John Saxon's preface to Algebra 2

Preface to Saxon Algebra 2

This is the second edition of the second book in an integrated three-book series designed to prepare students for calculus. In this book we continue the study of topics from algebra and geometry and begin our study of trigonometry. Mathematics is an abstract study of the behavior and interrelationships of numbers. In Algebra 1, we found that algebra is not difficult—it is just different. Concepts that were confusing when first encountered became familiar concepts after they had been practiced for a period of weeks or months—until finally they were understood. Then further study of the same concepts caused additional understanding as totally unexpected ramifications appeared. And, as we mastered these new abstractions, our understanding of seemingly unrelated concepts became clearer.

Thus mathematics does not consist of unconnected topics that can be filed in separate compartments, studied once, mastered, and then neglected. Mathematics is like a big ball made of pieces of string that have been tied together. Many pieces touch directly, but the other pieces are all an integral part of the ball, and all must be rolled along together if understanding is to be achieved.

A total assimilation of the fundamentals of mathematics is the key that will unlock the doors of higher mathematics and the doors to chemistry, physics, engineering, and other mathematically based disciplines. In addition, it will also unlock the doors to the understanding of psychology, sociology, and other nonmathematical disciplines in which research depends heavily on mathematical statistics. Thus, we see that mathematical ability is necessary in almost any field of endeavor.

Thus, in this book we go back to the beginning –to signed numbers—and then quickly review all of the topics of Algebra 1 and practice these topics as we weave in more advanced concepts. We will also practice the skills that are necessary to apply the concepts. The applicability of some of these skills, such as completing the square, deriving the quadratic formula, simplification of radicals, and complex numbers, might not be apparent at this time, but the benefits of having mastered these skills will become evident as our education continues.

We will continue our study of geometry in this book. Lessons on geometry appear at regular intervals, and one or two geometry problems appear in every homework problem set. We begin our study of trigonometry in Lesson 43 when we introduce the fundamental trigonometric ratios—the sine, cosine, and tangent. We will practice the use of these ratios in every problem set for the rest of the book. The long-term practice of the fundamental concepts of algebra, geometry, and trigonometry will make these concepts familiar concepts and will enable an in-depth understanding of their use in the next book in the series, a pre-calculus book entitled Advanced Mathematics.

Problems have been selected in various skill areas, and these problems will be practiced again and again in the problem sets. It is wise to strive for speed and accuracy when working these review problems. If you feel that you have mastered a type of problem, don’t skip it when it appears again. If you have really mastered the concept, the problem should not be troublesome; you should be able to do the problem quickly and accurately. If you have not mastered the concept, you need the practice that working the problem will provide. You must work every problem in every problem set to get the full benefit of the structure of this book. Master musicians practice fundamental musical skills every day. All experts practice fundamentals as often as possible. To attain and maintain proficiency in mathematics, it is necessary to practice fundamental mathematical skills constantly as new concepts are being investigated. And, as in the last book, you are encouraged to be diligent and to work at developing defense mechanisms whose use will protect you against every humans’ seemingly uncanny ability to invent ways to make mistakes.

One last word. There is no requirement that you like mathematics. I am not especially fond of mathematics—and I wrote the book—but I do love the ability to pass through doors that knowledge of mathematics has unlocked for me. I did not know what was behind the doors when I began. Some things I found there were not appealing while others were fascinating. For example, I enjoyed being an Air Force test pilot. A degree in engineering was a requirement to be admitted to test pilot school. My knowledge of mathematics enabled me to obtain this degree. At the time I began my study of mathematics, I had no idea that I would want to be a test pilot or would ever need to use mathematics in any way.

I thank Tom Brodsky for his help in selecting geometry problems for the problem sets. I thank Joan Coleman and David Pond for supervising the preparation of the manuscript. I thank Margaret Heisserer, Scott Kirby, John Chitwood, Julie Webster, Smith Richardson, Tony Carl, Gary Skidmore, Tim Maltz, Jonathan Maltz, and Kevin McKeown for creating the artwork, typesetting, and proofreading.

I again thank Frank Wang for his valuable help in getting the first edition of this book finalized and publisher Bob Wroth for his help in getting the first edition published.

John Saxon
Norman, Oklahoma



Beautiful.

The third editions of the Saxon books seem to have done away with John Saxon's prefaces; at least, that's the case with the 3rd edition of Algebra 1/2.

Thanks to our ktm Book Fairy, I have a copy of the 2nd edition of Algebra 1/2, so I'll post that preface, too.

The books themselves don't seem to have been changed in other bad direction. If you're interested in buying the 2nd edition, though, Rainbow Resource seems still to have them. So does Seton Books. I'm sure other homeschooling stores do as well.



Wilfried Schmid on procedures and understanding

''I'm a professional mathematician, and I myself very often use mathematical methods that I understand only imprecisely,'' he said. ''It is while I use them that I begin to understand. After a while, the use and the understanding are mutually supporting.''

source:
The New, Flexible Math Meets Parental Rebellion (scroll down)
By ANEMONA HARTOCOLLIS (NYT) 2403 words
Published: April 27, 2000