Conditions of progress in mathematics teacher education

Abstract

The progress of mathematics teacher education as a field of study depends on theoretical and empirical work. Both kinds of work are intimately related. Any scientific article that reports an empirical study needs to be based in theoretical constructs, and, at the very end, should contribute to a better understanding of these concepts or, at least, of their power for understanding specific problems, and any theoretical work, to make sense, requires some sort of empirical application. The articles in this issue of JMTE draw on several key theoretical concepts in mathematics teacher education: content knowledge and pedagogical content knowledge (Davis), teachers’ beliefs (Cross, Davis), teachers’ practices (Cross, Ryken), and teacher learning (Ryken). As a subfield of the social sciences, we cannot expect that all the authors share the same view about such notions. However, we must be able to understand how they conceptualize their major theoretical concepts, relate them to each other, note their similarities and differences, and regard the implications of the different choices. Teachers’ knowledge of mathematics includes teacher knowledge of mathematical facts and representations, concepts, procedures, and other information, as well as the ability to solve problems, to construct and use models, to establish connections within and outside mathematics, to reason, to prove, and to evaluate results. In this issue, Davis, in his article titled ‘‘Understanding the influence of two mathematics textbooks on prospective secondary teachers’ knowledge’’ draws on the distinction between factual knowledge and conceptual knowledge that points toward different levels of elaboration. Other dimensions of knowledge in action, which are captured by the notions of problem solving, modeling, proving, and evaluating, are at the core of the current mathematics curriculum orientations for students’ learning and also need the attention of mathematics teacher education researchers. Teachers’ pedagogical content knowledge blends ‘‘pedagogy’’ and ‘‘content’’ in a special way. Davis stresses two aspects, the educative representations that include ‘‘the most powerful analogies, illustrations, examples, explanations, and demonstrations’’, and