Achieving the meaning of algebraic representations and being able to differently interpret them in relations to the context are central aspects in the teaching and learning of algebra. According to Arcavi’s (1994) idea about development of an effective symbol sense in students, we are working with groups of Secondary school pre and in-service teachers with the main aim of making them aware of the importance of developing in students a conception of algebra as a tool for thinking (Arzarello et Al., 1994, 2001). In this perspective, a fundamental part of our work with them are activities on proofs in arithmetic. In this paper we face the question of the use and the role of algebraic language in the development of such proofs, presenting an initial analysis and classification of trainees’ behaviours in facing a proof problem in arithmetic. The classification is realized according to interpretative keys based on the following theoretical aspects: a) The activation of conceptual frames through which interpreting the expressions produced during the proving activity (Arzarello et Al. 1994, 2001); b) The role of anticipatory thoughts (Boero, 2001); c) The use of conversions and treatments in the coordination between different registers of representation (Duval, 2006).

Future teachers facing proof problems: games of interpretation, anticipating thought and coordination between verbal and algebraic register / A., Cusi; Malara, Nicolina Antonia. - STAMPA. - 2(2009), pp. 25-38. ((Intervento presentato al convegno the 5th Colloquium on the Didactics of Mathematics tenutosi a University of Crete, Rethymnon, nel April 2008.

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