Commentary on Theories of Mathematics Education

604 N. Sinclair
students in France. Half of these students had chosen the literary stream while the
other half had chosen the scientific/mathematical stream. Nimier was interested in
understanding how students experience mathematics, what it represents for them,
and how the answers to these questions might differ for students in the different
streams. The almost complete absence of his work in the anglophone mathematics
education literature is hard to explain, but might be related to the psychoanalytic approach
Nimier took in conducting and interpreting his interviews. As will become
clear, Nimier focuses more on the notion of ‘coming to know mathematics’ than
on different possible ways of knowing. In his analysis, he highlights several important
themes, including the perceived dangers involved in doing mathematics. For
example, one male literary-stream student speaks of the risk of solitude, of being
abandoned:
For example, in comparison with literature, one can relate to novels and even to the charactersinthenovelsorevenwiththeauthorswhocanl...,Idon’t
know...,comfortyou, let’s
say, support you; but with mathematics, there is no one, one is alone. (p. 56, my translation)
For this student, coming to know mathematics involves being alone, losing empathy.
The next excerpt, also from a male literary-stream student, suggests risks that lead
to more permanent losses associated with doing mathematics:
S.—I believe that we should instruct ourselves in languages instead of learning another
discipline like mathematics, which troubles the mind.
N.—How does mathematics trouble the mind?
S.—Yes, [it] troubles the mind, because mathematics is only logic. Logic is necessary. In
contrast, for languages, to do languages, you need a certain presence of mind; that is, the
mind works better with languages than it works with mathematics... And that’s why it
doesn’t come to trouble the mind. For example, when we do German during an hour, and
after we do math, well, we can’t remember what we’ve just done before. (pp. 59–60, my
translation)
These excerpts, and Nimier’s interviews are full of similar ones, show how students
come to talk about mathematics as being dangerous (especially by those in the literary
stream, but also the others). Nimier argues that the unconscious mind 7 sometimes
turns mathematics into a dangerous object much like children use witches
to explain their fears. He goes even further in trying to understand the fears that
mathematics supports, and fixes on castration as a strong possibility. This accounts
for the many of the sentiments expressed by the students, like being “cut off”, or
having the integrity of the mind challenged. It also accounts for the general feelings
of fatalism and randomness described by the students. Nimier argues that one
would expect to see several defense mechanisms in place to counter the underlying
anguish, and, indeed, finds several of them emerge in the interviews (for one of
the English-language sources of Nimier’s work, see his 1993 article in the special
7 Here he refers to the Freudian unconscious, the store of information, including memories, thought
patterns, desires and sense impressions, that has been repressed, and that remain largely inaccessible.