Commentary on Theories of Mathematics Education

Knowing More Than We Can Tell 605
issue 13(1) of For the Learning of Mathematics, which is devoted to the theme of
psychodynamics and mathematics education).
In addition to the dangers of mathematics, Nimier identifies a theme of mathematics
in relation to order, which is manifested in three ways: mathematics as an
object of constraint, as a self-ordered object, and as an object creating order within
an individual. In the following excerpt, the fantasy of order has prevailed over the
female scientific-stream student—and the reader might find it interesting to recall
Mei in this context:
N. —You like order?
S. —Yes, I’m not orderly, but I like order! Yes, I like order. Order is part of the world, the
world must be well ordered; well, there’s a succession of . . . a succession of eras that are
the well-ordered society. Well, it’s good. Well, for me it’s good.
N. —Everyone must be in their rightful place.
S. —Yes, we are each in our rightful place. Obviously, there’s no reason to be narrowminded,
we must still look around us, but we must be..., weareeach in our place, in our
position.
N. —We have a position?
S. —Well, I mean that for example in the world right now, if we each put ourselves in the
place of another, then returned to our old position, it would be a mess, it would not be clear.
We all have a goal, a place, and we must try to reach that goal while remaining in place.
(pp. 37–38, my translation)
Nimier’s interpretation of extracts such as these involves seeing the student’s
affective relations as being not so much about mathematics, but rather about
mathematics-as-object, which the student’s unconscious can use toward its own
ends:
we are no longer talking about mathematics as an exact science, but of mathematics-asobject,
which the student has apprehended for herself and on which the unconscious has
inflicted an imaginary transformation in order to put it to her own service and thus to be
able to use it. (p. 49, my translation)
Nimier’s focus on the role of the unconscious in students mathematical experience
may seem unusual to some readers, but it is perhaps surprisingly continuous with
the writings of some French mathematicians. For example, in his famous description
of mathematical invention, the French mathematician Henri Poincaré (1908) states
that “Le moi inconscient ou comme on dit, le moi subliminal, joue un rôle capital
dans l’invention mathématique” (the unconscious ego, or, as we say, the subliminal
ego, plays a fundamental role in mathematical invention, p. 54). For him, the
unconscious work is that which happens while the mathematicians is at rest, not
thinking specifically about a mathematical problem. To illustrate the functioning of
the unconscious, and further his claim that it is necessary for mathematical creation,
Poincaré recounts his own experience around the discovery of what are now called
Fuchsian functions. His insights and discoveries related to these functions did not
happen when he was consciously working on them at his desk, but, instead, while
stepping on a bus en route to a geological excursion. He goes on to argue that the
idea rose to consciousness thanks to the work undertaken by his unconscious, which