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-

process, such as using a ruler to simulate pushing by hand to systematise
measurement, and plotting the outcome on an SPC chart, the trainees were
encouraged to see how the process could become more tightly controlled

With the TEBO we developed, shown in Figure 3, the employees could
generate trials of 50 ‘flicks‘ in a simulated shove ha‘penny game and the TEBO
plotted where the coin stopped each time on the chart. Employees could therefore
generate large data sets, watch the time series and the histogram of the data grow
simultaneously, and thus observe the key ideas more readily: notice trends over time,
aggregate statistical patterns, see how they emerged from individual trials and how
they were constrained within certain limits in situations of random variation. Our
study indicated that our design was largely successful in enabling the mathematical
underpinnings of the SPC charts to, at least to some extent, be revealed while
maintaining a link with the practice; to ‘reduce the magic‘ as described by one
worker.

Figure 3. The TEBO: automating the processes underlying the construction of an SPC chart

Our research indicates an important, and in the context of this paper, ironic
point about outsourcing (both social and technical) of processing power. The
calculations that powered our TEBO were, of course, outsourced to the machine so
became invisible. Yet for effective communication, we took careful design decisions
so that some of the processes underlying this outsourcing - which parameters were
crucial, how the different representations contributed to the calculated results -
became more visible; and, as we pointed out above, we designed in layers that

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