Provided by Institute of Education EPrints
International Journal of Computers for Mathematical Learning 9, 3, 309-326
On the Integration of Digital Technologies
into Mathematics Classrooms
Celia Hoyles, Richard Noss and Phillip Kent
Institute of Education, University of London
Abstract
Trouche‘s (2003) presentation at the Third Computer Algebra in Mathematics Education Symposium
focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual
transformation of learner and artefact in the course of constructing knowledge with technology; the
latter concerning the problem of integrating technology into classroom practice. At the Symposium,
there was considerable discussion of the idea of situated abstraction, which the current authors have
been developing over the last decade. In this paper, we summarise the theory of instrumental genesis
and attempt to link it with situated abstraction. We then seek to broaden Trouche‘s discussion of
orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated
abstraction could be used to make sense of the evolving mathematical knowledge of a community as
well as an individual. We conclude by elaborating the ways in which technological artefacts can
provide shared means of mathematical expression, and discuss the need to recognise the diversity of
student‘s emergent meanings for mathematics, and the legitimacy of mathematical expression that may
be initially divergent from institutionalised mathematics.
Introduction
This paper originated as a response (Hoyles, 2003) to the presentation by Luc Trouche (2003)
at the Third Computer Algebra in Mathematics Education (CAME) Symposium1. Trouche‘s
paper represents another instalment in the formidable sequence of contributions made by
French mathematics educators to the developing theory of computationally-mediated
mathematical knowledge: see, for example Lagrange (1999), Guin & Trouche (1999), and also
the presentation in 2001 at the Second CAME Symposium by Artigue and the responses by
Ruthven and Cuoco (Artigue, 2002; Ruthven, 2002; Cuoco, 2002). The idea of this paper is to
1 See the CAME website: www.lonklab.ac.uk/came