### Didactic transposition: a tool for analysis

The theory of the didactic transposition, proposed by Yves Chevallard in the 1980s, corresponds to the first developments of the ATD. The focus is on the knowledge to be taught, a new entity that is usually taken for granted in educational research, and its relations with the scholarly knowledge and the knowledge actually taught. You will see in this module the kind of object of study defined by the ATD, which can initially appear as unconventional to the newcomer. The example of proportionality illustrates the type of analyses proposed.

*Recommended readings*

*A short and easy-to-read article about Didactic transposition in the Encyclopedia of Mathematics Education:*

• Chevallard Y., Bosch M. (2014). Didactic transposition in mathematics education. In: Lerman S. (Ed.), *Encyclopedia of Mathematics Education*. Springer, Dordrecht.

*An old text explaining the origins of the didactic transposition theory and pointing at some of its crucial notions, such as the notion of didactic phenomenon and the opposition between the school actor’s point of view and the didactician’s theoretical construction:*

• Chevallard, Y. (1989). On didactic transposition theory: some introductory notes. In H. G. Steiner & M. Hejny (Eds.), *Proceedings of the International Symposium on Selected Domains of Research and Development in Mathematics Education* (pp. 51−62). University of Bielefeld, Germany, and University of Bratislava, Slovakia.

*The text of a conference given by Yves Chevallard in Osaka (Japan) in October 2016, presenting the main elements of the ATD. The theory of didactic transposition is presented in section 2:*

• Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: an attempt at a principled approach. *Hiroshima Journal of Mathematics Education, 12, *71-114.