An ITS at secondary school conceived from the didactic of mathematics that integrates the approach by competences to the mathematical knowledge

Our aim in this paper is to show how students at secondary school level can improve their argumentative competence by means of an Intelligent Tutorial System (ITS) designed for learning geometry. After establishing the theoretical frame for our research, we compare the heuristic and discursive characteristics of some tutorial systems, including the one developed by our research team. Afterwards, we tackle the subject of complementarity between knowledge and competence in math class, and then we present an evaluation strategy of argumentative competence on the basis of relations within the subject-milieu system. Our study includes, particularly, structures of cognitive, semiotic and situational control associated to the development of argumentative competence in an e-Learning Environment. We also address the specificity of reference knowledge, the decontextualization of learning, the idea of mathematical proof, and the role of didactical agents.