Teachers’ mathematics as mathematics-at-work

ABSTRACT

Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five characteristics highlighted in Noss' work (2002). We use this parallel to develop a conceptualisation of teachers’ mathematics in their practice, and in turn to suggest implications concerning teachers’ mathematical preparation.

KEYWORDS:

• Mathematics-at-work
• teachers’ mathematics in practice
• situated cognition

Disclosure Statement

No potential conflict of interest was reported by the authors.

Notes

1. See also Williams and Wake (2007) and William, Wake, and Boreham (2001) for other examples of this process of crystallisation.

2. See also Williams and Wake (2007) on their use of breakdowns in their methodological approach.

3. In Pozzi et al. (1998), nurses are described as performing calculations to transform prescription quantities in reference to particular drugs (here diathanol), taking into account the drug packaging to determine what to give to patients. For example, by doubling and adding a zero in between or dividing by 10, as one nurse explained: “the concentration is 10 mg in 2mls; so if you have 0.4 mg prescribed, you need to give 0.08ml” (p. 110). Whereas it could be seen as technical or coming from a meaningless trick, as Pozzi et al. explain, it was a very effective transformation for that particular drug (the same being true for another, named amikacin), whereas for other drugs like “odansetron [sic], you only need to half it” (p. 110). Again, they display knowledge grounded in the field of practice, anchored in an intimate knowledge of the drugs itself. Noss et al. (1999) also show, e.g. that some nurses have developed mathematically “questionable” views of average, using a “midpoint combined with a mode strategy” to interpret the blood pressure charts. However potentially “judged ‘wrong’ on the straightforward criteria of general mathematical correctness  …  they made perfect sense and were correct as estimates of the child’s blood pressure” (p. 35), since these were “tailored to the particular nature of [blood pressure] information and how it is displayed on the ward, rather than generic methods applied to this type of data” (pp. 35–36).

4. Knipping and Reid (2015) developed a similar argument in relation to the teaching of proofs where, building on the literature on proving, they explain that there are “pedagogical and practical motivations that shape [teachers’] practices in the classroom”, those being “a complex response to the challenge of teaching proofs and of engaging students in proving” (p. 79), adding that these proving schemes employed by teachers (and students) might be considered as “illogical” by a mathematician or in comparison to “the patterns of formal mathematics”.

5. See also Janvier et al. (1992) on concept transformation in professional settings, where electricity technicians using series circuits developed prototypical models different from those generally used in physics.

6. We can observe similar findings in Williams and Wake (2007), where different conventions were used by industrial chemists and college students to interpret graphs. But, as pointed by Noss (2002) and by us here, it is not only a question of the conventions underlying graphs being different; conceptualisation of graphs themselves change within professional activity.

Additional information

Funding

This work was supported by the Social Sciences and Humanities Research Council (SSHRC Standard Research Grants): [Grant Number #410-2008-0284].