Review of Foerster's Algebra 1 with a Home Study Companion − Algebra 1 by David ChandlerAs of this writing (2008), some of the most popular and respected algebra 1 programs among homeschoolers are:
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. However, I also feel I need to disclose one drawback (to homeschoolers), which is that as of this writing, the publisher, Prentice Hall, refuses to sell the solutions manual to homeschoolers. In the back of the book you'll find answers to odd-numbered problems, but not full solutions. This doesn't have to pose a problem per se IF the student has someone to fall back on in case he gets stuck (restricting the student to the odd-numbered ones is not a problem since there are plenty). 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
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: 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! 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. As of this writing, the 1994 edition of Foerster's Algebra I: Expressions, Equations, and Applications Home Study Companion − Algebra 1 by David Chandler
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.
David Chandler has also made a Home Study Companion for a very good geometry book called Geometry: A Guided Inquiry Algebra I: Expressions, Equations, and Applications Home Study Companion - Algebra 1 by David Chandler. Price $59 + sh. Review by Maria Miller, MSc, author of HomeschoolMath.net |
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