Addressing Eurocentrism and Androcentrism in Mathematics:The Development and Teaching of a Course on Mathematics, Gender and Culture
Addressing Eurocentrism and Androcentrism in Mathematics:by John Kellermeier.
Published in:
(1998). In K. Conway-Turner (Ed.), Women Studies in Transition: The Pursuit of Interdisciplinarity, Newark, DE: University of Delaware Press.
What does a mathematician look like? Pause for a moment and visualize for yourself an answer to that question. Notice what this person looks like. Notice the sex and the race of this person. Chances are you pictured a white male. In fact, whenever I have tried this exercise with my students or in a workshop the majority of people do indeed picture a white man.
I recently received a birthday card with the popular media image of a mathematician: a white male, middle aged or older with gray hair and a beard and standing before a blackboard covered with mathematics symbols and notation. There is no doubt that this is what a mathematician looks like. This image is so pervasive in our society that it's use immediately implies a mathematician. Images like this appear in cartoons such as Gary Larsen's syndicated cartoon The Far Side or those appearing in The Chronicles of Higher Education (Hobart, 1992, Richter & Bakken, 1993).
These images inform us that our society perceives mathematics as the domain of white men. In fact, it is, at least in academia. Out of Ph.D.s in mathematical sciences given to U.S. citizens, approximately three out of four go to white men and only one out of 100 go to women of color (National Research Council, 1989). The production and teaching of mathematics in our society is overwhelmingly in the hands of white men.
Now, let me ask you to pause a moment and picture the first people to do mathematics. What race and sex did you see? This exercise usually elicits one of two responses. The first is cave men, that is, hairy white men wearing animal skins. The second response is Greek men. Again the origins of mathematics are seen as coming from white men.
Most histories of mathematics state that mathematics began with Greek men from about 600 BCE to 300 CE, went into decline through the "Dark Ages," was rediscovered by European men during the Renaissance and was developed from there by Western men. This history is described by Joseph (1987) as "the 'classic' Eurocentric approach," and as a result, "Mathematics is perceived as an exclusive product of white men and European civilisations." According to Joseph, this eurocentric bias results from:
However, the reality is that the first mathematicians were women and most likely African women. The oldest known mathematical activity is calendar making. Bone fragments with incisions have been found in Europe and Africa dating back as far as 37,000 BCE. The most famous of these is the Ishango bone found on the shore of a lake in Zaire, Africa (Zaslavsky, 1992). The incisions on these bones correspond to lunar cycles or lunar calendars. This is the earliest mathematics, the recognition of the basic periodicity of nature.
And when we ask which sex is most likely to have first developed an understanding of lunar cycles, the answer is women. One obvious reason is the menstrual cycle. A second reason is that early agriculturalists used calendars. But again these were women. This was an expression of mathematics that was not elitist, not divorced from the surrounding world by logical reasoning. Rather this mathematics was based on what Sjöö and Mor (1987) call organic reasoning, emerging "from a desire to cooperate with the natural world, and from a real integral observance of the needs and rhythms of the personal self and the human community."
Since these early beginnings, all cultures have developed mathematical ideas. Yet today, Western society has an androcentric and eurocentric view of mathematics that self perpetuates in the training of mathematicians. What we usually think of as mathematics, the way it is done and taught and even conceived in our society, is in fact eurocentric and androcentric, in other words, racist, sexist and elitist.
This paper will describe a course on Mathematics, Gender and Culture I developed to address the eurocentrism and androcentrism in mathematics. This course was developed during the spring of 1993. At that time, I took part in a faculty development seminar designed to help faculty at SUNY Plattsburgh develop courses for our General Education category of Perspectives on Global Issues.
Several years earlier I had proposed a course on gender and mathematics dealing exclusively with gender differences in mathematics. That course was quickly rejected by the Mathematics Department because it was perceived as having no "real" mathematics content. Since then, I have also been teaching Introduction to Women's Studies. Teaching this course has taught me the importance of dealing with issues of race and class as well as gender.
The new course was to be developed for the Perspectives on Global Issues category which would require a global perspective and, in the words of our General Education Program, "substantive inclusion of recent scholarship on women and minorities." Consequently, this course was designed with two objectives: first, to examine from a global perspective the experiences of women and people of color with mathematics, and second, to consider the effects of culture, particularly non-white culture, on the development and doing of mathematics.
The first of these objectives would make use of the extensive scholarship on woman and mathematics from the past two decades. Much of the information on scholarship from North America is available in Mathematics and Gender edited by Fennema and Leder (1990) while a global perspective can be found in Gender and Mathematics: An International Perspective edited by Burton (1990).
Including issues of race and class is not as easy. As Campbell (1989) points out, in a review of the literature on equity in mathematics, while research on sex discrimination in mathematics is extensive, similar research on racial discrimination is limited. "Social class and socioeconomic status are equally important variables that are even more rarely factored into the mathematics and equity equation." Both Campbell and Reyes and Stanic (1988) discuss the lack of and need for research on the interaction of gender, race and class effects on equity in mathematics. An examination of this lack of research then became another objective of the course.
The second course objective constitutes the study of ethnomathematics. Ethnomathematics is a field that was developed in the early 1980s. The man usually credited with coining the term is a Brazilian educator, Ubiratan D'Ambrosio (1985, 1990). He breaks the word down into "ethno" meaning "cultural environments," "mathema" meaning "explaining and understanding (the world) in order to transcend, managing and coping with reality in order to survive," and "tics" meaning "technics."
Thus, ethnomathematics studies how people within a given culture develop techniques to explain and understand their world and to solve their daily problems. Culture is defined rather loosely and may include traditional, small-scale cultures or historical cultures such as indigenous cultures of the world (Hadingham, 1992; MacPherson, 1987), the pre-Columbian cultures of the Americas (Ascher & Ascher, 1981; Ortiz-Franco, 1993), the historical cultures of Africa (Zaslavsky, 1973), or American folk cultures (Zaslavsky, 1990). It may also include subcultures such as the children candy sellers of Brazil (Saxe, 1988), or contemporary U.S. video game "kid culture" (Shirley, 1991) or carpet layers (Masingili, 1993).
The Mathematics, Gender and Culture course then has two themes: 1) the study of gender and race differences in mathematics and 2) the study of ethnomathematics. While it is an approved course within the Mathematics Department, it is also cross listed with the Women's Studies Program at SUNY Plattsburgh and is an elective for the Minor in Women's Studies.
The course is organized primarily as a discussion course. In addition, I use a variety of group activities and hands-on exercises.
The assignments for the course include:
After teaching this course for two semesters I believe it has been successful. In end-of-the-semester comments, many students said that at the beginning of the course they could not see how mathematics, gender and culture were related. However, by the end of the semester their primary comment was that their eyes had been opened, and that they were now aware of the sexism and racism within mathematics. For many students this was the first course in which they had dealt with sexism or racism in a substantial way.
For many students, mostly female, this course enabled them to put their own experiences with mathematics into perspective. One female student wrote,
"This class was a real eye opener for me. It has helped me make a lot more sense out of my own education. I realize that if I was encouraged to do well in math and expected to do as well in math as I did in other areas, I might have done better."
For another female student, this awareness lead to a sense of empowerment:
"I have gained so much after taking this class. I am not only aware of the problems inside the mathematical system but I have gained a better sense of myself. I now can evaluate my own life and see how I was discouraged from math. I have also gained a great amount of math confidence which I can use for future classes. Although I vowed never to take another math class I am actually contemplating registering for one."
For many education students, both primary and secondary, a newly found awareness of the sexism and racism in the education system gave them the resolve to monitor their own future efforts in the classroom. A female secondary education mathematics student, who had previously described her experiences with sexist and racist mathematics instructors, wrote:
"Overall, this course has helped me to realize that helping a single individual by teaching mathematics and telling students about my bouts with ethnocentric and gender biased individuals is a worthwhile venture."
Since most students took this course to fulfill a general education requirement, there were many, female as well as male, who would not otherwise be inclined to take a women's studies course. Many of them were surprised to find a mathematics course with women's studies content. Although there was hostility from some male students at first during one of the semesters, it soon dissipated. I believe this was due to two demonstrations. The first day of class I asked students to visualize a mathematician as I discussed at the beginning of this paper. The overwhelming number of white males visualized was undeniable evidence of bias in mathematics. Secondly, I asked students who were skeptical of our readings to simply count how many times instructors in their other classes called on males and females. The overwhelming amount of bias against female participation in the classroom soon became apparent to these students in their own classes. Once they granted that bias did in fact exist, they were willing to hear the remainder of the messages about sexism and racism in mathematics. In the words of one of these students:
"The first few days of class, I thought you made all men out to be pigs, and thus, began to develop an immediate negative impression of you. After a few weeks, I began to see some of the points you made in class when I started doing surveys of my own in my other classes. I began taking notice of the attention my professors gave to males over females and the amount male students spoke out over female students in classes. By seeing first hand what you discussed in class, made a compounding impression. I realized then the difference between making men out to be pigs, and trying to fight for the rights of women."
I also expect that nearly all students have at one time or another been subjected to the elitism that pervades mathematics. Students' own experiences of "math abuse" (Kellermeier, 1994), even among those students who were successful in mathematics, gives them an intuitive understanding of elitism and consequently sexism and racism in mathematics.
All of the assignments used in the course proved to be successful. While there were some initial complaints about the daily reading quizzes, students quickly learned that a combination of active reading and taking notes greatly increased their scores and added to the quality of class discussions.
Student journal writing is a fairly standard feminist pedagogy strategy that I incorporate in all my classes (see Kellermeier, 1994). In this course, it provided an opportunity for students to confront the personal nature of the gender and race discrimination we were studying. Journals also provided a way for me to listen to what students were thinking and saying and to communicate privately with them.
The most important lesson students learned from doing the biographies is the scarcity of information on mathematicians who are not white males. There are many available sources on white male mathematicians, but to find a person of color and/or a woman who is a mathematician requires diligent research. The second lesson learned is that this diligent research generally results in finding mathematicians who are white women.
One semester, after two days of presentations about mostly white women, we realized that we had listened to story after story of women throughout the centuries who had struggled to work in the field of mathematics. We ended with a biography of a contemporary woman. We noted that she was the same age as many of those currently teaching in academia. Her struggles to achieve in mathematics echoed those struggles of the women throughout the centuries of whom we had just heard. The class concluded that little progress had been made for women's equality in t he field of mathematics.
The students presented a variety of action plans for addressing the eurocentrism and androcentrism in mathematics. Some of those who were education majors developed lesson plans for teaching mathematics from a multicultural perspective using ideas learned from the study of ethnomathematics. Other education majors discussed the ways in which they intended to incorporate feminist pedagogy and other strategies for encouraging people of color and women in mathematics into their future classrooms.
During the course we learned that a lack of perception of the usefulness of mathematics was a major factor in explaining both gender and particularly race differences in mathematics achievement (Campbell, 1989; Reyes & Stanic, 1988; Schindler & Davison, 1985). Consequently, many students dealt with ways to help children see mathematics as useful and related to their lives, including such daily activities as cooking, shopping, gardening, and game playing.
Lastly, several students used their action plans to deal with their own experiences with mathematics with some resolving to take another math class.
The ethnomathematics project provided students with the opportunity to see mathematics as creative and fun, something which we learned was an important component of successful mathematics instruction (Campbell, 1989). Ethnomathematics projects presented by students included examples from the cultures we had studied such as the Incan quipu and various board games from Africa and New Zealand. One student even built an igloo to scale out of ice cubes, bringing the igloo to class in a cooler.
There were many examples of students' own artwork such as string art, cross-stitch, sand painting, quilt making, origami, and ceramics complete with a description of the mathematics required to do the art. In addition, one student used the culture of car racing for his project. He gave a description and explanation of the mathematics needed in the preparation of an automobile for racing.
The group problem solving assignments were, for many students, the most instructive aspect of the course. Students felt they learned about gender differences in problem solving. My intention in developing this assignment was to have students experience the doing of mathematics (as opposed to the learning of mathematics in the traditional sense). I assigned students to groups and then gave them a problem to solve. They were given one to two weeks to solve the problem on their own outside of the classroom. Students were told that the point of this assignment was not to determine the right answer but to look at the process of solving a problem. During class time each group presented their solution to the problem. This was followed by a discussion of the process that the groups went through to solve the problem.
By assigning the students to groups by sex and mathematics background, I intended to manipulate the problem solving environment so that students could experience the effect this would have on the group process. In particular, I expected students to discover gender differences in problem solving.
What we found was that females in same sex groups tended to work cooperatively, deriving a solution in collaboration with others in the group. Males in same sex groups, on the other hand, tended to work individually first and then combine their individual solutions into a group solution. In mixed sex groups, males tended to take leadership roles, females tended to speak less. At the same time, there were exceptions to these behaviors, both in females and males.
I also chose the problems in order to give students a variety of experiences with mathematics and problem solving. For the first set, I assigned students to same sex groups with homogeneous math background. The problem assigned to these groups was a variation of a problem used by Buerk (1982) in her work with math avoidant women:
Suppose that all the people in your group want to meet by shaking each other's hands. You need to determine how many handshakes this would mean. How would you envision the number of handshakes? Suppose there were 10 people in your group, how many handshakes would be required? What about 20 people, 50 people, 100 people? How could you make a formula to represent the problem?
Buerk intended this problem to help the women from a view in which mathematics is seen as consisting of only right and wrong answers to a view in which mathematics is also seen as a dynamic process, involving creativity and intuition. My students' reactions to this problem were consistent with this intent. Students arrived at a solution using a variety of methods. It built confidence among students who initially viewed themselves as weak in mathematics. And depending on how they viewed handshakes, there was more than one answer presented.
This problem served as an excellent introduction to the group problem solving assignments. Since there were so many ways to solve the problem and more than one possible answer, it became clear to the students that the process of solving the problem, the process of actually doing and creating mathematics, was more important than getting the "right answer."
For the second group problem students were again assigned to same sex groups but this time with a mixed mathematics background. For this assignment I chose a problem from the traditional male activities of roofing. Unfortunately, this problem turned out to be much harder than I expected. For the second semester I changed to the following problem:
How many square feet of carpet would be required to carpet the Blue Room in the Angell Center? Take into account the following constraints:
- Carpet comes in 12' wide rolls.
- Carpet throughout the room must have the nap running in the same direction.
- Consideration of seam pattern is very important because of traffic patterns.
The Blue Room is a large public room in our student center, the Angell Center, so named because of its blue carpeting. This problem was inspired by the work of Masingili (1993) on the ethnomathematics of carpet laying. The male groups tended to be more comfortable than the female groups with both the roofing and carpet laying problems. The need to do measuring for both of the problems lead to a gender difference in measuring techniques. The female groups tended to measure with tape measures while the male groups tended to pace off the distances.
Solutions to these problems varied greatly, not only in approach but in actual answers. We never did determine the "correct" answer for either problem. This helped students understand that the mathematics involved in applications as these is never as "neat" as it is taught in academic mathematics.
Students were assigned to the third groups based on a homogeneous math background. However, mixed sex groups were used. The gender mix was chosen to keep all groups at about the same ratio of males to females. For this assignment, I countered with a problem from the traditional female activity of sewing. Each group was given an identical set of pattern pieces. They werre asked to determine how much fabric of various widths would be needed to cut out the pattern. They were reminded to take into account the nap of the fabric. While it was agreed that this problem derived from traditional women's experience, very few of the students of either gender had any sewing experience. Several groups made a trip to a local fabric store to seek advice and a definition of nap.
The last groups were chosen by the students themselves. This gave them the option to choose same sex or mixed sex groups as they wished. In both semesters there were a mix of female, male and mixed sex groups. For the fourth problem I used a set of fifteen math puzzles intended for use in the middle grades (Jamski, 1991).
Many students had begun the semester expecting to have to find "the method" to get "the answer" whenever confronted with a mathematics problem, not able to think creatively or to question the validity of the stated problem. Now, however, when confronted with problems from what we had come to see as the culture of academic mathematics, the attitude and approach of the students had changed. For example, they were quite willing to accept multiple answers for the question "How many times will your heart beat this month?", depending on whose pulse rate was used as a base for the problem. No one asked, "How many heart beats a minute should we use?"
The following problem pointed out the contrived nature of many of the problems encountered in academic mathematics.
With a seven-minute sand timer and an eleven-minute sand timer, what is the easiest way to time the boiling of an egg for fifteen minutes?
One group presented the "correct" answer. This was to start both timers at the same time and wait until the seven minute timer is done. Then start to boil the egg. There will be four minutes left on the eleven minute timer. When those four minutes are over, restart the eleven minute timer. Then the four minutes and the eleven minutes will make the required fifteen minutes. After this solution was presented, another group suggested that the easiest approach would be to use the seven minute timer twice and then count to sixty. "After all", a spokesperson for the group said, "hard boiled eggs aren't that precise. And besides, you get to eat your egg seven minutes earlier." This was a critique of academic mathematics that the students in that group would probably have been too intimidated to express at the beginning of the semester.
Overall, I believe that this course effectively met both objectives: 1) to examine from a global perspective the experiences of women and people of color with mathematics, and 2) to consider the effects of culture, particularly non-white culture, on the development and doing of mathematics.
Students learned that not all mathematicians are white males standing in front of a blackboard. They learned that women of color were the first mathematicians, that mathematical ideas come from many cultures not just Western society, and that mathematics is something they successfully do everyday of their lives. As one student said,
"Now I see that a construction worker is a mathematician just as much as a baker is and a math teacher is."
This course is a first step toward changing student's perceptions of mathematics and making them aware of the sexism, racism, and elitism in mathematics. In the words of one of the students,
"I learned about the effects of thinking who the mathematicians of the past were... about the importance of finding the relevance of math... that math is everywhere such as cooking and sewing. I think the biggest thing I learned is that we can all do math but we need support and encouragement from others. I now know that there are no differences in the genes of females or Blacks which do not allow them to do math as well as other groups."
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