Commentary on Theories of Mathematics Education

640 K. Yasukawa
This opens up the question with which scholars in the science and technology
studies (STS) have been grappling (see for example Bijker and Law 1992;
Bijker et al. 1987; Mackenzie and Wajcman 1999): is there a need to understand
technology in ways other than the purely instrumentalist view of technology as a
‘neutral, value-free’ tool for solving particular problems? STS scholars reject the
separation of ideology and technology, but continue to struggle with what exactly
is the relationship between the two. Is technology a resource for achieving some
ideological motive? This is what Langdon Winner (1986) argued when he discussed
how class and racial biases can be ‘designed into’ technological artefacts such as a
bridge. Winner cites as an example an overpass bridge in New York that was too low
to allow buses carrying mostly poorer black people to get through, and which was
designed by Robert Moses, who, according to his biographer had social and racial
biases that were reflected in his designs (Winner 1986, p. 23). This social determinist
view of technology can be contrasted with other kinds of determinist views.
Borgmann’s device paradigm might be argued as an economic determinist view of
technology: technologies are designed with particular economic goals in mind such
as achieving greater efficiency and productivity outcomes. Others might take the
view that technologies are ‘autonomous’: once it is let ‘loose’ it is unstoppable in its
advancement into bigger (or perhaps ‘smaller’ is now the more appropriate symbol
of progress) and faster technological artifacts and systems. Some of the more recent
literature in STS examines technology as a social practice—technology as emerging
from and within cultural practices: we as humans are built into the world that we
are building (Davison 2004). Actor-network theorists such as Latour (1987, 1999)
reject the idea of there being clear boundaries between humans and technologies.
Their approach to studying a technological system or artifact is an ethnographic approach
of ‘following’ the actors (humans and artefacts) as they participate in a series
of translations of their different interests, build alliances of common interests until
they build a solution—an artifact, a computer software, a work practice—that is then
accepted and disseminated more widely as a ‘black-box’. The ‘black-box’ cannot be
opened once it is released for use and all of the beliefs, differences in interests, compromises
and negotiations that were part of the trajectory of this ‘solution’ cannot
be uncovered or easily recovered (Latour 1999).
This brings my attention back to the notion that technology might ‘push society’
into adopting particular views about the relationship between technology and
mathematics education. Computer technology has certainly brought into question
the mathematical theories humans need to know in order to do mathematics—at
least the mathematical activities involved in our everyday life. Indeed, we do alot
of mathematics without even being aware of the presence of mathematics. As illustrated
in Skovsmose and Yasukawa (2004), we can do encryption using the most
sophisticated encryption algorithm that are based on theoretical results from classical
number theory without realising that there is a mathematical basis to this procedure.
The mathematics has been ‘black-boxed’ or packaged, and we, as users of the
package, are not encouraged to look inside the box. It’s a package—take it or leave
it!
But where do we draw the line between mathematics and technology given that
the ‘package’—be it an encryption software, a room booking system, a weather