Commentary on Theories of Mathematics Education

<strong>Commentary</strong> on Politicizing Mathematics Education 641
forecasting program or a currency converter cannot be deconstructed into its component
bits. Could we not argue that this is increasingly the form that mathematics
takes in our world today? We do not need to go back to first principles of number
theory, probability theory or whatever to do mathematics. Much of the mathematics
today comes in a package that requires other kinds of knowledge and skills to be
able to do—how to install the package on the computer, how to save the results, and
so on. Perhaps ‘advanced mathematics’ can be understood not only in terms of the
traditional trajectories of theories about the structures at higher and higher levels
of abstraction, but by the complexity of the socio-technical system in which it is
constituted. Who is to say that there is only one way of defining what is ‘advanced’
mathematics?
There is a political tension that emerges here, of a different sort to what Sriraman,
Roscoe and English have brought out in their chapter. They say that the
current education system ‘denies’ learners, particular if they are women or from
lower socio-economic backgrounds, from any deep understanding of mathematical
concepts. This is true, if we put a boundary around what we mean by ‘deep understanding
of mathematical concepts’ around the kinds of mathematical learning that
have historically been valued in the academy. As a product of the academy myself,
I share some of the excitement and beauty that both Sriraman, Roscoe and English
see in academic maths, and also the mathematics from non-Western mathematics
that the authors note are most often left out of the academic study of mathematics.
But there seems to be a problem in critiquing on the one hand, the omission of
Arab, Indian, and Chinese contributions to mathematics but not being inclusive—
for the purposes of a study of mathematics—of the contributions of ‘other’ cultures,
for example, the technological culture that dominates today. I would also add the
contributions of neo-liberalism and the military to this mix—not because I personally
believe that they have made contributions for the ‘betterment’ of humanity, but
because they are also cultures that are involved in the production and shaping of
mathematics. More importantly, much of the mathematics that is produced is, as
Sriraman, Roscoe and English observe, concealed, while at the same time, mathematics
is a vital constituent in more and more ‘systems’ that influence the way we
live and interact with each other in the world.
Bloomfield (1991) examines the way in which the everyday work practices of
health professionals in the UK national health system were transformed when a
new information management system was introduced that effectively described their
work in terms of measures that could easily be related to certain efficiency indicators.
The practices changed focus from quality of care to quantity of care. This
tendency to enumerate, list, tabulate, rank has been examined by Callon and Law
(2003) as a process of qualculation, a term originally coined by Cochoy (2002, cited
in Callon and Law 2003) whereby ‘entitities are detached from other contexts, reworked,
displayed, related, manipulated, transformed, summed in a single space’
(p. 13). In the case of the health professionals in the UK national system, their relationship
with particular patients with particular illnesses who have come to see
them in a particular hospital is stripped of these factors that bind their treatment to
the real and specific, so they can be more easily tabulated and summed with the