ABSTRACT
This chapter examines the notion of “teaching trade” and the difficulties that appear in the exercise of the trade. It looks at the role of teacher training or teacher education in the evolution of this trade towards a more professional status. Before discussing the training of mathematics teachers, the chapter explains about the trade of mathematics teaching based on Chevallard. The didactic analysis revealed recurrent difficulties encountered by teachers in the exercise of their trade, even if the inquiry started from those encountered by a group of student teachers. Furthermore, it also provided some tools for the development of new teaching praxeologies. Within the framework of a training project aimed at encouraging the involvement of student teachers in the design of mathematical and didactic praxeologies in a scientifically sound manner, the question of didactic infrastructures in training arises, in the dual sense of the content at stake and of the direction of the study.
