Argumentation and proof in mathematics

During the mid 90s this issue was not highly developed.
Existing researches in this field highlighted that it was important to anticipate proof with an argumentation activity that could support students to overcome some difficulties involving the construction of proof. The hypothesis of these researches was that there would usually be a continuity, named "cognitive unity", between these two processes. Nevertheless, the theoretical framework of reference did not provide tools to validate this. A scientific contribution was developped by ITD team in a specific frame for mathematics argumentation with the aim to compare it with proof. On the basis of contemporary linguistic theories (Toulmin, Perelman & Olbrechts-Tyteca, Anscombre and Ducrot, Plantin) a theoretical framework was constructed to "model" a mathematical argumentation, to compare it with the proof and to describe cognitive processes involved in this process. The cognitive analysis is based on a methodological tool (Toulmin's model integrated with the "conception" model of Balacheff) that can be used to compare and analyse students argumentations and proof. This tool and the obtained results by using it in different mathematical fields (geometry and algebra) are the innovative aspect of this study. The importance of these results is witnessed by some publications in national and international magazines, by some organisation assignments in working groups related to argumentation and proof (Working Group 4 "Argumentation and proof" of CERME 3), by the editorial work of the Educational Newsletter « La Lettre de la Preuve » (four-month-magazine on-line about proof in mathematics education followed by more than 4000 persons).