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-
manufacturing plant. Our example indicates that outsourcing is not unproblematic. It
does not remove the necessity to understand at some level, and it neither removes the
necessity for pedagogic design, nor the need to make visible some of the processes
underlying the outsourced mathematics. While the devolution of mathematical
technique to the machine is a superb advance for mathematics as a discipline, it
nonetheless presents a major challenge for learning scientists who must decide, first
what needs to be maintained as visible - the parameters and variables, relationships
and techniques that contribute towards ‘epistemic’ development - and second, how to
present these key factors in a layered learning sequence.
In considering the question of representational infrastructure, we noted that
there were sufficient indications that many commonly encountered obstacles to
understanding mathematics lay in the chosen representational infrastructure, rather
than any in the complexity of the idea itself. Put another way, we might conjecture
that Bruner‘s often-quoted aphorism could be rephrased as: any mathematical idea is
learnable and teachable, provided we find the right representational infrastructure
within which to express it. We would prefer not to be taken literally: but we do think
that research is beginning to point to instances of how technology can be utilised to
realise this aim.
Finally, we considered the question of connectivity, and gave two ways in
which it may have implications for mathematical development; in the possibility of
bringing students‘ constructions together as objects for reflection and manipulation in
a shared space, and in the need for explicit formal expression of mathematical ideas
when they are to be shared at a distance. This area of research is in its infancy: it is,
after all, much harder to think of ways that connectivity could revolutionise
mathematics than almost any other domain. One reason is that the balance between
information in the form of facts, and concepts is titled strongly on the former.
Nevertheless, there are signs that there may yet be the beginnings of, not just a
pedagogical transformation but also an epistemological one, catalysed by
connectivity.
We conclude by noting that there are two key unifying ideas in this paper. The
first is design, the obvious but often overlooked fact that technology per se is unlikely
to influence mathematical development in any significant ways, it is how it is
designed to support learning and how it is embedded in activities designed with
21