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-
of roles external symbolic processing might play in the generation and shaping of
mathematical meaning.
There is little doubt that the outsourcing of processing power holds significant
potential for the learning of mathematics. All too often, students become bogged
down in procedures, lose touch with the problem they are tackling, make careless
errors and lose motivation. In the case that calculation, technique, is required to
achieve a numerical or algebraic result, then the devolution of processing power to the
computer is unproblematic - and potentially renders all but a tiny part of conventional
curricula redundant. However, if the goal is to achieve insight rather than answer -
and such is typically the case in learning mathematics - then offloading technique
may or may not be desirable. The difficulty resides in the recognition that, as we
pointed out earlier, there exist facets of the technical alongside the conceptual that
appear to be central to the process of semiotic construction. Thus, indiscriminate
outsourcing of technical expertise from the learner to machine can make it more
difficult still to foster in the learner the sense that mathematics is a coherent whole
(Goldenberg 2000). Clearly, we need to exploit the massive processing power now
at hand in ways that provide some glimpses of the structures that underlie calculations
and manipulations. Put another way, students need to have some idea what produces
the numbers or outcomes and at the same time gain some ownership of the process.
We have had some experience of how to deal with the problem of outsourcing in
the context of the workplace, as part of the project, Techno-mathematical Literacies
in the Workplace5, in which we investigated the mathematical needs of employees in
‘modern‘ workplaces, that is workplaces increasingly dependent on computer
systems. In such workplaces, there tends to be a wide range of artefacts, many, if not
most of which are mathematical, in the sense that mathematical relations drive their
output. But this mathematics is largely invisible, outsourced to a computer system
and hidden behind computer printouts, graphic displays, or dynamically-presented
tables and figures.
Thus a key utility of the artefact seems to be precisely that the mathematics is
safely outsourced to the technology or to an expert team (see for example, Kent &
Noss, 2000). But we found that judgement of implications of the output could not
simply be left to the machine, but rather demanded some mathematical interpretation.
5 Grant number: L139-25-0119 (Economic and Social Research Council, UK).