Description: General hypothesis for didactics of mathematics rising as a scientific domain is that knowledge undergoes transformations in order to be taught and learnt within instructional institutions. Considering that a given content knowledge typifies social interactions in the classroom, didactical researches take into account the relationships within the teacher, students and knowledge triplet, taken as a dynamical system. However, most studies usually tend to focus on one dimension of the triplet for the purpose to examine influences from the two others. In order to elaborate a theory of the didactical action, we hypothesize that interpretation of classroom events cannot be performed by focusing solely on neither the teacher's actions nor the students' ones. In addition, we consider that some of the didactical phenomena observed in classrooms may be determined by "external" processes such as the teacher's preparation of his lessons and his practical epistemology in which a theory of knowledge is embedded. The aim of this paper is to unfold a three-level description of the teacher's action. We shall elaborate the concept of "didactical game" in order to show how the three types of description are connected to each other. In particular, we shall focus on a first type of description where we take into account the "joint" action of the teacher and the students in the classroom activities. Empirical analysis of videotaped episodes selected in mathematics lessons at primary school will be presented, using a set of categories such as "learning games" (Sensevy et al, 2005), "didactical contract" and "milieu" (Brousseau, 1997), "mesogenesis", "chronogenesis", and "topogenesis" (Sensevy et al, 2000 ; Schubauer-Leoni et al, 2004, Mercier et al., 2005). The generic relevance of these categories will be examined and so the necessity to specify them in order to understand how the content knowledge at stake may shape the patterns of the "joint" action. We will compare these categories with some theoretical tools used by mathematics education researchers (Cobb et al, 2001; Lobato et al, 2005; Leinhardt & Steele, 2005; Steinbring, 2005), and address the possibility of using our categories in the study of other contents than the mathematics' ones. We claim that such a theoretical framework provide a complex system of thick descriptions (Geertz, 1973) in order to understand and explain the practical sense (Bourdieu, 1990) of the teacher and the students in the joint action.