9358517 Philipp knowledge for teaching has been an area of much research in the past decade. Today some of the domains of knowledge identified include knowledge of subject matter, pedagogical content knowledge, knowledge of the curriculum, and knowledge of learners. Research has shown that experimental teachers who have had access to research about students' thinking within well- defined mathematical content domains listen to children explain their mental processes used when solving problems and accept a larger variety of strategies than control teachers. These experimental teachers also spend less time during class on drill activities and more time on problem solving. The research extending this work to preservice teachers is just emerging, and one area that has not yet been investigated is the relationship between teachers' content knowledge, pedagogical content knowledge, conceptions of mathematics, and understanding of students' mathematical thinking. This project will research the relationship between preservice teachers' mathematics content knowledge, their pedagogical content knowledge, their conceptions of mathematics, and their understanding of students' mathematical thinking at different points during their teacher preparation. These findings will be compared to the relationship between these forms of knowledge possessed by inservice teachers. This knowledge/belief will be operationalized through videotapes of preservice and inservice teachers interviewing and tutoring children.
