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-
development. Some researchers have suggested that simple statistics on thread
lengths in threaded discussion systems indicate that communication does not usually
continue long enough to get much beyond chatting (Stahl, 2001, p. 179). Thus a
particular requirement suggests the need to support interactions so that
communication is stimulated and maintained over time as well as space. We had some
success in our work by contriving competitive challenges that stimulated a game-like
discourse. Other possible strategies include pointing to conflicting arguments from
others in the group that have to be resolved. This strategy can be used by a teacher
but, we now think, more effectively supported by the technological system itself,
Although it is outside the scope of this paper, we note that it is this realisation that has
stimulated our latest research, MiGen11, in which we seek to introduce various
supports from the computational system (see Noss, Hoyles, Geraniou, Gutiёrrez-
Santos, Mavrikis & Pearce, under review).
6. Conclusions
This paper has raised issues concerning the ways that mathematical meanings
are shaped by the symbolic tools in use, and the representational infrastructures that
hold them together to express mathematics and to communicate and share
mathematical ideas. We have distinguished different ways that tools can shape
mathematical cognition: these require future investigation to establish if they do
reliably enhance learning.
We began with the idea of dynamic and graphical tools, and our example
involved ‘sketching‘, as a way for students to consider and choose for themselves on
what it is important to focus. This is a key obstacle in learning mathematics: ironically
enough, given that the search for variants and invariants is, perhaps, the crucial
mathematical activity. And ironic too, in that sketching - which does not, at least in
our example, involve rigorous expression of mathematical ideas, but rather getting a
sense of the possible relationships involved - and only subsequently employing the
computer in its most obvious role, as a mechanism for expressing rigour.
We then considered the implications of the outsourcing of processing power
to the technology, and chose as our example, our research intervention in a car
11 Funded under the ESRC/EPSRC, TLRP-TEL programme Grant reference RES-139-25-
0381.
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