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.