Commentary on Theories of Mathematics Education

Feminist Pedagogy and Mathematics 441
disciplines so that they were more inclusive and inviting to women (Warren 1989) 3
One issue is the absence of women from the discourse about who does mathematics.
Given the attention that the recent proof of Fermat’s Last “Theorem” has received,
one needs to wonder if Emmy Noether had written some margin notes stating she
had the proof of a conjecture, whether her statement would have been called a theorem
and whether other mathematicians would have exerted so much energy in
trying to prove her theorem. Fortunately, there are several materials (Osen 1974;
Perl 1978, 1993) that enable faculty to include women mathematicians in their discussions
of mathematics.
The invisibility and lack of recognition of the accomplishments of women mathematicians
can be simply handled. There are more fundamental and subtle issues that
need to be addressed to make mathematics more hospitable to females. Damarin
(1990a, 1990b) discusses the language used in describing mathematics as being
alienating to females. Problems are tackled and content is mastered; faculty torpedo
students’ proofs and students present arguments. Students are expected to defend
their solutions rather than work together to improve them. Students are not expected
to integrate their solution strategies into their cognitive structures nor do faculty
help students write more elegant proofs. Such a confrontational environment is not
hospitable to many females, particularly adolescents for whom getting along with
peers is so important. Yet, a subtle change in the language of discourse can make
being in a mathematics class more comfortable for females. Noddings (1990) also
stresses the use of “functional modes of communication” rather than an emphasis
on precise mathematical language.
A reexamination of Chart 2 raises another issue regarding the dualistic views of
the two aspects of procedural knowing.
Think of what it is that mathematicians do. They work as connected knowers.
Only after they have completed their connected knowing do they (sometimes) put
on their separate knowing hat, and prove what they have discovered. Yet the mathematics
that is presented to students in the classroom is separate knowing. Students
never get to see their professor’s waste paper basket when they first use a new textbook.
Mathematicians are constructed knowers, using both connected and separate
knowing, but most importantly it is the connected knowing that leads to the need for
separate knowing. Also, most individuals, including scientists, applied mathematicians,
and everyday users of mathematics, are more concerned with the mathematics
that comes from connected knowing rather than the mathematics that comes from
separate knowing.
Finally, as the discipline of mathematics is explored, the issue of what constitutes
a proof, what is sufficient evidence so that something is known to be true or valid in
mathematics, needs to be addressed. Barrow (1992) provides an eloquent discussion
of the history of knowing in mathematics. If females are more likely to be connected
knowers, then there is a need to reexamine the emphasis on deduction overall of the
3 Warren (1989) offers a detailed analysis and critique of McIntosh’s theory of curriculum transformation
calling for a more involved transformation, particularly in fields that she classifies as
“gender-resistant.”