This research is aimed at questioning the semiotic mediation process that takes place in teaching and learning sequences using an artefact and conceived for constructing the notions of variable, function and graph of function. It develops according to three main research axes: I. the conception of a sequence of activities, starting from the unusual geometrical context provided by Cabri-géomètre. By offering a model of the geometrical objects in terms of variables objects, this context can lead to a dynamical and co-variational apprehension of the notions of variable, function and graph of function. II. The reflection on the possible articulation between the two theoretical paradigms by which we built up the teaching and learning sequence of activities, that is to say between “the theory of the semiotic mediation” inspired by Vygotski and mainly developed in Italy and “the theory of didactical situations”, elaborated in France at the beginning by Brousseau. III. The analysis of the teacher's role in orchestrating the collective discussions. In fact, in the semiotic process, the teacher's role is crucial and critical: by providing specific tasks, he organizes the access to certain signs and, by orchestrating the collective discussions. He supports the eventual internalization of these signs by the students.
Theory of Situations, semiotic mediation and collective discussions in teaching sequences that use Cabri-géomètre and that are aimed at the learning of the notions of function and graph of function