Future teachers facing proof problems: games of interpretation, anticipating thought and coordination between verbal and algebraic register
Cusi, A., Malara, N.A. (2009). Future teachers facing proof problems: games of interpretation, anticipating thought and coordination between verbal and algebraic register
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This contribution is part of a wider work, involving pre- and in-service teachers, aimed at making teachers aware of the importance of developing in students an effective symbol sense. In this perspective, a fundamental part of our work with teachers consists of activities of proof in elementary number theory. At the same time we are interested in analysing the use and the role of algebraic language in the development of such proofs. In this paper we present an initial analysis and classification of trainees’ behaviours in facing the proof of a conjecture that arises from their exploration of a proposed numerical situation. The analysis of teacher protocols has been conducted by reference to particular interpretative keys that reflect our thinking about the abilities required for the deployment of algebraic language in proofs. They are: the application of specific conceptual frames, the games of interpretation between different frames, anticipatory thoughts, the use of conversions and treatments and coordination between different registers of representation. From an educational point of view this analysis can be used as a methodological tool to both help teachers identify their own difficulties in algebra and to promote communication with and amongst them.
