Revisiting the French Didactic Tradition through Technological Lenses

Michèle Artigue,Luc Trouche

doi:10.3390/math9060629

Abstract

There is, in France, a long-term tradition of research in the didactics of mathematics. In this paper, we revisit this tradition using, as a specific lens, the research carried out on the educational use of digital tools and resources for teaching and learning mathematics. We first briefly introduce this tradition and the three main theories at the base of it: the theory of didactical situations, the theory of conceptual fields, and the anthropological theory of the didactic. Then, considering three different technological lenses, i.e., dynamic geometry environments, computer algebra systems, and digital resources, we show how these theories and the long-term connection established in this tradition with the fields of cognitive ergonomics and computer sciences have influenced technological research and its outcomes. We also show that, conversely, didactic technological research has led to original and influential theoretical constructions, such as the instrumental approach and the documentational approach to didactics, and that it has contributed in a substantial way to the opening of this didactic tradition to other didactic cultures and other communities, beyond the didactic one.

Highlights

There is a long-term tradition of research in the didactics of mathematics in France, with characteristics that distinguish it from other didactic traditions, even within continental Europe [1]
In the fourth section, addressing calculators and computer algebra systems (CAS) allows us to look at the French didactic tradition through the development of the instrumental approach that emerged in this context in the mid-1990s, before being extended to other technologies such as spreadsheet, dynamic geometry, and online tutorials and resources
This tradition has been nurtured and has fed in return the conceptualizations at work in the international community of mathematics education, as evidenced in two key conferences organized by the International Commission on Mathematics Instruction dedicated to technologies

Summary

Introduction

There is a long-term tradition of research in the didactics of mathematics in France, with characteristics that distinguish it from other didactic traditions, even within continental Europe [1]. In the fourth section, addressing calculators and CAS allows us to look at the French didactic tradition through the development of the instrumental approach that emerged in this context in the mid-1990s, before being extended to other technologies such as spreadsheet, dynamic geometry, and online tutorials and resources. This lens allows us to show the influence of the connection mentioned above with researchers in cognitive ergonomics, as well as the roles played in the development of the instrumental approach by the Theory of Conceptual Fields (TCF) [9]. We examine the potential and limitations of this particular lens to approach this tradition

The French Didactic Tradition

A Tradition Seen through the Lens of Dynamic Geometry

A Tradition Seen through the Lens of Calculators and Computer Algebra Systems

A Tradition Seen through the Lens of Digital Resources

Discussion