Expertise in Developing Students' Expertise in Mathematics: Bridging Teachers' Professional Knowledge and Instructional Quality

This paper provides a survey of the research on the relationship between teachers' professional knowledge and their instructional quality in the domain of mathematics education. First, an overview is provided of the way in which mathematics professional knowledge has been conceptualized. Second, the relation between mathematics teachers' professional knowledge and instructional practice is outlined, with a special focus on the mediating role of teachers' professional beliefs and teachers' situation-specific knowledge and skills. Third, we describe the model of mathematics teachers' competence as an integrative model including knowledge, beliefs, situation-specific skills and observable classroom behavior. Fourth, we describe the current research on bridging teachers' professional knowledge and instructional quality, with special attention to recent issues with respect to the validation, development, and impact of professional competence. We end with some challenges for future research.