Epistemological models of mathematical structuralism in the french didactic tradition:

networking of theoretical frameworks

Resumo

In my research, different theoretical frameworks in the didactics of mathematics are used to study the teaching-learning phenomena related to mathematical structuralism at university level. The aim of this article is to discuss, in the context of this research, the specificity and complementarity of two frameworks from the French didactic tradition - the Theory of Didactic Situations (TSD) and the Anthropological Theory of the Didactic (ATD) from the point of view of the theorization of knowledge that these frameworks offer and of the epistemological postures that they assume, as well as their consequences for research. It is an opportunity to question the various meanings and uses of epistemology in current didactic research while returning to the sources of experimental epistemology, in the sense of Brousseau. Our corpus of data comes from the work of students engaged in solving tasks on classifying models of an invented axiomatic structure (the theory of banquets), after having learned Group Theory. While the underlying didactic engineering was designed within the framework of TDS, networking with ATD provides complementary insights into the observed phenomena and a space for dialogue between theo retical frameworks.