Introducing group theory with its raison d'etre for students

Hiroaki Hamanaka (1) , Koji Otaki (2) , Ryoto Hakamata (3)

1 University of Hyogo
2 Hokkaido University of Education
3 Kochi University

This paper reports results of our sequence of didactic situations for teaching fundamental concepts in group theory—e.g., symmetric group, generator, subgroup, and coset decomposition. In the situations, students in a preservice teacher training course dealt with such concepts, together with card-puzzle problems of a type. And there, we aimed to accompany these concepts with their raisons d'être. Such raisons d'être are substantiated by the dialectic between tasks and techniques in the praxeological perspective of the anthropological theory of the didactic.

Mots clés: Group theory; Raison d'être; Praxeology; Teaching and learning of specific topics in university mathematics; Teaching and learning of linear and abstract algebra.

Domaines: Education

Hiroaki Hamanaka, Koji Otaki, Ryoto Hakamata. Introducing group theory with its raison d'etre for students. INDRUM 2020, Université de Carthage, Université de Montpellier, Sep 2020, Cyberspace (virtually from Bizerte), Tunisia. ⟨hal-03113982⟩