Context This proposal concerns research on teacher’s practices as well as their organizational processes. It also aims to offer some « efficiency strategies » concerning didactic methods, bringing to light certain practical constraints and their consequences. The analysis emphasizes the didactic relationship, understood as their joint action, as well as issues of knowledge. Our study deals with the teachings methods of six mathematics teachers. Three of these teachers teach ordinary classes with mainstream students. Three others are specialized – they lead primary school classes for students with learning disabilities.We center our proposal presentation on the practical ingenuity of the specialized teachers who work with these “underperforming” pupils.

Elements of theoretical and methodological framework Producing results from a reduced sample requires a proper methodological framework as well as an empirical question that is at once theoretical and epistemological. In this study, we have collected two types of data. The first comes from filming participants’ behavior in a classroom or in group setting. The second comes from interviews with the six different teachers involved in the study. This large collection of data requires us to isolate remarkable events (Schubauer-Léoni, 2002) and to analyze them according to the theoretical framework documented and maintained by mathematical didactics (Brousseau, Chevallard) as well as the model of Joint Action Theory in Didactics (Sensevy and al., 2000). Considered together, these data help us to understand the teachers’ intentions and allow enable us to further contribute to the field of knowledge concerning this subject.

The methods employed by these specialized teachers show: - A detachment from imparting knowledge and a preference for more flexible learning games. - Frequent revisions to the original teaching objectives, even to the point of imparting no knowledge whatsoever. - An absence of a priori epistemic analysis, which impedes the anticipation of potential epistemic obstacles and possible reorganizations of the didactic situation. - A strong influence of the constructivist doxas. Conclusion The practical epistemology of these professors reveal a split between the role of a teacher and that of a psycholological counselor - this split is driven by their focus on students’ self-confidence and autonomy rather than their didactic progress. This situation is exacerbated by the lack of collaboration between mainstream and specialized teachers. Thus, the pupils showing the greatest learning difficulties are obliged to submit themselves to the challenges of having interruptions in two didactic situations.