11: Classroom Teaching of Mathematics

are his personal characteristics? What sort of preservice and inservice education is most appropriate for him? What teaching method is most effective in mathematics classes? Few questions in mathematics education are more important than these, and few generate more vigorous debate or consistent disagreement. Despite long and active interest in the prob-lems, research offers few important guidelines in the search for personal attributes, classroom styles, or educational preparation of successful teach-ers. Extensive investigation has failed to show significant or consistent correlation between fundamental characteristics of teachers—such as ex-perience, knowledge of mathematics, collegiate preparation, or attitudes toward mathematics—and the achievement or attitudes of their students. Evidence from comparisons of two or more teaching methods supports no one method as superior in mathematics teaching. Much current research in mathematics teaching continues the tradi-tional search for the elusive "good teacher. " However, there is growing evidence of creative, yet careful, new research strategies and techniques. This chapter covers research in mathematics teaching reported from 1964 through 1968. Significant results and promising direction for study are indicated; this chapter is not a catalog of research. Following a dis-cussion of the quality of current research, the review is divided into two major areas: 1) personal characteristics of teachers and 2) teacher class-room behavior, including methods of teaching. The quality and originality of recent research into characteristics and behavior of effective teachers were not evident in studies of preservice and inservice teacher education. Because of this weakness and space limitations, research in teacher educa-tion has not been included in this issue of the Review.