The course covers the foundations of didactics of mathematics: the didactic transposition, the organization of the learning situations, the analysis of the processes and the difficulties of mathematics learning (with references to the "theories" of Wertheimer, Piaget and Vygotsky). In the course some specific characteristics of teaching / learning mathematics will be discussed and compared to the other sciences and disciplines, with reflections on the relationship between teaching / learning in the university and in the secondary school. Students will be involved through problem solving, cultural reflection about setting and didactic approach to mathematical topics, including in relation to various possible uses of the computer.