Abstract

Lucia Grugnetti & François Jaquet
Local Unity of Math Education Research, University of Parma, Italy Math-Ecole, Switzerland

In this paper, some aspects of French mathematical education theory concerning “problem situations” is taken into account. In this theoretical framework, the choice of the problem situations is fundamental in order to allow pupils to make hypotheses, to mobilize their knowledge, to argue, and finally, to construct new knowledge. Certain factors concerning this choice are discussed, such as: designing features in the problem situation that allows students by themselves to check or rectify their method; the importance of collaborative work; what stages typically occur in solving a problem; how an a posteriori analysis can reveal students’ approaches not expected; and finally, the use of didactic variables to force students to develop over time more sophisticated tools and argumentation in problem solving and in doing proof.