ABSTRACT
Teachers across the country are being asked to transform their mathematics teaching. This transformation entails more than posing different problems, asking different questions, or calling on different students; it demands that teachers make changes in their basic epistemological perspectives, their knowledge of what it means to understand and thus learn mathematics, and their classroom practice (see Cobb, Wood, Yackel, & McNeal, 1993; Schifter & Fosnot, 1993, for elaboration of teaching for understanding). For the past 10 years, we have worked with teachers attempting to transform their mathematics teaching. We have watched, listened, questioned, and reflected on the ways in which the teachers have changed. In this chapter, we outline what we have learned about teachers transforming their mathematics teaching. Specifically, we discuss the patterns of changes in beliefs and classroom practice that we have seen as teachers engaged with knowledge of childrens mathematical thinking. We then discuss the role of practical inquiry in the changes of these teachers.
