Revisiting the French Didactic Tradition through Technological Lenses

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.

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

“…In our research we focused on a path which Koehlers' et al did not mention in their work: from TCK to TPACK. We did so because integrating the functionalities of different representation in the CAS system (such as graphical, numerical and/or formal computation) does not necessarily facilitate conceptualization [51] (this issue, p. 8)…”

Computer Assisted Proofs and Automated Methods in Mathematics Education

“…For other needs, the differences between numerical and symbolic algorithms led GeoGebra's developers to propose two kinds of output, for example, to the Relation command 4 . Figure 2 shows screenshots of the output.…”

“…it is performed as a dialog between man and machine. This is a nice opportunity to experience the mutual influence between the user and the software, and the teacher can observe a different processes of instrumental genesis among the students; see [72,3,4].…”

“…Section 1). It is not surprising that the instrumental genesis (see [72,3,4], etc.) of every single student and of the class as a whole is totally different every year.…”

Scheming and Re-scheming: Secondary Mathematics Teachers’ Use and Re-use of Resources

“…An overview of the theoretical and methodological developments of the DAD can be found inGueudet (2019) and its relation to the long-term tradition of research in the didactics of mathematics can be found inArtigue and Trouche (2021).2 We draw onGueudet (2017) to describe the four parts that consist the scheme of use while we exemplify these parts in the context of our study.…”