On the Integration of Digital Technologies into Mathematics Classrooms

International Journal of Computers for Mathematical Learning 9, 3, 309-326

1. The poor educational legitimacy of computer technologies as opposed to their high social
and scientific legitimacy. Artigue illustrates how the computer's high status and visibility is
expected radically to improve learning and teaching, while the values and norms of
mathematics teaching and what is to be learned remain essentially invariant. This leads to an
inevitable vicious circle of disillusion.

2. The underestimation of issues linked to the computerisation of mathematical knowledge.
Complex processes govern the transformation (—transposition” as it is called in the French
research) of mathematical knowledge in the classroom context. The computer adds new layers
of complexity, which if unrecognised (as has largely been the case to date) can lead to the
rejection of mathematical meanings and discourse fostered by computer use, due to the
(inevitable) discrepancy between this and the official mathematical discourse of the classroom.

3. The dominant opposition between the technical and conceptual dimensions of mathematical
activity, which allows a too-easy characterisation of the computer‘s role as —automatically”
diminishing the former and thus almost —inevitably” enhancing the latter. Trouche, Artigue and
other French researchers have carefully documented how attempts at integration which make a
simple demarcation of classroom activities into —technical” and —conceptual” — as expressed,
for example, in claims that technology will free the student from technical —details”
(techniques) in order to focus on mathematical concepts — drastically misjudge the complexity
of instrumental genesis.

4. The underestimation of the complexity of instrumentation processes. This is the key issue
that we shall address in more detail in what follows. For the time being, this problem can be
formulated as a failure adequately to recognise the full extent of the —new” mathematical and
technological demands placed on students, and the need to theorise ways to connect to the
standard mathematics curriculum, a changed (but, we argue, still mathematical) student body
of knowledge.

This set of problems points, in part, to a failure to theorise adequately the complexity of
supporting learners to develop a fluent and effective relationship with technology in the
classroom — by —effective” we mean helping learners engage with, develop and articulate
understandings of mathematical procedures, structures and relationships through the
technology and according time and status to this process. Moreover, the values attached to
mathematical knowledge can hardly remain invariant under technological transformation; else,
as Artigue (2000) puts it, —can the price which needs to be paid in order to transform complex
objects into efficient mathematical instruments be justified?”

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