This paper outlines some theoretical categories (i.e. the "meso-", "topo-", "chrono-geneses," the "milieu," the didactical contract and the learning games), providing a "model" to study mathematics teacher's action. In order to show what this model brings to the didactical analysis, we present the action of two teachers, on the same content, and we attempt a "threefold description," covering different scales of analyses of the teaching processes. To amplify the phenomena that are to be observed, we suggested the teachers include the "Race to 20" situation in their teaching. We expect that implementing an unusual teaching device should lead the teachers to take decisions and explain them more easily than in everyday lessons.