Conceptualizations of professional knowledge for teachers of mathematics
Different conceptualizations exist about the components of the knowledge teachers need to teach mathematics with professional consciousness, and a researcher needs to describe and assess that knowledge. The fact, however, is that different conceptualizations respond to different needs, and thus, the variety is even a chance to develop the field further, the field of mathematics-related knowledge for teachers and for teaching. This paper sketches basic ideas of selected theoretical approaches, their goals, their fields of application, and their methods. First, three quite influential projects are introduced: The “Michigan Project” (US), “COACTIV” (Germany), and “TEDS-M” (international). Then three conceptualizations with particular approaches are presented: “Mathematics-for-Teaching” (Canada), Rowland’s “Knowledge Quartet” (UK), and Lindmeier’s “Structure Model” (Germany). The paper closes with some remarks concerning horizons: The first remark points to the restriction of all models of evaluating teachers’ professional knowledge, namely, the everlasting gap between the knowledge per se and the need for acting in the classroom. The second remark reads the recently discussed idea of theory-building as a somewhat neglected aspect of professional knowledge. Thirdly, I discuss briefly how far the seminal CK/PCK distinction could really be an appropriate way into perceiving teachers’ professional knowledge. Finally, I close with a few words on the need not to forget the policy issues of our work. The basic overall idea of the paper is to create—within the limited space—a sufficiently broad spectrum of the issue itself, and what was done in recent years to find a basis for research into teachers’ knowledge as a salient issue for the effective teaching of mathematics.