The Professional Knowledge of German Secondary Mathematics Teachers: Investigations in the Context of the COACTIV Project

0 Introduction The relevance of teachers' domain-specific knowledge for high-quality instruction has been emphasised repeatedly, particularly in the context of mathematics teaching (e.g., Ball, Lubien-ski, & Mewborn, 2001). However, despite the eminent role that is attributed to teachers' professional knowledge for creating powerful learning environments, very few instruments are yet available to tap teachers' knowledge directly (Baumert, Blum, & Neubrand, 2004). As a consequence, many questions on mathematics teachers' knowledge, its content, structure, and the way it influences teaching and learning, remain empirically unresolved and, to some extent, unresearched. One of the aims of the COACTIV project (Cognitive Activation in the Classroom) was to conceptualize the professional knowledge of secondary mathematics teachers and, on this basis, to construct reliable tests. Following Shulman's (1986, 1987) taxonomy of teachers' professional knowledge, we distinguish theoretically between pedagogical content knowledge (PCK), which is essentially the knowledge of " how to make the subject comprehensible to others, " and content knowledge (CK), which is the " deep understanding of the domain itself. " Shulman further identifies pedagogical knowledge (PK) as subject-independent knowledge of how to optimize learning situations in the classroom in general, which we do not address in this paper. CK, PCK, and PK are today considered the core categories of teacher knowledge In this paper, we report key findings concerning the tests have been constructed to assess pedagogical content knowledge and content knowledge within the COACTIV project. In so doing, we condense and summarize information presented in Krauss et al. (in press, submitted). We start by introducing the COACTIV project and its technical and conceptual framework of test construction and administration.