Commentary on Theories of Mathematics Education

Feminist Pedagogy and Mathematics 439
can create her own truths. Many, if nor most mathematics students, are received
knowers. These are the individuals who when asked why you cannot divide by zero,
tell you that “My teacher told me so”. They return the words of an authority. It
never has dawned on them to ask why a given rule is so or to wonder who gave
their teacher the power to make such a decision. The authority that comes with
being a teacher is all that is required for these students to accept the truth of any
mathematical statement the teacher makes.
The Subjective knowing stage is a very powerful one for the knower and brings in
women’s intuitive way of knowing. Here knowledge comes from within. This stage
fits the stereotype of women’s intuition; of knowing that comes from that which feels
right. Knowledge no longer comes from outside the knower. There is an inner voice
that lets the individual know that she is on the right track. Men and women handle
this type of knowing differently. The men’s version conies from their rightfully held
opinion, “It is obvious”. For women this works differently. Though the knower holds
on to this knowledge, there is a concern that her views do not intrude on the views
of those holding opposing views. The women’s version is expressed conditionally,
“1 guess I feel so”.
To get to the Procedural knowing stage, the knower requires some formal instruction
or at least the presence of knowledgeable people who model providing
some evidence and can be seen as informal tutors. The question as to whether individuals
should be forced to move on to this type of knowing is one that is often
discussed in women’s studies. In mathematics this progression is essential. Some
contend that this view that there are ways of knowing that lead to greater certainty is
buying into a hierarchical value system. Nevertheless, procedural knowing is a key
in mathematics, and also an area of controversy.
There are two types of procedural knowing identified in Women’s ways of knowing.
Separate knowing is based on impersonal procedures for establishing truths.
It is particularly suspicious of ideas that “feel right” (subjective knowing). It often
takes an adversarial form (which is particularly difficult for girls and women) and
separate knowers” often employ rhetoric as if in a game. The goal of separate knowing
is to be absolutely certain of what is true. It is better to eliminate a possible truth
than to accept as true something which later may prove false. The separate knower
would turn to the rules of discourse to prove the statement.
Connected knowing builds on personal experiences. It explores what actions and
thoughts lead to the perception that something is known. Experiences are a major
vehicle for knowing something. Authority comes from shared experiences, not from
power or status. A creative process would be used to gain experiences from which a
conclusion could be made. In answering the question, “Why do you think that?”, the
separate knower would look to propositional logic. The connected knower would
want to know what circumstances led you to that conclusion. These ways of knowing
parallel deductive and inductive reasoning.
It is in this stage, procedural knowing, that there is the most conflict with the traditional
way of knowing in mathematics. If the only knowledge that is accepted as
valid is that which can be statistically demonstrated or is based on deductive logic
(methods that are independent of the knower’s actions), then that which I know