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-
using traditional paper and pencil infrastructures (see Mor, Noss, Kahn, Hoyles &
Simpson, 2006).
5. Connectivity and shared mathematics
Connectivity continues to change the landscape of human-human and human-
computer interaction. To what extent is this shift reflected in the mathematical
meanings learners develop? There is no lack of potential: indeed Roschelle, Penuel, &
Abrahamson (2004) have argued that the connectivity made possible by
computational media constitutes a profoundly important set of affordances, ranking
alongside the ‘representational-simulation affordances‘ of computational media as
described in the previous section. Given that this connectivity has only recently been
implemented and access is still an issue in many schools, there is rather limited
research at the time of writing this paper to test this conjecture or to identify in any
systematic way the implications of enhanced connectivity on mathematical
development. We draw from the work of the panel on connectivity that was brought
together by Study Group of the International Congress of Mathematics Instruction,
ICMI 17 (see Hivon et al, in press. While noting the technological challenge of
creating the appropriate means to share knowledge between students and teacher, the
authors also pointed to its potential for mathematical learning.
From this and other sources, we distinguish two areas where we consider
connectivity has considerable potential for enhancing the teaching and learning of
mathematics. First, for connectivity within and between classrooms, an individual‘s
communication can be changed into an object in a shared workspace, and thus
become available for collective reflection and manipulation by the originator of the
communication - but also by others. Second, the very need for remote
communication of mathematical ideas - either synchronous or asynchronous -
provides a motivation to produce explicit formal expression of mathematical ideas.
We now look at each of these scenarios in turn.
i. Objects for reflection and manipulation in a shared classroom space
There are technologies where each student in a class can build a particular
case or part of a mathematical object, and these different instances can be brought
together in a common workspace. Students can therefore view their own production
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