Some Contributions of Epistemology and Logic to Research in Didactics of Mathematics

The course will address topics of research at the interface between Didactics of Mathematics and Epistemology of Mathematics. The course is divided in three main parts: The role of epistemology in didactic research (6h); Syntax, semantic and pragmatics in mathematics education (6h); Logical issues in mathematics education (6h). In each of the three thematic, there will be an alternance between presentation of general features of the thematic, students activities in small groups, collective discussion and synthesis. Relevant didactical concepts, as well as key topics of epistemology of mathematics and logic, will be introduced along the session. The course will address issues that are relevant to understand students' difficulties at the transition between secondary school and university. The participants will become able to identify epistemological issues behind teaching choices and some motivations that help to interpret students' difficulties.