Commentary on Theories of Mathematics Education

608 N. Sinclair
and elation felt by mathematicians. Thom points out that his generation of mathematicians
was not subject to these tools of “modern mathematics,” and the embryos
of their unconscious mathematics had time to mature and gain meaning. For Thom,
the problem of mathematics teaching is that of “the development of ‘meaning,’ of
the ‘existence’ of mathematical objects,” and not of rigour (p. 202).
Thom places much blame for the lack of mathematical meaning experienced by
students on the insistent rigour and formalism of modern mathematics, but in her
book The Mastery of Reason Valerie Walkerdine (1988) offers a reading of mathematics
that explains both Thom’s loss of meaning and Maher’s desire for a unified
whole. Drawing on Lacan, and also post-structuralist thinkers such as Foucault,
Walkerdine interprets mathematics as a discursive practice involving the suppression
of both the metaphoric axis or reference out into the world and the subject
position (that is, the loss of “I” and “you”). This may pose problems for learners,
“who have to suspend or repress this content in order to operate in mathematics”
(p. 186)—as we saw exemplified in Nimier’s interview, where the student described
doing mathematics as requiring being alone. Mastery (of mathematics) thus entails
“considerable and complex suppression,” which is painful (separation, loss, death).
But it is also extremely powerful: “That power is pleasurable. It is the power of
the triumph of reason over emotion, the fictional power over the practices of everyday
life” (p. 186). For Walkerdine, the painful part of mastery cannot be blamed on
modern mathematics. For centuries, she argues, mathematics has claimed a kind of
universal applicability that offers “the dream of a possibility of perfect control in
a perfectly rational and ordered universe” (p. 187). The pain is thus linked to the
desire, or a fantasy of a discourse and practice “in which the world becomes what
is wanted: regular, ordered, controllable” (p. 188). Again, Nimier’s interviewees
speak of this fantasy of control, and the subsequent effect it has on the world. The
pain comes from the suppression of value, emotionality and desire that is contained
within the signifying chain.
From Walkerdine, we sense some of the psychological cost of engaging in mathematical
discourse, and we see this extracted by Nimier’s delicate interviewing. And
we also see, in Walkerdine’s analyses of classroom mathematics lessons, how traces
of the suppression demanded by the discourse are manifest in many of the mistakes
made by learners. Walkerdine provides empirical examples of this herself, in her
analysis of classroom situations in which the effects of suppression are argued to
account for children’s mistakes. However, more surprisingly, examples have been
offered by other authors. For example, the therapist (and mathematics teacher) Lusiane
Weyl-Kailey, in her book Victoire sur les maths (1985), describes many case
studies of children for whom basic mathematical difficulties intermingle tightly with
emotional disturbances (see Tahta 1993, for a review of this book).
One of her clients, Gilles, provides an example that connects well to some of
Walkerdine’s themes. He was initially referred for his unsatisfactory mathematics
work and general apathetic attitude. He also had a very disturbed family background
with a depressive mother and absent father. After some initial, unsuccessful work
directly with mathematics, Weyl-Kailey switches to a different tack, in which she
slowly allowed Gilles to take control of what happened in their sessions together