**2.2 The theoretical framework of the dual didactic-ergonomic approach**

The general theoretical framework of Chanudet's PhD is based on the study of practices using the dual didactic-ergonomic approach developed by Robert and Rogalski [14, 15]. This framework invites us to take into account both the generic, by looking at the constraints weighing on the teacher as he or she exercises his or her profession, and the individual, by considering the margins of freedom remaining to him or her and the way in which he or she invests them. Five components are highlighted by the authors to study teachers' practices. The first two, cognitive and mediative, are linked to observations of classroom sessions and possible student activities. The cognitive component relates to the mathematical content presented to students (tasks, their articulation, *etc.*) and provides information on what the authors call the cognitive itinerary proposed to students. The mediative component focuses on the progress of classroom sessions (forms of work, assistance provided by the teacher, exchanges, and interactions with students). The combination of these two components enables us to describe the mathematics that teachers introduce their students to and to identify the logic of their actions. To integrate the fact that teachers' practices are the expression of their work, three other components need to be taken into account: social, institutional, and personal. The social component takes into account the social dimension of the teacher's work (students, parents, colleagues). The institutional component concerns common constraints (programs, timetables, textbooks). The personal component incorporates everything that is specific to the teacher as an individual (his or her representations of the profession, mathematics, knowledge, experience, *etc.*).
