Students conceptions: an introduction to a formal characterization

Nicolas Balacheff (1) , Nathalie Gaudin (1)

1 Leibniz - IMAG - Laboratoire Leibniz

We investigate in this paper the complexity of modeling students knowing of mathematics under the constraints of acknowledging both their possible lack of coherency and their local efficiency. For this purpose we propose a formalization of the notion of "conception" as a possible tool to answer the epistemological problem we identify. We apply then this approach to the study of the possible conceptions of "function", from an historical and then an epistemic point of view. We report the result of a case study in order to illustrate the benefit we expect from this approach. The notions of "conception", "knowing" and "concept" are then related the one to the other within the model presented.

Mots clés: didactic of mathematics; conceptions; errors; knowledge modelling

Domaines: Environnements Informatiques pour l'Apprentissage Humain

Nicolas Balacheff, Nathalie Gaudin. Students conceptions: an introduction to a formal characterization. 2002. ⟨hal-00190425⟩