MATHEMATICS TEACHING AND LEARNING

Overview
This chapter focuses on advances in the study of mathematics teaching and learning since the publication of the first edition of the Handbook of Educational Psychology (Berliner & Calfee, editors) in 1996. Because of the scope of the review, comprehensive coverage is not possible. In what follows I have chosen to focus thematically on major areas in which progress has been made or where issues at the boundaries of theory and practice are controversial. These areas include: research focusing on issues of teacher knowledge and aspects of professional development; issues of curriculum development, implementation, and assessment; issues of equity and diversity; and issues of learning in context(s). The chapter concludes with a discussion of the state of the field and its contextual surround.

Teacher Knowledge
Significant progress has been made over the past decade in understanding mathematics teachers’ knowledge, how it plays out in practice, and how it can be developed. The field can boast of two major books and two additional programmatic bodies of work, all of which add significantly to our understanding. Over the past decade, two major works have emerged that expand the field’s conception of the nature and complexity of the knowledge that teachers bring to the classroom. Liping Ma’s 1999 book Knowing and teaching elementary mathematics demonstrated the unique character of highly accomplished mathematics teachers’ knowledge – a knowledge clearly different from knowledge of the mathematics alone. Magdalene Lampert’s
2001 book Teaching Problems and the Problem of Teaching offers a remarkably detailed empirical and theoretical examination of the multiple levels of knowledge, planning, and decision-making entailed in a year’s teaching. Next, I briefly describe Deborah Ball, Hyman Bass, and their colleagues’ studies of the mathematical knowledge that supports effective teaching, and the work of Miriam Sherin in describing teachers’ professional vision. Like the work described before it, this work sheds light on the character of knowledge that enables teachers to interact effectively with students over substantial mathematics. This work is followed by a description of the work by the Teacher Model Group at Berkeley, which has worked to characterize both the nature of teacher knowledge and the ways that it works in practice. Like the work of Ball, Bass, and colleagues, this work characterizes teaching as problem solving. It contributes to the problem solving and teaching literatures by describing, at a theoretical level of mechanism, the kinds of decision-making in which teachers engage as they work to solve the problems of teaching.