School Math Fundamentals provides a look at many of the algorithms present in pre-calculus mathematics. The book consists of a treatment of the mathematical topics of multiplication and division; basic operations; proportion; quadratic equations; trigonometric and inverse trigonometric functions; the Pythagorean Theorem and the Law of Cosines; and exponential and logarithmic functions. Each topic is given a separate chapter. Each chapter contains a brief discussion of the topic, occasionally accompanied by figures, along with definitions, examples and some proofs.
The treatment of topics is mostly algorithmic. For example, the discussion of division of rational numbers uses a numerical example to demonstrate that the algorithm for division of rational numbers p1 and p2 (where p2 is not zero) is to multiply p1 by the reciprocal of p2. A similar approach is taken in most of the chapters, where numerical examples are used to motivate the symbolic algorithm. Other than the discussion of the basics of multiplication, the approach taken in this book does not provide mathematical explanations that include concrete or pictorial representations. Instead, it relies on inductive reasoning from particular cases and either generalizes to the symbolic result or simply states the symbolic result.
A few issues are handled unsatisfactorily. In the chapter on basic operations, the discussion of the multiplication algorithm refers to “adding a zero” to the right hand position of a number when multiplying by ten. While this is common English usage, a mathematical text should be more precise about its use of mathematical language. “Appending a zero” would be a simple change that would improve the clarity of this discussion of the algorithm for multiplication of a whole number by ten. Secondly, the discussion of exponential functions uses limit notation and concepts without addressing the concept of limit. This is not atypical of pre-calculus treatments of limit topics, and yet a book that claims simple explanations of school mathematics would be improved by more attention to this concept than referring to a limit using the vague language of “approaching.”
This book is presumably aimed at successful mathematics undergraduates who know the algorithms of high school mathematics and want a second look at them. Such students will likely appreciate the discussion of multiplication of negative numbers. The book does not offer many concrete explanations, making it unsuitable for those who want conceptual understanding rather than symbolic.
Elizabeth Burroughs is an Assistant Professor of Mathematics Education in the Department of Mathematical Sciences at Montana State University. She is a 2003 Project NExT fellow.