I realize now that the obstacles I have encountered in encouraging students to grapple with a problem - experience it, discuss it, share ideas about it, take it home and dream on it - are the result of this dualistic/hierarchical/patriarchal way of dealing with mathematics. Students often need a larger context in which to consider a problem. When a grade nine class discovered a pithy problem for which none of the students had an immediate answer, I asked them to ponder it for homework. I was accused by an observing administrator of avoiding the issue because he thought I did not know the answer. However, the students came back the next day eager to continue the discussion and were able to resolve the problem with very little help from me.
In yes/no, right/wrong teaching methods, students realize that getting the answer is where a teacher puts priority. An answer can be checked by glancing quickly at the solution without working through every step. Students who give a wrong answer in class frequently feel self-conscious and embarrassed; those that refrain from answering have learned about the embarrassment and will not risk it.
Students would feel less self-conscious if opportunities were provided for them to avoid giving wrong answers. One technique I use is to pose a question and then ask several students whether they have an answer (or even whether they want to answer), and then choose one who has agreed to respond. One day I told my students that I do not want to put them on the "hot seat". A couple of days later I asked a student a math question. Her response was, "I don't want to be on the hot seat." I apologized and went on.
Students would also feel less self-conscious if the continuum from wrong to right were recognized by teachers. A student of mine got a whole page of subtraction questions wrong, until I noticed that she started her subtraction at the decimal point, subtracting the whole number portion to the left and the fractional portion to the right. Using her rule, all the answers were correct. She was thrilled when I told her they were right by her method, but that she should learn the common method of subtraction unless she wanted to teach everyone her method. She learned it quickly and retained it.
A professor of mathematics (a woman) told me once that women students can be frustrating in their pursuit of the larger context. Just as the lecturer gets to the key teaching point, a women student may ask a question concerning an idea on the fringe of the main lesson. That student has to be satisfied with an answer before she is able to absorb the main point of the lesson, even though other students and the professor herself may find the question irrelevant. If we can find links between the pure mathematical concepts and the learning styles of women, and if teachers can respect and hear their students so they feel a sense of accomplishment and avoid frustration, we will soon have a more perfect wine to taste.
Elaine Harvey, a secondary school mathematics teacher for twenty-five years, has modified both her teaching and curriculum in response to a growing feminist awareness. She is the founder of the Women and Mathematics Committee of the Ontario Association for Mathematics Education and has served as Women and Mathematics editor of the Ontario Mathematics Gazette. She has written articles and made presentations on women and mathematics and was an author for Prentice Hall's Math scope series-textbooks for the intermediate levels. She is presently chair of the Advisory Committee for the Women's Studies Certificate Program at St. Lawrence College.
Margaret Benston, "Feminism and the Critique of Scientific Method" in Feminism in Canada, ed. Angela R. Miles and Geraldine Finn. (Montreal: Black Rose Books, 1982).