This book begins with a historical and social foundation for belief in the arbitrary nature of the traditional mathematics curriculum. Chapters reflect the way the author learned while working with children. Each chapter is a complete idea and it is not necessary to read them sequentially. Each chapter is illustrated by stories of different work…

If equivalent operations are performed on the left term and right term of an equation, a new equation results. This principle allows one to produce equations with a variable isolated on one side and its value(s) on the other. It also underlies problem-solving in situations where equations are not explicitly used, but the problem calls for…

Achievement on the final exam was the dependent variable in an experiment involving two college algebra classes. The experimental class was allowed retesting on unit tests while a control class took the unit test once. No significant differences were obtained. (JP)

The author provides an example of obtaining the correct answer to a problem through a so-called nonsense solution. The conditions under which this incorrect method will yield a correct solution are examined. (JP)

Using the computer to calculate the probability that a quadratic equation will factor over the integers is discussed. (DT)

Examples are given of problems that have solutions or discriminants'' similar to that of the quadratic formula; theorems pertaining to these problems are stated and proved. (DT)