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-

and that of their peers and all responses can become an object of collective reflection
and can be manipulated accordingly. This affordance appears to have - so far from
mainly anecdotal evidence - a marked impact on mathematical learning. As Trouche
and Hivon argue (in the case of a class of students working with TI Navigator):
—Each student becomes detached from his/her production as a distance is created
between student and the expression of his/her creation and this distance seemed to
improve collective reflection on practice. The student becomes involved in the class
activity in a different way as the tool maintains this distance between a student and
the results proposed to the class and to the teacher”. (Trouche & Hivon, in press).
This type of connectivity might have considerable impact on the potential of dynamic
and graphical tools for the development of mathematical meanings as set out in
section 2 in this paper, since the sketch is now available to all for collective
consideration.

While this observation refers to the effect of connectivity on teaching and
learning, there are epistemological possibilities as well. Consider, for example,
viewing a family of objects in the shared space, with each object belonging, say, to a
single student. The group as a whole can view the family as a new mathematical
object with its own parameters. This potential for the study of hitherto inaccessible
mathematical objects and relationships is a largely untapped, but nonetheless
tantalising, prospect (see for example Hegedus & Penuel, 2008). One set of studies
that deals with this epistemological dimension has been reported in a series of papers
by Wilensky and his colleagues. They report on studies that have added synchronous
connectivity to the agent-based system NetLogo, so the students in a class can all
become engaged in a participatory simulation rather than simply a modelling activity
(see, for example, Wilensky & Stroup, 1999, Wilensky, & Reisman (2006). These
studies have pointed to a range of benefits for learning, not least that it introduced a
shared experience of a complex system: —There are very few opportunities, in the
classroom or in life, for students collectively to witness the same complex system
unfolding. Focal attention to such a system is hard to achieve outside of the virtual
and, even when achieved, if the viewing does not connect the micro-level behaviour
to the macro-level outcomes, then only the appearance is shared, not the mechanisms
of action” (Wilensky, in press).

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