- Hardcover: 721 pages
- Publisher: Addison-Wesley; 3rd edition (January 1994)
- Language: English
- ISBN-10: 0201860945
- ISBN-13: 978-0201860948
- Product Dimensions: 1.2 x 8.2 x 10 inches
- Shipping Weight: 3.1 pounds
- Average Customer Review: 22 customer reviews
- Amazon Best Sellers Rank: #565,930 in Books (See Top 100 in Books)
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Algebra I: Expressions, Equations, and Applications 3rd Edition
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A beginning algebra textbook with instructions for the teacher on how to present the material to students.
Top customer reviews
Paul Foerster takes a delightfully different approach. In this gem of a book, mathematics is not merely something to be memorized, but something to be digested and savored - and most importantly, understood. Consider the addition property of equality, that is, if a, b, and c are real numbers, and a = b then a + c = b + c. Simple enough. Yet in the Algebra 2 Saxon text, John Saxon writes that "it is important to understand why we do things in Algebra, but it is also important not to let the emphasis on understanding interfere with our ability to do." And then he proceeds to illustrate his point by giving a very shallow presentation of this very simple - and very important - property of mathematics. He simply tells students - literally - "change sides, change signs." Paul Foerster, however, writes that "a transformation such as adding 3 to each member can be thought of as adding equal weights to both sides of a balance. If it was balanced before, it will still balance afterward. But if you add weight to only ONE side, it no longer balances!" And then he follows by giving a pictorial representation of what he means.
Again, a very simple, almost trivial example, but it represents one of the fundamental differences between Foerster's pedagogy and the pedagogy of the vast majority of textbook authors. Here's another example. Consider the definition of negative exponents. x^-3 is defined as 1/x^3. Saxon tells students that there is nothing to understand about this because it's merely the result of a definition. What he fails to tells students is that this is the only LOGICAL definition of a negative exponent, and is NOT merely arbitrary or conventional. Foerster, however, explains the logic behind the definition of a negative exponent and shows how it follows NECESSARILY from the ratio of two positive exponents. For example, if you go from top to bottom in this following expression, you go x^3/x^4 --> xxx/xxxx --> 1/x (you've cancelled all the other x's); however, if you go from bottom to top, you end up with x^-1, but negative exponents are meaningless, so we are FORCED to define x^-1 as 1/x^1 = 1/x.
Foerster thus shows that mathematics is a LOGICAL system, that it makes *sense*, and that it is *not* just a collection of formulas to be memorized, whereas Saxon - along with most authors - does quite the opposite.
Some parents and some students might opt for another text because this text has some challenging problems. But if you **carefully** read his explanations, the challenge problems instead of becoming the rough meat of a meal, become the delicious desert that follows it. Rest assured that there is no challenge problem in his book that cannot be deduced from Foerster's explanations. In fact, I even wish more such problems were included!
Foerster's books *will* prepare you for the rigors of any acclaimed college math program (e.g. Harvard, MIT, Cal Tech); you cannot go wrong with Foerster.
There is a video that supports this book if the student needs help. It does not follow exactly on the older edition, but does cover the subjects. The video is for the 2006 edition. [...]
Depending upon the child's learning style, this book works well with the current child I am teaching. It keeps moving forward building on what you have learned. This book does not do the continual review of old information.