Didactics and Epistemology of Mathematics

Director: Nicolas Saby 

Research Topics :

This team’s research work lies at the intersection between epistemology and didactics.
The team’s work is structured in three topic areas :
– Didactics and epistemology of higher education
– Cognition and mathematical learning
– Didactics and epistemology in interactions between mathematics and computer science.
There is also a underlying theme of logic, language, reason, and proofs in the learning of mathematics.

Didactics and epistemology of higher education :

The work on higher education is part of national and international dynamics to which the DEMA team has strongly contributed through the initiation and development of international network INDRUM and national network DEMIPS, which resulted in the creation within INSMI of GDR DEMIPS on January 1st, 2020.
Main topics developed :
– Didactics and epistemology of algebraic structuralism
– Physical mathematical structures, the case of quantum mechanics
– Study of researchers’ practices
– Real numbers and completeness
– Integration and theory of measurement

Cognition and mathematical learning :

The studies conducted at the intersection of cognitive and mathematical learning concern all levels of education with four main themes :
– Teaching and learning mathematical models
– Games and mathematical learning
– Relationships between sciences and society: critical thinking and different mathematical thinking
– Teaching and learning from preschool to university
– Taking into account linguistic and cultural diversity.

Didactics and epistemology in interactions between mathematics and computer science :

The aim is to propose an epistemological and didactic study of computer science and mathematical relations. The tools for thinking about teaching and learning the two disciplines, their interactions, and research ingenuity linking the two disciplines are developed around the following themes :
– Didactics of algorithms and programming
– Links between recurrence and recursitivity (1 study in progress)
– Logic, language, and proofs between mathematics and computer science
– Mediation and disconnected computing.

Underlying Themes :

The relationship between logic, language, reasoning, and proofs is at the heart of mathematical learning no matter what level is considered and is crucial to the high school to university transition and in higher education. It also plays an essential role in many works in Philosophy in Mathematics and Cognitive Sciences. These themes feed many of the works on the DEMA team.