ABSTRACT KNOWLEDGE AND REASONING IN MATHEMATICAL PEDAGOGY: EXAMINING WHAT PROSPECTIVE TEACHERS BRING TO TEACHER EDUCATION By

This study focuses on the knowledge and beliefs about mathematics and the teaching of mathematics held by prospective teachers when they enter teacher education. It offers frameworks for thinking about the role and relationship of different kinds of knowledge in teaching mathematics. Grounded in a vision of a particular mathematical pedagogy, these frameworks are constructed around teacher knowledge, beliefs, and dispositions in the domains of subject matter, teaching and learning, students, and context. A two-part interview was designed to explore prospective teachers ' ideas and thinking about mathematics and the teaching and learning of mathematics. Nineteen prospective teachers were interviewed. The study's results include description and appraisal of the participants ' understandings and ways of thinking about the subject matter, teaching and learning, the teacher's role, and students. These results suggest categories useful for examining what prospective teachers bring with them to their professional preparation to teach mathematics. Focal subject matter knowledge categories included the explicitness and connectedness of substantive understandings, as well as ideas about the justification and nature of mathematical knowledge and activity. With respect to teaching and learning, centra