Published in Nunes,T (ed) Special Issue, ‘Giving Meaning to Mathematical Signs: Psychological,
Pedagogical and Cultural Processes‘ Human Development, Vol 52, No 2, April, pp. 129-
interactive, dynamic representations that digital systems afford - at least when
designed thoughtfully - expression via tools that diverge from standard mathematics
(recall Papert‘s point: standard expression may not be a particularly good vehicle for
fostering what we are trying to teach!). We also recall Balacheff‘s argument (1993),
when discussing the idea of ‘computational transposition‘, that computer tools
introduce a new model of knowledge related to the functioning of the machine and the
interface designed for the software: i.e. the knowledge instantiated in a computer
system is no longer the same knowledge. We seek here to present some elaboration of
this idea.
In what follows, we present four categories that distinguish different ways that
digital tools have the potential to shape mathematical cognition. We provide at least
one illustrative example in each category. First, we will consider dynamic and
graphical tools and ask how their use shapes mathematical activity and the kind of
knowledge that is fostered by their use. Next, we consider how tools that outsource
processing power from mind to machine can allow us to develop in more detail the
didactical consequences of Artigue‘s epistemic/pragmatic distinction to which we
referred above. Third, we will look more broadly at forms of new representational
infrastructures, before finally considering the implications of the advent of high-
bandwidth connectivity on the nature of mathematics activity and mathematical
learning both within and across classrooms.
2. Dynamic and graphical tools
Digital technology can provide tools that are dynamic, graphical and
interactive. Using these tools, learners can explore mathematical objects from
different but interlinked perspectives, where the relationships that are key for
mathematical understanding are highlighted, made more tangible and manipulable.
The crucial point is that the semiotic mediation of the tools can support the process of
mathematising by focussing the learner‘s attention on the things that matter: as Weir
(1987) puts it, —the things that matter are the things you have commands to change.”
(p. 65). The computer screen affords the opportunity for teachers and students to
make explicit that which is implicit, and draw attention to that which is often left
unnoticed (Noss & Hoyles, 1996).