Chapter 6: Mathematics Instruction: Cognitive, Affective, and Existential Perspectives

The intent of this chapter is to explore why math teaching is out of line with the expectations of the mathematics education community as detailed in the NCTM standards. It begins by presenting two examples of research-based math teaching, one at the college level and the other at a middle school, to illustrate the NCTM vision in practice. This is followed with an analysis of the research on math teaching as a way to understand why research-based teaching is rarely seen. Included in this section are the multiple perspectives or meta-theories that are used to structure studies on teaching. This is followed by examples of frameworks developed from these perspectives. The chapter ends by suggesting a theoretical framework that uses an existential view to look at the interactions between teachers and students in classrooms. This perspective allows us to recognize that teaching and learning are part of a dialectical whole that includes the ways that teachers and students are in the educational situations that they create through the choices that they make.