ABSTRACT
This chapter addresses the following questions: How will students encounter algebra in school? What is mathematics? And how do human beings think about mathematics? A. Herbert Simon, a Nobel prize winner for his work in economics, should spend time studying the teaching and learning of ninth-grade algebra is a provocative piece of evidence. Simon has suggested that algebra may do for cognitive science what drosophila did for genetics—provide a convenient problem area of appropriate relevance and complexity, within which important advances may be possible. Some courses combine the usual content of algebra with other topics, including computer programming, geometry, logic, or probability and statistics. In some cases these additional topics are dealt with only briefly, but sometimes they are a major focus of time and attention. By far the most important variation in algebra courses occurs in the kinds of experiences that are provided for the students.
