L'inférence figurale: Un pas de raisonnement discursivo-graphique

This article aims at legitimating the use of the graphic registers in the written expression of mathematical reasoning. More than the defence of this legitimacy, the article shows also the risks of its use: the problems of communication which it causes as well as the difficulties, for the teachers, to evaluate the reasoning of the pupils when they integrate these registers into their solutions, and for the pupils, to understand the mathematical texts which use these registers in their discursive expansions differently than optional illustration. With the concept of graphic expansion and figural inference, the article claims to supplement the inferences in Raymond Duval's discursive plans whilst respecting the reasoning functional definition. Having considered the cognitive and semiotic aspects in the definition of figure, the article shows the use of drawings in the reasoning structure of a pupil at secondary level. Figural inference born from this study is examined then defined in terms of function, structure and quality.