A critical look at the anthropological theory of the didactic

The aim of this paper is to discuss and challenge some basic premises of the Anthropological Theory of the Didactic, as introduced by its founder, Yves Chevallard. Using the theory of limits as a historical study as well as a number of research articles, I investigate the relation between the types of mathematical knowledge, as given in the theory of didactic transposition. I also argue that the concept of praxeology does not capture the intrinsic difficulty of the concept of limit, which many students encounter. This paper is also a call for researchers within the Anthropological Theory of the Didactic to enter into a critical discussion of its basic tenets, and to engage in dialogue and networking with other educational platforms to help improve and develop the theory.