A mathematical competition as a problem solving and a mathematical education experience

In this paper, some aspects of French mathematical education theory concerning “problem situations” are taken into account. In this theoretical framework, the choice of 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: (1) designing features in the problem situation that allow students, by themselves, to check or rectify their method; (2) the importance of collaborative work; (3) what stages typically occur in solving a problem; (4) how an a posteriori analysis can reveal students' unexpected approaches; and (5) the use of didactic variables that will compel students to develop, over time, more sophisticated tools and argumentation in problem solving and in constructing proofs.