Commentary on Theories of Mathematics Education

444 J.E. Jacobs
impeccable reasoning of the professor of “how a proof should be done” is presented
to the students for them to mimic, is not a particularly effective means of learning for
women. These approaches arc particular issues for women if the professor is male.
In “connected teaching”, the teacher and students would engage in the process of
thinking and discovering mathematics together.
In this community of learners, an instructor can design learning activities that
enable students to use their experiences, either “real” world or classroom based, to
enable them to learn (Giroux 1989). These should actively involve the learners, causing
them to engage in inquiry and reflect on their work (Hanson 1992), Alternate
methods of solutions would be encouraged, where finding another way to solve a
problem would be more valued than solving a similar problem in the same way. The
emphasis would be on generating hypotheses rather than proving stated theorems.
Given the work which indicates that for women connecting with people is important
to their performance and decision making (Peterson and Fennema 1985), these
activities can done be cooperatively rather than competitively or in isolation from
others. Simply creating cooperative experiences, though, is not sufficient. Females
are often at a disadvantage in mixed-sex groups, receiving less information and
are less likely to have their views prevail (Webb and Kenderski 1985; Webb 1984;
Wilkinson et al. 1985). Instructors must monitor cooperative learning experiences
to prevent males from dominating the interaction and to use these opportunities to
help females learn to lead, assert, and present their views while respecting the input
and roles of the others in the group. Lastly, a classroom in which feminist pedagogy
is the predominant mode of instruction will make extensive use of writing as
a means of learning mathematics (Buerk 1985, 1992). Narrative writing can be a
powerful tool for females. It lets them express themselves in a connected way and
share what they know mathematically. This writing can take the form of journals
in which students detail their mathematical experiences, describing their stumbling
blocks or their breakthroughs. They can include how mathematics appears in their
lives. Reaction papers in which students briefly express what they just learned or
questions they have about the content just studied can become a two-minute part
of a mathematics class. In addition to letting students verbalize the current state of
their knowledge, they provide instructors with feedback as to how class was going
at a crucial point in the learning process. Students can prepare research papers on
a myriad of topics, from famous mathematicians (with women mathematicians on
the distributed listed), to how mathematics is used in their other courses. Having
a student observe another student and write down the processes that student used
highlights the hidden thought processes used in solving a problem that are used
and often never discussed. Interviewing someone, having them describe how they
solved a problem and then writing up the interview can provide insight into others’
solution process. This assignment often provokes considerable discussion, for the
hidden steps and assumptions would need to be verbalized (“How did you know to
try 5 and not 6?”). Lastly, students can be asked to make oral presentations of their
written work. This will force them to communicate their ideas clearly, for if other
students do not follow what they have done, they will ask for clarification. Again, in
a feminist class, the goal is to help each other do the best job possible, not to show
who knows more.