The technological mediation of mathematics and its learning

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-

possibly amended models (see for example, Simpson, Hoyles, & Noss, 2005). This
work built on the importance for learning of externalising cognitive processes and
sharing these externalised representations: for example, Scardamalia & Bereiter had
argued that an electronic and networked discussion board would foster conversations
between students and thus would —contribute to the development of a —knowledge
building community” (Scardamalia & Bereiter, 1996). Our key idea was that learners
could not only discuss, conjecture with and comment upon each others' ideas, but they
could also inspect and edit each others' working models of ideas, the computer
programs - so that the processes underlying the outcomes were made visible at least
to some extent. Again, the idea of appropriate layers of visibility was crucial in the
design. This proposed functionality of collaborative knowledge construction is, at
least so far, one of the most promising avenues we perceive of connectivity: the
possibility of building mathematical understandings in shared remote space, in
settings that transcend that of a single classroom¹⁰.

To sum up the outcomes of these two projects, (see also Noss & Hoyles,
2006), we note that where we did achieve success, engagement tended to derive from
the sense of audience we created and the need to make arguments explicit when
removed from the presence of others. This led to some interesting discussion threads
about deep mathematical topics - it is not commonplace to have students routinely
chatting about mathematics! Nevertheless, there were considerable challenges
concerning the need to take account of the mediation of tools operating at two levels,
first in the construction process and second in the communication infrastructure: both
influenced the development of mathematical meanings. The teacher had to cope with
these twin challenges in orchestrating optimal student-student and student-teacher
interaction in relation to the knowledge at stake.

For interaction at a distance to lead to developing mathematical meanings,
there needs to be more investigation of the kinds of support required to foster longer
communication turns by each contributor. It appears evident that a necessary - but far
from sufficient - condition for connectivity to foster learning, is for interaction to be
extended and productive: off-task interaction is unlikely to lead to mathematical

¹⁰ It is worth noting that had this project been a few years later, we could have employed one
of the many ‘social networking‘ sites to achieve much the same effect at a fraction of the time and
effort).

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