A. Foerster’s texts for Algebra 1, Algebra 2 and Trigonometry, Precalculus, and Calculus. The Math Without Borders Geometry video instruction supports the text Geometry: A Guided Inquiry by Chakerian, Crabill, and Stein rather than a text by Foerster. The videos provide students with the presentations of an experienced teacher. Both videos and textbooks are required, but textbooks must be purchased separately.
Each course needs to be copied from the flash drive onto your computer. Your computer needs to have speakers or headphones for the student to listen to the audio tracks for the instruction. Students will need either a downloaded scientific calculator they can use on their computer or a handheld calculator for all courses. Some courses benefit from the presence of a spreadsheet program; Microsoft Excel works as do the free Open Office Calc or Libre Office programs. The GeoGebra program is optional for Algebra 1.
While there are a number of somewhat similar math courses on DVD-ROM or through the internet, most of those designed for homeschoolers use texts that are not as challenging as those used with this series. Foerster’s books, in particular, have long been recognized as among the best high school math texts. However, they assume the presence of a teacher and are too difficult for students to use on their own. The level of the math taught in each text is above average. For example Foerster's Algebra 1 includes functions, trigonometric functions, and quadratic functions, topics often covered at higher levels in other series.
The Home Study Companions will work with earlier editions of each text, so you might find used copies at lower prices.
For the three courses using Foerster’s textbooks, experienced teacher David Chandler talks students through each of the key concepts in each section of the textbook using a whiteboard to teach the concepts and work through examples. He follows the text, occasionally teaching in a slightly different fashion for the sake of clarity. Chandler sometimes expands on a topic that he knows is particularly troublesome to students. He pulls up an online calculator and other tools such as Geogebra (a free, computer-based substitute for a graphing calculator available at http://www.geogebra.org/cms/download) to illustrate lessons. I very much appreciate his instruction on how to use a scientific calculator in many different instances. (Students will need either a downloaded scientific calculator they can use on their computer or a handheld calculator.)
After he’s taught the concept, he typically works through a fair number of examples before he leaves students to work through problems on their own. Answers to odd problems are at the back of the texts. Chapter reviews and/or chapter tests within the textbooks can be used for assessment. All of the courses have narrated solutions for about half of the problems (the recommended assignment) worked out on video. A separate solutions manual for each course is available from the publisher of each text, but these are probably not necessary.
For Home Study Companion: Algebra 1, you should read through Chandler’s notes online at http://mathwithoutborders.com/?page_id=4. The text you will need is Algebra 1: Expressions, Equations, and Applications. You will probably want a solutions manual. (Chandler tell you how to order the solutions manual.) The free Graphmatica shareware graphing program is helpful for Algebra 1 although it isn’t required.
The full title of the Algebra 2 text is Algebra and Trigonometry: Functions and Applications. Students will need a spreadsheet program for this course. Chandler advises that you probably don’t need the solutions manual for this course since he works through so many of the problems on the video. Read Chandler’s notes for this course at http://mathwithoutborders.com/?page_id=9.
Precalculus with Trigonometry: Concepts and Applications is the text for Home Study Companion: Precalculus. Go to http://
mathwithoutborders.com/?page_id=11 for Chandler’s notes for this course. Chandler comments there, “I have taught out of several other Precalculus textbooks, but none of them is in the same league with Foerster when it comes to teaching problem solving and real-world applications.” While Foerster’s text has gone through a number of editions, the third edition is the best fit for this course since content (while similar) was rearranged from the second to the third edition. Video solutions are provided for a large enough number of problems that you are unlikely to need a solutions manual. Students continue to use the free on-screen scientific calculator, Calc98 (http://www.calculator.org/download.aspx) and GeoGebra. In the last quarter of this course, he also introduces students to an even more advanced calculating program called Sage.
The Calculus course uses the text Calculus: Concepts and Applications, 2nd edition. While students will use a scientific calculator and Geogebra, Chandler also teaches them how to use a spreadsheet program (Excel or the free program Libre Office "Calc") as a calculation tool.
You can see from the technological tools Chandler uses that these courses are more sophisticated than many others used by homeschoolers. They will provide excellent preparation for those who will continue with higher math after they graduate. Familiarity with the “tools of the trade” will be a big bonus.
The Geometry course (combined video instruction and text) differs from the others with greater use of the textbook and less video instruction. Students work through a “Central Problem” that begins each chapter. The Central Problem itself is used to teach new material. Students study examples, work through practice problems, and do investigations. Throughout this introductory section, new concepts are introduced to lead the student toward a solution of the Central Problem. The result is all of the content is introduced in the context of a problem where it is immediately useful, rather than being left asking, "When will I ever use this?" Following this are a self-quiz, a review section and a review self-test. While answers to all of these problems are at the back of the book, the Home Study Companion for Geometry: A Guided Inquiry includes video solutions to problems in the review section.
Each chapter also has a projects section that expands upon concepts taught in the Central Problem section. This section has its own set of problems to solve.
While the Home Study Companion: Geometry has video solutions for the Central review section, it also has PDF files with complete solutions for all problems in both the Central and Project sections. (The text has answers but not solutions.) Solution sections often have additional commentary that is helpful to students.
Some chapters have “extensions” on the Home Study Companion to cover topics in the math standards that were not covered in the textbook. Sections for algebra review are also included.
Demonstrations using GeoGebra are used throughout the Geometry course. Students will also create their own geometric constructions, so they need to have a ruler (showing metric units), a protractor, and a compass. Graph paper and a scientific calculator are also required.
Sample Home Study Companion lessons are available on the Math Without Borders website. You might want to read Chandler’s notes for each course (links listed above) before purchasing since they provide detailed information about scheduling and course content that is very helpful.
Doing a quick scan on Amazon, it looks like all of the texts are readily available with the most expensive around $70 and most much less than that. So the combined cost of text and Home Study Companion is quite low for courses of this caliber.
Homeschoolers should find Home Study Companions one of the least expensive ways to complete high school math courses at challenging levels with interesting course content. This combination of outstanding textbooks and an experienced teacher on the computer should make these courses practical even when parents lack math background.
Maths Without Borders Home Study Companion ni kitabu cha masomo ya shule ya sekondari ya hisabati, kilichochapishwa na David Chandler na kuchapishwa kwenye diski za flash. "Kama ilivyoelezwa katika makala ya kwanza ya makala ya ""Algebra,"" ""Algebra 2,"" na ""Trigonometry,"" ""Precalculus,"" na ""Calculus"" ya Paul A. Foerster." Mafundisho ya video ya Hisabati Bila Mipaka ya Jiometri inasaidia maandishi ya Jiometri: Utafiti ulioongozwa na Chakerian, Crabill, na Stein badala ya maandishi ya Foerster. Video hizo huwapa wanafunzi maonyesho ya mwalimu mwenye uzoefu. Video na vitabu vya masomo vinahitajika, lakini vitabu vya masomo vinapaswa kununuliwa kando. Kila kozi inahitaji kunakiliwa kutoka kwa kiendeshi cha flash kwenye kompyuta yako. Kompyuta yako inahitaji kuwa na wasemaji au vichwa vya sauti kwa mwanafunzi kusikiliza nyimbo za sauti kwa ajili ya mafundisho. Wanafunzi watahitaji ama downloaded kisayansi calculator wanaweza kutumia kwenye kompyuta yao au calculator mkono kwa ajili ya kozi zote. Baadhi ya kozi kufaidika na uwepo wa programu spreadsheet; Microsoft Excel kazi kama kufanya bure Open Office Calc au Libre Office programu. Programu ya GeoGebra ni hiari kwa Algebra 1. Ingawa kuna baadhi ya masomo ya hesabu sawa kwenye DVD-ROM au kupitia mtandao, wengi wa wale iliyoundwa kwa homeschoolers kutumia maandishi ambayo si kama changamoto kama wale kutumika na mfululizo huu. Vitabu vya Foerster, hasa, vimekuwa vikitambuliwa kwa muda mrefu kuwa miongoni mwa maandishi bora ya hisabati ya shule ya sekondari. Hata hivyo, wao kudhani uwepo wa mwalimu na ni vigumu sana kwa wanafunzi kutumia peke yao. Kiwango cha hisabati kufundishwa katika kila maandishi ni juu ya wastani. Kwa mfano, Foerster's Algebra 1 inajumuisha kazi, kazi za trigonometric, na kazi za quadratic, mada ambazo mara nyingi hufunikwa katika ngazi za juu katika mfululizo mwingine. Kwa kuwa kitabu cha Home Study Companions kinachapishwa katika matoleo ya zamani ya kila kitabu, huenda ukapata nakala zilizotumiwa kwa bei ya chini. Kwa kozi tatu zinazotumia vitabu vya Foerster, mwalimu mwenye uzoefu David Chandler anawafundisha wanafunzi kupitia kila moja ya dhana muhimu katika kila sehemu ya kitabu cha masomo kwa kutumia ubao mweupe kufundisha dhana na kufanya kazi kupitia mifano. Yeye hufuata andiko hilo, na mara kwa mara anafundisha kwa njia tofauti kidogo ili jambo liwe wazi. Chandler wakati mwingine anaeleza zaidi juu ya habari ambayo anajua ni yenye kusumbua hasa kwa wanafunzi. "Kutumia programu ya ""geocalculator"" na ""geocalculator"" (mfano wa kompyuta ya bure ya ""geocalculator"" inapatikana katika http: www.geocalculator.org) ni rahisi na rahisi." Ninathamini sana mafundisho yake juu ya jinsi ya kutumia hesabu ya kisayansi katika visa vingi tofauti. Wanafunzi wanaweza kutumia kompyuta yao au kompyuta ya mkononi. Baada ya yeye ni kufundishwa dhana, yeye kawaida kazi kupitia idadi nzuri ya mifano kabla ya yeye huacha wanafunzi kufanya kazi kupitia matatizo juu yao wenyewe. Majibu ya matatizo yasiyo ya kawaida yapo nyuma ya maandishi. Makala mapitio na / au sura vipimo ndani ya vitabu vya masomo inaweza kutumika kwa ajili ya tathmini. Kozi zote zimeelezea suluhisho kwa karibu nusu ya matatizo (kazi iliyopendekezwa) iliyofanya kazi kwenye video. Mwongozo tofauti wa suluhisho kwa kila kozi inapatikana kutoka kwa mchapishaji wa kila maandishi, lakini hizi pengine si muhimu. Kwa ajili ya Home Study Companion: Algebra 1, unapaswa kusoma kupitia maelezo ya Chandler mtandaoni katika http: mathwithoutborders.com?page_id=4. Maandishi utakayohitaji ni Algebra 1: Maonyesho, Mlinganisho, na Matumizi. Yaelekea utataka kitabu cha suluhisho. (Chandler kukuambia jinsi ya kuagiza mwongozo wa suluhisho.) Free Graphmatica shareware graphing programu ni muhimu kwa Algebra 1 ingawa si required. Kichwa kamili cha maandishi ya Algebra 2 ni Algebra na Trigonometry: Functions na Maombi. Wanafunzi watahitaji programu ya karatasi ya tafiti kwa ajili ya kozi hii. Chandler anashauri kwamba pengine huna haja ya suluhisho mwongozo kwa ajili ya kozi hii tangu yeye kazi kupitia matatizo mengi sana juu ya video. Soma maelezo ya Chandler kwa ajili ya kozi hii katika http: http: mathwithoutborders.com?page_id=9. Precalculus na Trigonometry: Dhana na Maombi ni maandishi kwa ajili ya Home Study Companion: Precalculus. Kwa mfano, unaweza kutumia http: www.mathwithoutborder.com au www.mathwithoutborder.com ili kupata maelezo ya Chandler kuhusu masomo haya. "Chandler anasema, ""Nimefundisha kutoka kwa vitabu vingine kadhaa vya Precalculus, lakini hakuna hata moja ambayo ni sawa na Foerster linapokuja suala la kufundisha ufumbuzi wa tatizo na matumizi ya ulimwengu halisi.""Wakati maandishi ya Foerster yamepitia matoleo kadhaa, toleo la tatu ni bora zaidi kwa kozi hii tangu maudhui (wakati sawa) yalipangwa upya kutoka toleo la pili hadi la tatu." Video ya ufumbuzi ni zinazotolewa kwa idadi kubwa ya matatizo kwamba ni uwezekano mdogo wa haja ya ufumbuzi mwongozo. Kwa mfano, unaweza kutumia Calculator ya kisayansi ya bure ya Calc98 (www.calculator.org) na Geogebra. Katika robo ya mwisho ya kozi hii, yeye pia anawajulisha wanafunzi kwa programu ya hesabu hata zaidi ya juu inayoitwa Sage. "Kama ilivyoelezwa katika makala ya kwanza ya ""Calculus: Concepts and Applications,"" ni muhimu kutambua kwamba"" Calculus: Concepts and Applications, 2nd Edition.""" Wakati wanafunzi watatumia calculator ya kisayansi na Geogebra, Chandler pia anawafundisha jinsi ya kutumia programu ya spreadsheet (Excel au programu ya bure ya Libre Office "Calc") kama chombo cha hesabu. Kwa mfano, kwa kutumia teknolojia ya Chandler, unaweza kuona kwamba masomo hayo ni ya hali ya juu kuliko mengine mengi yanayotumiwa na wanafunzi wa nyumbani. Wao kutoa maandalizi bora kwa wale ambao wataendelea na hisabati ya juu baada ya kuhitimu. Ujuzi na "vifaa vya biashara" itakuwa ziada kubwa. Kozi ya Jiometri (kuunganisha mafundisho ya video na maandishi) inatofautiana na wengine na matumizi zaidi ya kitabu cha masomo na mafundisho kidogo ya video. Wanafunzi kufanya kazi kupitia <unk>Central Tatizo<unk> kwamba huanza kila sura. Tatizo la Kati lenyewe hutumiwa kufundisha habari mpya. Wanafunzi hujifunza mifano, hufanya kazi kupitia matatizo ya mazoezi, na kufanya uchunguzi. Katika sehemu hii ya utangulizi, dhana mpya zinaanzishwa kuongoza mwanafunzi kuelekea suluhisho la Tatizo la Kati. Matokeo ni kwamba maudhui yote ni kuletwa katika muktadha wa tatizo ambapo ni mara moja muhimu, badala ya kuwa kushoto kuuliza, "Wakati mimi milele kutumia hii?" Kufuatia hii ni binafsi-quiz, sehemu ya mapitio na mapitio ya binafsi-mtihani. "Kama majibu ya matatizo haya yote ni nyuma ya kitabu, ""Home Study Companion kwa Geometry: A Guided Inquiry"" inajumuisha video ufumbuzi wa matatizo katika sehemu ya mapitio." Kila sura pia ina sehemu ya miradi ambayo inaendeleza dhana kufundishwa katika sehemu ya Tatizo Kuu. Sehemu hii ina seti yake mwenyewe ya matatizo ya kutatua. Home Study Companion: Geometry ina suluhisho la video kwa sehemu ya Mapitio ya Kati, pia ina faili za PDF na suluhisho kamili kwa matatizo yote katika sehemu za Kati na Mradi. (Maandishi yana majibu lakini si suluhisho.) Sehemu za suluhisho mara nyingi huwa na maelezo ya ziada ambayo ni yenye kusaidia kwa wanafunzi. Baadhi ya sura zina <unk>extensions<unk> juu ya Home Study Companion kufunika mada katika viwango vya hisabati ambayo hayakuwa kufunikwa katika kitabu cha masomo. Sehemu za ukaguzi wa aljebra pia zimejumuishwa. Maonyesho kwa kutumia GeoGebra ni kutumika katika kozi yote ya Jiometri. Wanafunzi pia wataunda miundo yao wenyewe ya kijiometri, kwa hiyo wanahitaji kuwa na mpangaji (anaoonyesha vitengo vya metri), kipima-mzunguko, na dira. Karatasi ya grafu na mashine ya kuhesabu ya kisayansi inahitajika pia. Mifano ya masomo ya nyumbani ya Msaidizi inapatikana kwenye tovuti ya Math Without Borders. Unaweza pia kusoma maelezo ya Chandler kwa kila kozi (viungo vilivyoorodheshwa hapo juu) kabla ya kununua kwani hutoa habari ya kina juu ya ratiba na yaliyomo kwenye kozi ambayo ni muhimu sana. Kwa kuangalia kwa haraka kwenye Amazon, unaweza kuona kwamba maandishi yote yanapatikana kwa urahisi, na gharama ya juu ni karibu $ 70. Kwa hiyo gharama ya pamoja ya maandishi na Home Study Companion ni ya chini sana kwa ajili ya kozi ya kiwango hiki. Homeschoolers wanapaswa kupata Home Study Companions moja ya njia za gharama nafuu za kukamilisha kozi za shule ya sekondari za hisabati katika viwango vya changamoto na maudhui ya kozi ya kuvutia. Mchanganyiko huu wa vitabu vya masomo bora na mwalimu mwenye uzoefu kwenye kompyuta inapaswa kufanya kozi hizi ziwe za vitendo hata wakati wazazi hawana msingi wa hisabati.