Thematic Group 4 EUROPEAN RESEARCH IN MATHEMATICS EDUCATION III A. Heinze K. Reiss, 1 REASONING AND PROOF: METHODOLOGICAL KNOWLEDGE AS A COMPONENT OF PROOF COMPETENCE 1 Aiso Heinze, Kristina Reiss Universität Augsburg, Germany Abstract: Methodological knowledge is an important component of proof competence. In this paper, we argue that three different aspects of methodological knowledge may be distinguished, which we describe as proof scheme, proof structure, and chain of conclusions. These theoretical aspects guided part of an interview study on secondary students’ methodological knowledge, which serves as a qualitative supplement of a large-scale quantitative study. We present some results of this investigation in which the students had to evaluate correct and incorrect proofs. 1 Introduction During the last few years, reasoning, proof and argumentation in the mathematics classroom has become an important issue in mathematics education research. There is an increasing number of empirical studies on this subject; their results were partly supported by the outcomes of international comparative studies like TIMSS or PISA and their intensive discussion in the scientific community. Our research is part of this context. Its aim is to identify cognitive and non-cognitive factors which play a role in proof competencies of students. We will suggest a theoretical framework and present empirical results, which demonstrate that the methodological knowledge of students is an important prerequisite of their proof competencies. 2 Theoretical framework and research questions 2.1 The role of proof in mathematics and in the mathematics classroom Axioms, definitions, theorems and their proofs, and conjectures form the scaffold of mathematics as a scientific discipline. Mathematics is a proving discipline, which represents the main difference between mathematics and any other scientific discipline. Obviously, mathematics is also the result of social processes, but there is a relative high degree of coherence and consensus among mathematicians (Heintz, 2000; Manin, 1977). For evaluating a proof, the mathematical community uses the theoretical construct of a formal proof: starting from a “real” proof one tries to approach a formal proof by adding information (which is part of the general knowledge shared by the scientific community) until mathematicians are convinced that the real proof is correct. The role of proof in mathematics has consequences for teaching proof in the mathematics classroom. On the one hand, the shared knowledge basis of students differs from that of the mathematics community. Consequently, one has to accept 1 This research is funded by the Deutsche Forschungsgemeinschaft (RE 1247/4).