# Review of Foerster's Algebra 1 with a Home Study Companion − Algebra 1 by David Chandler

As of this writing (2008), some of the most popular and respected algebra 1 programs among homeschoolers are:

- Saxon math,
- Harold Jacob's Algebra,
- Teaching Textbooks Algebra 1.

I certainly recognize each program has its followers and its good points − yet they do have their drawbacks as well.

For example, Teaching Textbooks is known for its thoroughness and being a very very comprehensive program since all solutions are provided in full on a DVD. However, people also generally consider it as not challenging.

Saxon math employs an incremental approach that introduces a new concept every day (every lesson). Many kids grow bored on it, or they can't get the concepts when new stuff comes along so soon.

Harold Jacob writes in a different, lighthearted style, with some cartoons. This book is praised a lot by homeschoolers as very interesting. People say it's good for kids who have intuition with math. But did you know what Jacobs himself *recommends* as a followup to his algebra program? Paul Foerster's Algebra II, Trig, and Calculus.

So I want to present another alternative: start using **Paul Foerster's texts at Algebra 1** level, alongside with the **Home Study Companion video lessons** made by David Chandler.

I feel this option, in general, is EXCELLENT, because of the quality of the text and of the video lessons. It serves BEST those students who don't mind − or who even *want* to have something a little challenging − and who want to gain a very strong background in mathematics.

For the rest of this review, I will now present some details from both the book and the video lessons.

## Review of Algebra 1: Expressions, Equations, and Applications by Paul Foerster

Foerster's Algebra texts are exceptional in several ways. Many people keep give them high acclaim. Look at for example Foerster's algebra 1 review written by the folks at MathematicallyCorrect, or the comparison chart at MathematicallyCorrect.com that compares several algebra 1 texts from well-known publishers. FACE recommends Foerster's texts in its Noah plan.

Personally, I have to praise the book as well. After seeing a competitor product (traditional algebra 1 text) that starts every lesson with a confusing real-life example, Foerster's Algebra 1 looked fantastically clear, teaching the concepts and techniques in small steps, allowing for plenty of practice. The book is very comprehensive, very logical, and often goes deeper into the topics than some other books.

And it's not just that. The way concepts are presented, developed, and practiced, he has managed to weave algebra 1 topics into a connected body of knowledge. Everything new is based on previously learned concepts, and connections between the concepts are emphasized. The text just reads great.

For example, in the whole book, Foerster has a UNIFYING THEME: that of an *expression*. In his own words:

For increasingly complex expressions, students do these three things:

- Write an expression representing a variable quantity in some real-world situation,
- Find the value of the expression when x is known,
- Find x when the value of the expression is known.

In each lesson, after the main part of explaining the concept, the text presents several examples. Foerster intends the student to cover the answers to these examples, then try to solve the problems, and then uncover the solutions. Each lesson has plenty of practice problems (BTW it's not intended that every student work every problem). The end of each chapter has a section of applications via numerous word problems.

His word problems are excellent. They are multi-step problems, and are not just the typical knock-off problem categories (D=RT problems, work problems, mixture problems, etc.) with the numbers changed. The mathematics needed to attack the problems vary from problem to problem, and the student needs to combine techniques he's learned. He is teaching the student how to think analytically.

Yet I have to mention this also: the examples in the lessons full of word problems are written so that the many questions in the examples actually guide you step-by-step in how to think and build your equation. You will not see that in every algebra text.

Foerster doesn't forget humor, either. He has livened up the word problems with clever character names and silly puns. In general, his writing style is warm and approachable by students.

David Chandler, the author of the Homeschool Companion to Foerster's algebra 1, points out a few other good points of this text and Foerster's other books:

They have a real sense of "authorship." Most math textbooks seem to be written by a committee controlled by the publishers. Paul Foerster is an ex-engineer turned teacher who has an intimate sense of the usefulness and power of mathematics as a tool for solving real-world problems. His writing comes across like a conversation with a real author. He is also a good writer!

He has a good balance between rigor and intuition. It is more important at the introductory level to have an intuitive grasp of an issue (negative numbers, distributive law, etc.) and how to use them in a problem-solving context than to see rigorous proofs of mathematical properties. The rigor is not brushed aside: it is simply handled in a balanced way.

Some people may object to the untraditional sequence of topics, where quadratic equations are presented about in the middle of the whole text, instead of near the end.

Foerster himself mentions this in the foreword and says:

"This ... is made possible by technology, specifically, the use of calculators to evaluate radicals. As a result, students are able to work more realistic word problems in which answers are decimals."

Quadratic equations are presented in the 6th chapter of a total of 14 chapters. In chapter 6, students learn to complete the square, which is then used to prove the quadratic formula, and applications follow. Solving quadratic equations by factoring is much later, in chapter 10. This approach allows for the inclusion of quadratic equations in the problem solving sections of the second half of the book − and remember, the word problems in the various chapters are excellent!

Used and new copies are easily available at Amazon.com or other bookstores. At Amazon, you can find these editions, either used or new:

Algebra I: Expressions, Equations, and Applications (1994 edition)

Algebra 1: Expressions, Equations, and Applications (1999 edition), and

Algebra 1: Expressions, Equations, and Applications (2006 edition).

## Home Study Companion − Algebra 1 by David Chandler

Who is David Chandler? He is a mathematics teacher with BS in physics, MA in Education, and MS in Mathematics Harvey Mudd College, Claremont Graduate University, and California Polytechnic University). He's been teaching for 30 years in public, private, international, and charter schools at all levels from 2nd graders on up, through the full high school and junior college math and physics curriculum.

David Chandler has put together A Home Study Companion - Algebra 1, which consists of whiteboard video lessons to accompany every lesson in Foerster's Algebra 1 book. You can fast forward or rewind these lessons at will, to find the exact spot you're looking for.

In these lessons, he usually presents the concept at hand, just like a normal teacher would do in class. He then goes through and explains in detail several examples from the corresponding lesson in Foerster's book.

In essence, you get to listen to an excellent, experienced math teacher explain the complete Algebra 1 class: the concepts and solved examples.

Below are some screenshots. Click them to enlarge.

David Chandler is not just doing example problems from the book. He is actually TEACHING you a complete lesson on the concept at hand. Based on his teaching experience, he is very conscious of the areas where students have conceptual difficulties and points out ways they can build intuition for what is going on behind the equations.

For example, Chandler explains and justifies the distributive property in more detail than the book itself. He constantly "throws in" or explains little "tricks of the trade", such as which of the x-terms you should get rid of in the equation with x-terms on both sides (for example 5x + 9 = 7x − 6), or where did the plus-minus ( ±) sign suddenly come from. Or, he takes little sidesteps to point out connections: "In fact, you've seen this before:.... ".

He mentions the "customary" ways of writing mathematics. For example, while solving a certain problem from the book, he changes the variable from x to *t* because it is the customary variable for time. After Chapter 6, he's even added a lesson of his own (outside of Foerster's) called "Getting Fluent", which explores ways that you can write down your equation solving more efficiently − the way mathematicians are accustomed to doing it.

All in all, Chandler "expands" the presentation of the topics and the example solutions as compared to the concise explanations in Foerster's text, adding in more detailed explanations. You'll also see exactly what buttons to push on the calculator in those problems that require such. Chandler talks and writes fairly slowly (view the sample video below) so your student should be able to keep up easily. Algebra isn't a speed contest anyway!

You could easily use these video lessons to accompany some other algebra text, as well. The example problems he uses are fully written out on the video.

Click to view a sample lesson, for Chapter 4, Section 6.

David Chandler has also developed a similar home study companion with videos to accompany Foerster's Algebra 2 book.

Besides algebra, he has made a Home Study Companion for a very good geometry book called *Geometry: A Guided Inquiry (the link goes to my review of it)*.

Algebra I: Expressions, Equations, and Applications by Paul Foerster.

Price: about $60 new; used copies vary in price from a few dollars on up. See these links that go to Amazon.com:

Algebra I: Expressions, Equations, and Applications (1994 edition)

Algebra 1: Expressions, Equations, and Applications (1999 edition), and

Algebra 1: Expressions, Equations, and Applications (2006 edition).

Home Study Companion - Algebra 1 by David Chandler. Price $69 + sh.

The solutions manual (ISBN 9780201861006) is available at Rainbow Resource and at By Way of the Family bookstore.

*Review by Maria Miller, MSc, author of HomeschoolMath.net*