Discrete mathematics as a resource for developing scientific activity in the classroom

In this paper we present a theoretical discussion on how problems issued from discrete mathematics can develop the attitudes, skills, and knowledge required for scientific mathematical activity in the classroom. We do so via the research situation for the classroom model by performing mathematical and didactical analyses of a problem issued from discrete geometry, and we present the results of a preliminary experiment conducted with Chilean students between the ages of 11 and 13. Our chosen problem asked students to tile a fixed square with a finite number of smaller squares. From the theoretical analysis and the preliminary experimentation, we conclude that this problem, and problems issued from discrete mathematics in general, can induce genuine mathematical activity in lower-secondary school students. In particular, we conclude that this problem is effective in developing the knowledge, skills and attitudes advocated in the Chilean mathematics curriculum.