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Digital Technology and Mathematics Education: Core Ideas and Key Dimensions of Michèle Artigue’s Theoretical Work on Digital Tools and Its Impact on Mathematics Education Research

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The Didactics of Mathematics: Approaches and Issues

Abstract

In this chapter, we revisit Michèle Artigue’s classic 2002 IJCML article and draw out what we consider to be the core theoretical ideas and key dimensions of the body of work on tools and tool use that Michèle not only elaborated but also inspired others to further develop. We trace the evolutionary path of these core ideas, noting the ways in which they theorise the four general key dimensions of learner, teacher, tool, and mathematics. We focus on seven core theoretical ideas that have been central to Michèle’s work and that have impacted in various ways the research of others: the instrumental approach to tool use, instrumental genesis, the pragmatic-epistemic duality, the technical-conceptual connection, the paper-and-pencil versus digitally-instrumented-technique relationship, the institutional aspect, and the networking of theories.

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Notes

  1. 1.

    Michèle would be the first to insist that the contributions we describe in this chapter were not hers alone, nor just those of her DIDIREM team in Paris, but were also based on collaboration that included a team in Rennes piloted by Jean-Baptiste Lagrange, and another in Montpellier piloted by Dominique Guin and Luc Trouche.

  2. 2.

    The TELMA cross-experimentation studies involved pairs of teams coming from different theoretical cultures, but both using the same digital technology—a technology that was well known to one of the teams but alien to the other.

  3. 3.

    The ReMath project relied on the TELMA meta-language of didactic functionalities and concerns, as well as the system of cross-experiments, but had somewhat different aims. It focused more specifically on representations and issues related to the design of digital artefacts and extended the TELMA methodology to include cross-case-study analyses. For further elaboration of the ways in which the ReMath project developed, modified, and extended the ideas initiated in the TELMA project, see the recently published Artigue and Mariotti (2014) paper, which appeared after this chapter was written.

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Authors and Affiliations

  1. Université du Québec à Montréal, Montreal, Canada

    Carolyn Kieran

  2. Institut Freudenthal, Utrecht University, Utrecht, The Netherlands

    Paul Drijvers

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  1. Carolyn Kieran
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  2. Paul Drijvers
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Correspondence to Carolyn Kieran .

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Editors and Affiliations

  1. Département de mathématiques et de statistique, Université Laval, Québec, Québec, Canada

    Bernard R Hodgson

  2. Laboratoire de Didactique André Revuz (EA 4434), Université Paris Diderot, Paris, France

    Alain Kuzniak

  3. Laboratoire de Didactique André Revuz (EA 4434), Université Champagne-Ardennes, Reims, France

    Jean-Baptiste Lagrange

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Kieran, C., Drijvers, P. (2016). Digital Technology and Mathematics Education: Core Ideas and Key Dimensions of Michèle Artigue’s Theoretical Work on Digital Tools and Its Impact on Mathematics Education Research. In: Hodgson, B., Kuzniak, A., Lagrange, JB. (eds) The Didactics of Mathematics: Approaches and Issues. Springer, Cham. https://doi.org/10.1007/978-3-319-26047-1_6

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