Concepções dos alunos: uma introdução a uma caracterização formal.

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 "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 a historical and then an epistemic point of view. We report the result of a case study to illustrate the benefit we expect from this approach. The notions of "conception", "knowing", and "concept" are then related one to the other within the model presented. [ABSTRACT FROM AUTHOR]