ABSTRACT
This article describes how principles relating to modeling theory can be used to understand teacher development and the nature of teacher knowledge. We will document and analyze the actual practices of teachers who are attempting to modify, revise, and refine their approaches to the teaching and learning of mathematics, and then identify some of the conditions that have motivated the changes. Understanding teacher development in this way is of great importance because there are many efforts underway which attempt to reform the teaching and learning of mathematics. A primary objective of these efforts is to help teachers move toward the teaching practices established by the National Council of Teachers of Mathematics (NCTM, 1989, 2000). These practices entail a “radical change in the mathematics taught in schools, the nature of students’ mathematical activity, and teachers’ perspectives on mathematics teaching and learning” (Simon & Tzur, 1999, p. 252). But, reforming teachers’ practice is not a simple matter. Stigler and Hiebert (1999), made the point that teaching is a cultural activity, and cultural activities “evolve over long periods of time… and rest on a relatively small and tacit set of core beliefs about the nature of the subject, about how students learn, and about the role that a teacher should play in the classroom” (p. 87). Stigler and Hiebert (1999) and other researchers underscored the difficulty in reforming deeply held and robust teaching practices.
