Instrumental Genesis in the Theory of MWS: Insight from Didactic Research on Digital Artifacts

Abstract

The central focus of this chapter is the relationship between the notions introduced by Vérillon and Rabardel (1995), 'artefact' and 'instrumental genesis', and the homonym notions in the theory of MWS. Following a brief overview of the Piagetian and Activity Theory perspectives which inspired Vérillon and Rabardel, we explore how didactic research on digital artefacts developed two viewpoints on the instrumental genesis: psychological and institutional. The idea of instrumental genesis in the theory of MWS is consistent with the concept of instrumented mediation by Vérillon and Rabardel, but is a more focused notion, since MWS include two additional geneses, semiotic and discursive. The theory of MWS moreover does not theorize about the mediation and as such, in a particular situation where a digital artefact is used, both viewpoints will be helpful. Regarding the poles of the instrumental genesis, we propose characterizing a digital artefact by the underlying data representations and algorithmic treatments, and constructions as data-result models of mathematical configurations, taking advantage of the representations and algorithms in the artefact. MotivationThe authors of this chapter are two researchers in mathematics education with a long experience in investigating the classroom use of digital artefacts and designing mathematical software environments. Like many other researchers in this field, we are inspired by Vérillon and Rabardel's (1995) approach of instrumental activity, using the notions of artefact, instrumental genesis and instrumented techniques. In parallel, we have drawn on the theory of MWS for specific research studies (Minh & Lagrange 2016, Richard & al., 2016. This theory also puts forward the notions of artefact and instrumental genesis, furthermore including two other geneses: semiotic and discursive.

Learning Mathematics with Large Language Models

“…These investigations study the impact of CAS on learning outcomes and attempt to identify the advantages and challenges associated with their integration into mathematics teaching. The instrumental approach serves as a conceptual framework that supports the research and integration of CAS in education [15,16]. According to this perspective, CAS are considered tools with which students can acquire mathematical knowledge, and at the same time, teachers have an essential role in orchestrating their use to facilitate student learning, turning CAS into an "instrument".…”