On the Integration of Digital Technologies into Mathematics Classrooms

International Journal of Computers for Mathematical Learning 9, 3, 309-326

would, of course, be wrong to think of any artefact as “just” an artefact — the whole point of
instrumental genesis (as well as current socio-cultural theories of learning) leads us to think
otherwise. But while it would be wrong to suggest that the meanings of artefacts for students
can be drawn directly from the intentions of their designers, it is helpful to think of the
possibilities that accrue in the uses by students of artefacts, especially when these artefacts are
designed with the intention of promoting learning outcomes for individuals or for groups. The
designs of computational tools — and these include the design of individual programs by
classroom teachers as well as the —global” design of hardware and software by professional
engineers/programmers — constrain the kinds of mathematical expression that is natural to
undertake with them, how meanings are constituted and how mathematical ideas are
communicated.

We do not mean to imply that the only, or even the primary, mechanism of orchestration is
invested in the technology. We do, however, insist that the medium - while not being the
message - certainly shapes what messages are natural, and how they might be expressed. We
have in the past expressed this by saying that there can be a mathematical epistemology —built
into” artefacts, provided we are clear that it is students who breathe life into the technologies
and rebuild the mathematical structures for themselves by means of their actions with them. In
fact, this is part of the webbing idea, the process by which the student infers meaning by
coordinating the structure of the learning system (including the knowledge to be learned, the
learning resources available, prior student knowledge and experience and constructing their
own scaffolds by interaction and feedback (Noss & Hoyles, 1996). The idea is that it is the
representational infrastructure, that is the artefacts together with the rules of discourse that
surround them, that provides a system that learners can draw upon and reconstruct to make
mathematical sense.

Thus in our view, the design of tools, activities and tasks is central. Of relevance here is that it
is the design of the tools with which individuals interact (i.e. what is and is not easily
expressible), and the design by which these tools are connected (i.e. what is and is not easily
communicable), which plays an important role in shaping the construction of the socio-
mathematical norms of the classroom (see for example, Cobb, Stephan, McClain &
Gravemeijer, 2001). Clearly, the teacher is central to this process. We simply wish to raise the
profile of the potential role of the technological tools and the kinds of symbolic language and
interactions that they might foster among learners. Consider, just as a simple example, a
learning environment that typically develops where rows of computers are physically fixed one

10

<<   7   8   9   10   11   12   13   >>

More intriguing information