International Journal of Computers for Mathematical Learning 9, 3, 309-326
provide an interpretation of Trouche's work from our own —Anglo-Saxon” perspective, and to
try to connect it - as part of the corpus of French didactical research - with other frameworks
and paradigms, and experience with other technologies.
A central focus of this paper, like that of Trouche‘s, will be on the notions of —instrumental
genesis” and —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, a problem that still requires
considerably more theoretical elaboration and empirical analysis. To this end, we will briefly
summarise what we interpret as the main points in the theory of instrumental genesis, and
attempt to compare and contrast it with description of the notion of situated abstraction, which
the current authors have been developing over the last decade or so. We then seek to broaden
the discussion of orchestration so as to elaborate the role of artefacts in the process, and return
to the notion of situated abstraction to describe how it might be used in analyses of the
evolving mathematical knowledge of both individuals and communities. We conclude by
stressing the need to recognise the diversity of students‘ emergent meanings for mathematics,
and to establish the legitimacy of mathematical expression that may (initially at least) be
divergent from institutionalised mathematics.
Setting the scene: The marginalisation of technology
Following a major national effort in France starting in the 1990s to implement the use of
mathematical technology (particularly CAS and dynamic geometry) in middle and high school
classrooms, there has been a considerable attempt among mathematics education researchers in
recent years in France to analyse both theoretically and empirically attempts at integration of
technology into classroom practices (see, for example, Artigue, 2000, 2002; Lagrange et al,
2001). Yet despite this level of effort, Artigue (2002) has pointed out that:
...difficulties are indeed persistent in France in spite of the continuous
governmental support given to integration for more than 20 years now. . the
complexity of instrumental genesis has been widely under-estimated in research
and innovation on [ICT in education], until quite recently. (Artigue, 2002, p.
253)
Artigue (2000) characterises the integration of digital technologies into mathematical education
as —marginal” and proposes four main reasons: