1INFLUENCING BEGINNING TEACHERS ' PRACTICE IN MATHEMATICS EDUCATION: CONFRONTING CONSTRAINTS OF KNOWLEDGE, BELIEFS, AND CONTEXT

preparing teachers—the primary agents of change in the nation's K-12 cl ssrooms. Two recent documents of the National Council of Teachers of Mathematics ([NCTM] 1989a, 1989b) describe a vision of mathematics classrooms where students and teacher form a community of learners engaged with one another in inquiry; where teachers provide situations that lead to learner inventions; where students become mathematical risk-takers—making guesses and pursuing hunches, making conjectures and marshalling arguments in support of them; where the criterion for what makes sense is determined by students and teacher working together. Creating a vision of classrooms that enable mathematical inquiry and that empower learners and teachers is one thing. Preparing teachers with the knowledge and disposition to construct real classrooms that embody this vision is quite another. The challenges that teacher educators confront are embedded in the deeply rooted ideas about teaching and learning mathematics that preservice teachers bring to their professional studies and the difficulty of professional study to overcome ingrained notions developed during previous schoo