Two complementary theories for thinking about and organizing mathematical learning
In the first part of this talk, I'll propose an introductory situation in literal arithmetic (Barallobres & Giroux, 2008) that will enable me to introduce and illustrate the main concepts and methodological tools of the theory of didactic situations developed by Guy Brousseau (Brousseau, 1997; Bessot, 2024). In the second part, I will give a brief presentation of Gérard Vergnaud's theory of conceptual fields (Vergnaud, 1990; Durand-Guerrier and Saby, 2023), then show how this theory helps to shed further light on the introductory situation.
The contributions of the anthropological theory of didactics
The Anthropological Theory of Didactics (TAD, Chevallard, 2001) aims to explain why and how a given knowledge lives in a certain institution, and/or is transformed as it passes from one institution to another. This perspective and some of its evolutions will be presented and illustrated in this talk.
Students' activities and teachers' practices in the mathematics classroom: analysis methodology with Activity Theory
In this talk, we will present the founding assumptions of the Activity Theory framework adapted to the Didactics of Mathematics (TADM, Vandebrouck, 2008), showing how this theory gives importance to fine-grained analyses of mathematical knowledge to appreciate classroom developments. We will then exemplify some of these aspects on the teaching of limits at university (Bridoux and Grenier-Boley, 2024).
Bibliography
Barallobres, G., & Giroux, J. (2008). Environmental deficiencies and regulations in validation situations. N. In Berdnaz, & C. Mary (Eds). L'enseignement des mathématiques face aux défis de l'école et des communautés. Actes du colloque EMF 2006 (CD-ROM). Éditions du CRP https://emf.unige.ch/application/files/1414/5390/4857/EMF2006_GT8_Barallobres.pdf
Bessot, A. (2003). An introduction to the theory of didactic situations. Cahiers du laboratoire Leibniz, 91. hal-00078794
Bridoux, S., & Grenier-Boley, N. (2024). What teaching practices should be used to introduce the limits of functions in the first year of university? A case study. In A. González-Martín, G. Gueudet, I. Florensa & N. Lombard (Eds.), Proceedings of the Fifth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024) (pp. 791-800). Escola Universitària de Sarrià. Univ. Autònoma de Barcelona and INDRUM.
Brousseau, G. (1997). Théorie des situations didactiques. Lecture given at the award to Guy Brousseau of the title of Doctor Honoris Causa from the University of Montreal. http://www.cfem.asso.fr/actualites/archives/Brousseau.pdf
Chevallard, Y. (2001). Organizing study: 1. Structures and Functions. In J.-L. Dorier, M. Artaud, M. Artigue, R. Berthelot, & R. Floris Proceedings of the XIe École d'été de didactique des mathématiques. (pp. 3-32). Editions la Pensée Sauvage.
Durand-Guerrier, V., & Nicolas Saby, N. (2023). Usages de la théorie des champs conceptuels en didactique des mathématiques. The example of transitivity. Caminhos da Educação Matemática em Revista, 13 (4),118-134. ⟨hal-04585866⟩
Vandebrouck, F. (dir.) (2008). La classe de mathématiques: activités des élèves et pratiques des enseignants. OCTARES Éditions.
Vergnaud, G. (1990). Conceptual field theory. Recherches en didactique des mathématiques, 10(2/3), 133-170.
