«FEMINIST pedagogy can be an important part of building a genderequitable multicultural classroom environment. Such a pedagogy builds on how students ...»
AUTHOR: Judith E. Jacobs; Joanne Rossi Becker
TITLE: Creating a Gender-Equitable Multicultural Classroom
Using Feminist Pedagogy
SOURCE: Yearbook (National Council of Teachers of Mathematics)
1997 107-14 '97
FEMINIST pedagogy can be an important part of building a genderequitable multicultural classroom environment. Such a pedagogy
builds on how students come to know mathematics. It also requires
examining the discipline of mathematics from a feminist perspective.
A FEMINIST PERSPECTIVE ON KNOWING As with many other theoretical frameworks, Perry's model (1970) of how students acquire knowledge was developed using an all-male sample, then generalized to include women. One of the major advances in our understanding of women's development of knowledge comes from Belenky, Clinchy, Goldberger, and Tarule's (1986) all-female sample.
In their work, Women's Ways of Knowing, they describe the following five categories that describe how women come to know things: * Silent knowers accept what they know without stating what it is they know. * Received knowers focus on attaining knowledge from authority figures, usually through listening. * Subjective knowers listen to their own internal voices. * Procedural knowers fall into two categories: separate and connected. Separate knowers learn separately from others. Connected knowers gain knowledge through access to others' experience. * Constructed knowers judge evidence within its context--an integration, the book's authors maintain, of both separate and connected approaches. More detail on interpretations relating this theoretical model to mathematics can be found in Becker (1995) and Jacobs (1994). The most important point to stress here is that in the procedural knowing category, Belenky, Clinchy, Goldberger, and Tarule (1986) found women predisposed to be connected knowers, whereas Perry's studies (1970) had found separate knowing more prevalent in male populations. Mathematics has traditionally been taught in a manner more consistent with separate knowing: stressing deductive proof, absolute truth, and certainty; using algorithms; and emphasizing abstraction, logic, and rigor. To build on the strengths and propensities of connected knowers as well, our teaching needs to include more intuition and experience;
conjecture, generalization, and induction; creativity; and context.
FEMINIST PEDAGOGY IN THE MATHEMATICSCLASSROOM This new knowledge gleaned from Women's Ways of Knowing provides directions for pedagogical strategies that facilitate using connected teaching to reach all students. Four principles of feminist pedagogy will be discussed here as an approach to building a gender-equitable, multicultural mathematics classroom. These four principles are using students' own experiences, writing, cooperative learning, and developing a community of learners.
USING STUDENTS' OWN EXPERIENCES TO BUILDKNOWLEDGE As illustrated by our discussion of Women's Ways of Knowing, connected knowing is an important perspective, especially for women. In this stage, the student builds knowledge from personal experience. Instruction should include experiences designed to allow students to build on their intuitive understanding, to provide insight into the reasons for the area of study, and to encourage activity versus passivity. Such instruction might involve applications, drawing and constructing models, using visual representations of mathematical concepts, and using technological tools such as calculators and computers. Everyday uses of mathematics can help promote the study of particular topics by connecting mathematics to experiences from everyday life. As Meiring, Rubenstein, Schultz, de Lange, and Chambers (1992) point out, giving applications more prominence can bring out the relevance of mathematical ideas and help motivate reluctant learners (p. 117).
EXAMPLE 1 A real-life problem involving force relates to air bags in the front passenger seat of a car when an infant or child seat is being used. Why might one want not to use an air bag in that situation? Could the air bag be modified to help prevent possible injuries to the child, better complementing the protection the child seat provides?
EXAMPLE 2 High school students might choose a problem of importance to them, their school, or their community to survey, analyze, and present results to an appropriate agency to seek change.
Potential topics might be a survey and analysis of the food that is thrown away uneaten in the school cafeteria, with recommendations to cafeteria staff about menu changes; an analysis of crime statistics, comparing those of a shopping center having a liquor store to those of one without a liquor store, with a report and recommendations to the city council; or a survey and analysis of local traffic bottlenecks, with a report to appropriate officials.
EXAMPLE 3 Another way to involve students' lives occurs in December and early January, when many ethnic and religious groups celebrate holidays. Multiculturalism is not just a means of affirming one's own identity; it also should promote knowledge and understanding of others. Looking at different groups' celebrations helps us know each other better. Western- and Eastern-rite Christian churches celebrate Christmas, Jews celebrate Chanukah, and African Americans celebrate Kwanzaa. Many different mathematical questions arise from studying these celebrations. Why is Kwanzaa celebrated between Christmas (25 December) and New Year's (1 January)? Why do the different Christian churches celebrate Christmas on different dates? How many different New Year's Days are celebrated around the world? Why are the dates different from year to year for many of these holidays? Seven candles are used for Kwanzaa, symbolizing the seven days of celebration and the seven beliefs that are held by people in many parts of Africa. There is one black candle, three red candles, and three green candles. On the first night the black candle is lit in the middle position. The second night the black candle and a red candle are lit. The third night the black, the red, and a green candle are lit.
This pattern continues with each night having an additional candle lit, alternating red and green as the additional candle. On the seventh night, all candles are lit, with three red, then a black candle, and then three green. If each night's candles are burned completely in a single night, what is the total number of candles used and how many of each color are used over the seven days? Chanukah involves lighting candles on a menorah (a candlestick with holders for nine candles).
The first night the shamus, or worker, candle is lit; it then lights one other candle commemorating the first night. On the second night the shamus candle lights two candles; on the third night, three candles;
and so on. Chanukah lasts eight nights, and each night's candles are all burned completely in a single night. How many candles are needed for all eight nights? Chanukah and Kwanzaa present opportunities for finding the sum of arithmetic progressions as students find the answers to the questions posed above. In addition to all the mathematics involved, students can learn about the cultures and religions and bring in their own customs for these celebrations. The possibilities are endless.
WRITING IN THE MATHEMATICS CLASSROOM A great deal of attention has been paid of late to using writing in mathematics.
Writing is essential to connected teaching for a number of reasons. First, writing out explanations helps students develop their own voices and move away from the authority of the teacher. It allows the learner to gain a sense of self and become more independent.
Sharing writing with other students allows one to listen to others' reasons and ideas and learn from the variety of approaches that might be taken on any one problem situation. Writing emphasizes the process, not just a correct answer. There are a number of ways to integrate writing into the mathematics classroom. Students can give feedback on the class, anonymously if need be. Students of most ages can inform the teacher about the pacing of the class, whether specific activities or topics were interesting or boring, or how they prefer to work and learn. A journal might be used to gather both affective and cognitive information from the student. Prompts related to specific concepts can furnish the teacher with considerable information about students' understanding, both individually and for the class as a whole.
In algebra, for example, students can explain what an algebraic expression and an algebraic equation are and compare the two concepts. A journal can also be used to gather important infomation about students' feelings about themselves as learners of mathematics.
A mathematics autobiography early in the academic year and followups throughout the year will give the teacher a wealth of knowledge about what past experiences affect students' current learning patterns. Writing out a full explanation of how a problem was solved, including dead ends, encourages students to reflect on their own thinking and learning processes and to learn from their mistakes.
At the same time, it gives the teacher insight into problem-solving abilities.
COOPERATIVE LEARNING IN THE MATHEMATICSCLASSROOM There is evidence that women (and students of color) not only prefer a more collaborative, less competitive atmosphere in the classroom but that they achieve more in that milieu as well (AAUW 1992). Traditional mathematics classrooms of the past might best be described as appealing most to Anglo-European male students in terms of both content and mode of instruction. Some men, however, do equally well in a collaborative environment. For many girls and young women, successful learning takes place in an atmosphere that enables students to enter empathetically into mathematics through connected knowing. Although not the only methodology to achieve connected teaching, using collaborative, small groups is one of the best ways to accomplish several goals. Developing the student's voice and ability to learn autonomously is hypothesized to be essential for eliminating gender differences in mathematics (Buerk 1985; Fennema and Leder 1990).
In groups, students develop and support their own justifications, struggle for solutions to problems, and share problem solving. Morechallenging problems can be chosen because a group has the benefit of several minds working toward a solution. With guidance from the teacher, students in one group can carry out investigations in further depth than other groups on a problem that interests them. But one cannot view cooperative learning as the solution to all genderequity problems. Although some advocates of cooperative learning stress the use of heterogeneous groups, cross-gender relationships may be more difficult to achieve than cross-race friendships or friendships among students with and without disabilities. Students may prefer working in single-gender groups. Also, gender differences in communication and interaction patterns may hinder effective cross-gender group dynamics. Research indicates that boys in small groups are more likely to receive help from girls when they ask, but that girls' requests are more likely to be ignored by boys (AAUW 1992). The teacher must therefore constantly monitor the groups' activities not only for mathematical content but also for the group dynamics to ensure that sex stereotyping is not reinforced and females' achievement is not impaired.
DEVLOPING A COMMUNITY OF LEARNERS One of the hallmarks of a feminist classroom is that it is a community of learners.
Although teachers retain ultimate responsibility and authority, all in the class are there to learn together and from each other. Students need to validate their answers and generalizations so that their peers as well as their teacher understand and accept their work. In doing this, they often discover their own misunderstandings and correct them. Students need to be clear about how they arrive at their conclusions. When words fail, they often resort to graphic or pictorial displays or explanations that rely on counterexamples. Students also need to determine what they will learn and how they will learn it.
For example, if a school district decides to adopt a dress code, students usually will oppose this decision. After discussing the decision, students can explore its implications. Given the parts of the uniforms--skirts, long pants, short pants, blouses or shirts, blazers, vests, types of shoes and socks or stockings--students can determine how many different outfits they can wear (a counting problem). They can examine the cost factor involved, survey students' feelings about a dress code, and present their findings. An interesting twist to the problem would be to have them use the same data and present supportive or nonsupportive reports, addressing different audiences that are affected by, or involved in, the decision--such as students, parents, teachers, or the school board.
REEXAMINING MATHEMATICS AS A DISCIPLINE Anotherway that feminist pedagogy changed the way we function in the classroom was by examining different academic disciplines to see how the disciplines themselves promote male involvement and discourage that of females. Mathematics needs to be examined from that perspective. We have already mentioned the emphasis in mathematics on deductive proof (the more male way of knowing) and a lack of emphasis on induction and experience (the more female way of knowing). In support of using different modes of knowing mathematics and understanding the fundamental basis of mathematics, we present the following two examples.