ABSTRACT
The "new math" movement of the 1960s attempted in introducing some new ideas and new approaches into algebra instruction. But the changes that have persisted into today's curriculum have been more cosmetic than substantial. The emergence of sophisticated calculators and computers as tools in both computational and abstract mathematics have changed the way that mathematicians do mathematics and the way that scientists, engineers, and social scientists use mathematics. All mathematics instruction and algebra instruction in particular, should be designed to promote understanding of concepts and to encourage thinking. The chapter discusses the three criteria: intrinsic value, pedagogical value, and intrinsic excitement or beauty. In algebra, exponential growth and decay, especially if taught within the context of population dynamics or pollution control, can fit the criterion of intrinsic excitement. Existing software packages will simplify algebraic expressions; add, subtract, multiply, and divide polynomials and polynomial fractions.
