Our research is motivated by a lack of theoretical tools to analyse the Japanese mathematics lessons with their specificities: the approach by problem solving, the collective dimension of the teaching, and the focus on the development of mathematical thinking. We introduce the concept of collective milieu in order to take into account the collective dimension of the teaching, the lesson as a whole, and the epistemological dimension of the lesson. This research highlights a collective construction of the inquiry or the problem solving process step by step, in terms of the collective milieu.