Study of primary school teacher's practices for a lesson after a Lesson Study process in mathematics

International audienceThis study presents the analysis of primary school teacher's practices in mathematics for a lesson that has taken place after a professional development training called lesson study (LS) in Lausanne, Switzerland. Practices are analysed in a double didactical and ergonomical approach. The methodology used is a case study of the particular teacher's practices. Results about the teacher's practices after the LS process are discussed. Teachers' practices are analysed using the following theoretical framework: the "double approach" based on a French didactical approach (Robert & Rogalski, 2002, 2005) and an ergonomical approach based on activity theory (Leontiev, 1975; Leplat, 1997). This "double approach" distinguishes the task, the "goal to be attained under certain circumstances" and the activity, what the teacher engages in during the completion of the task (Rogalski, 2013, p. 4). The prescribed work fits the prescribed task (in our context: what the teacher must do according to Teacher's Handbook and the official program) and the real work fits the conducted task (in our context: what the teacher does in reality during the lesson). To appropriate the prescribed task, the teacher should modify it. Thus, a gap exists between the prescribed task and the conducted task: the reasons can be a lack of the necessary competencies or an inappropriate representation of the task for example (Ibid.). Leplat (1997) adds two levels of tasks: the represented task (in our context: how the teacher represents the prescribed task and what he thinks we attend of him) and the redefined task (in our context: the teacher redefines his task according to the prescribed task and his own professional goals). These levels of tasks are neither hierarchical nor time: the teacher can represent the prescribed task and can redefine a new task before and during the lesson in taking into account different sources (students' activity, his own activity, institutional constraints). The teacher combines professional acts and knowledge (mathematical, didactical, pedagogical) in his representation of the prescribed task and in his redefinition of the represented task. This study focused on these professional acts and knowledge at stake in these representation and redefinition. Thus, the teacher's activity is analysed as a process of modifications between the prescribed and conducted tasks (Leplat, 1997; Mangiante, 2007)