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-
Thus there was a need for employees to appreciate this ‘concealed‘ knowledge, at
least at some level. In addition, we found that the mathematical knowledge was
shaped by the artefacts and systems within the workplace and the justifications had to
adhere to the discourse of the workplace. We identified what we called
technomathematical literacies; ‘technomathematical‘ to express the idea that the
mathematics is expressed with and through the artefacts and ‘literacies‘, to underline
the idea that making meaning out of computational artefacts requires interpretation
and familiarity considered as a cultural form (for details of the research and the
evidence from which the following example is based, see Hoyles et al, 2007).
The symbolic artefacts on which we centred our attention in this research were
intended as catalysts for communication between different layers of the workforce —
such as between the manufacturing shop floor, middle and senior managers, and
process/systems engineers. Middle-level employees were key in this communicative
task, but were often at a loss as to how to exploit the artefacts to facilitate their
interactions, to explain where and why the outputs had arisen. In other words, the
artefacts generally failed in their intended function as boundary objects, that is
affording the communication of meanings across communities (see, for example,
Bowker & Star, 1999). From our observations of workplaces, it was evident that for
the artefacts to serve as boundary objects, some grasp of the mathematical
underpinnings needed to be communicated, and this we set out to undertake in the
second phase of our study. Since it was clear that a deep and detailed mathematical
appreciation was neither necessary nor feasible, we set out to design for ‘layered
learning‘ (see Kahn et al., 2006), that is, to construct a pedagogical and technical
approach that allowed our learners (shop floor employees for example) to drill down
to an ‘appropriate layer of detail‘- to ‘get the idea‘ or glimpse the relevant structure.
The example we will briefly outline is derived from our case study in a car
factory, where it was evident that one artefact the SPC6 chart was supposed to serve
as a boundary object. This time-series graph was generated by the workers on the
production line to monitor a wide range of processes (see Figure 2 for an example).
The chart is intended as a means to share information between shop floor and
management as to how any given process was performing The workers enter figures
6 SPC means statistical process control SPC a set of techniques widely used in workplaces as
part of process improvement activities (see for example, Oakland, 2003),
10