Volume 4 Number 2, May 1989


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ISGEm Advisory Board

Gloria Gilmer, President
Milwaukee, WI 53205

Ubiratan D'Ambrosio, Vice President
Universidade Estadual de Campinas

Gilbert J. Cuevas, Research Coordinator
University of Miami

Patrick Scott, Editor
University of New Mexico

Elisa Bonilla, Assistant Editor
Centro de Investigación del IPN

Claudia Zaslavsky, Secretary
New York, NY 10040 USA

Luis Ortiz Franco, Member-at-Large
Chapman College

David Davison
Eastern Montana University

Anna Grosgalvis, Treasurer
Milwaukee Public Schools

Sau-Lin Tsang, Research Coordinator
Southwest Center for Educational Equity

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ISGEm NEWS

Minutes of the meeting of the ISGEm in Orlando, Florida, as reported by Luis Ortiz-Franco.

The annual business meeting of the ISGEm was held on Thursday, April 13, 1989, during the Annual Meeting of the National Council of Teachers of Mathematics (NCTM). We saw some familiar faces and many new faces. The fact that there were many new people in the meeting is a sign that we are growing. The meeting was chaired by Dr. Gloria Gilmer and the agenda included the following items:

1. Kathy Layton from NCTM conveyed information to ISGEm regarding affiliation with NCTM and the benefits that accompany such a relationship. Some of those benefits are: consultant services available at no cost; national and regional representatives are available to affiliates; NCTM underwrites conferences, membership drives, and provides grants for special projects and mailing labels. NCTM can also provide assistance in incorporating without paying legal fees provided the constitution and by-laws of the group seeking affiliation contain a dissolution clause and a non-restrictive membership clause. The current draft's of ISGEM's constitution and by-laws do contain these clauses so it looks like we are a good position to proceed with affiliation with NCTM if we so desire.

2. Rick Scott, editor of the ISGEm Newsletter, reported on the newsletter and explained the process for submission of articles. He also outlined the four current foci of activities in Ethnomathematics and the respective coordinators: 1) Research in Culturally Diverse Environments (Luis ORtiz Franco, Coordinator); 2) Curriculum and Classroom Applications (David Davison, Coordinator); 3) Out of School Applications (Gloria Gilmer, Coordinator); and 4) Theoretical Perspectives (Ubiratan D'Ambrosio, Coordinator). These four foci will serve as the organizing nucleii for planning sessions and presentations at the next International Congress on Mathematics Education (ICME VII) to be held in Canada in 1992.

3. David Davison reported on the membership of ISGEm. He made an appeal for all members to stay current with their membership dues. He said that currently there are over 250 on our mailing list, representing countries from all continents of the globe. So, ISGEm is truly an international group. Please, everybody send in your membership dues.

4. Gloria Gilmer stated that ISGEm is looking toward establishing regional resource centers to house Ethnomathematics materials. So far this idea is in the planning stage and suggestions are welcomed to implement these plans.

5. Ubiratan D'Ambrosio made a short presentation covering the interdisciplinary literature related to Ethnomathematics. This presentation was particularly useful for new members present at the meeting.

6. The last item on the agenda asked the meeting participants to break up into four separate discussion groups organized around the four research areas in Ethnomathematics as outlined above. This proved to be an excellent idea for new members to get acquainted with other members of ISGEm. An additional benefit of this activity was that it offered an opportunity to discuss in more detail the particular interests of individual members and make tentative plans for organizing sessions at ICME VII.

The meeting ended when each of the four groups concluded their discussions.

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Research Presession at the NCTM 1989 Annual Meeting

reported by Luis Ortiz Franco

The Research Presession entitled "Ethnomathematics: Theoretical Foundations and Research Methodologies" was organized by Rick Scott and was held on Tuesday, April 11, 1989 From 1:00 PM to 5:00 PM. The panelists were Ubiratan D'Ambrosio, UNICAMP, Brazil; Pat Rogers, York University, Canada; Gloria Gilmer, Math-Tech Connection, USA; and Rick Scott, University of New Mexico, USA. The discussant was Luis Ortiz-Franco, Chapman College, USA.

D'Ambrosio offered na general survey of the literature from anthropology, psychology, mathematics education, history of mathematics and world history related to culture and mathematics (i.e. Ethnomathematics). The overall flavor of his presentation his philosophical perspective of Ethnomathematics for cultural affirmation.

Rick Scott attempted to define "Ethnomathematics" and outlined the different prevailing theoretical orientations in this emerging field of mathematics education. He identified three main, often related, currents in this field: 1) Ethnomathematics for cultural reaffirmation, 2) Ethnomathematics in the teaching of mathematics characterized by attempts to bring the world into the mathematics classroom, and 3) The study of mathematics of nonliterate peoples. According to Scott these three perspectives offer an opportunity for researchers to approach the investigation of the teaching and learning of mathematics from a multidisciplinary perspective that calls for the integration of qualitative and quantitative methodologies. At the same time, Scott acknowledged the difficulty of trying to arrive at a succinct definition of Ethnomathematics.

Pat Rogers described her experiences in trying to teach mathematics to university students in a way which empowers students in a social and academic sense. She observed that when teachers (professors) attempt to "share power" with students in the teaching-learning process they all search for ways to overcome the psycho-social effects of the dominant-dominated relationship in which teacher and students are accustomed to interact. According to Rogers, the dominant-dominated dialectical relationship between teacher and students impacts the way in which we represent knowledge in the classroom. The goal of empowering students and sharing power with students involves finding new ways to convey and represent knowledge in the classroom.

Gloria Gilmer commented on her observations in the teaching and learning of mathematics in the culture of the family among Blacks in Milwaukee, Wisconsin. Analysis of video taped interactions between children and parents engaged in processing technical information reveals a marked mismatch between family culture and the school mathematics curriculum, according to Dr. Gilmer.

Luis Ortiz-Franco offered a brief summary of the above discussions. He observed that the diversity of perspectives currently prevalent in Ethnomathematics are a sign of an exciting and healthy discipline with the mathematics education. He also remarked that the lack of a precise definition of Ethnomathematics should not deter scholars from engaging in the dialogue because the history of human is replete with examples of intellectual endeavors which have taken much time to define. He concluded by saying that in this respect we are in good company with our ancestors (i.e. this is Ethnomathematics as cultural reaffirmation in the broadest sense).

The presession was well attended (up to 25). The audience participated enthusiastically. They were given many opportunities to discuss the presentations in dyads, and to make comments and ask questions of the panelists.

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HAVE YOU SEEN

"Have You Seen" is a feature of the ISGEm Newsletter in which works related to Ethnomathematics can be reviewed. We encourage all those interested to contribute to this column. Contributions can be sent to:

Rick Scott, ISGEm Newsletter Editor
College of Education, University of New Mexico
Albuquerque, NM 87131 USA

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Ascher, Marcia (1988). Graphs in cultures (II): A study in Ethnomathematics, Archive for History of Exact Sciences, 39(1), 75-95.

Marcia Ascher discusses the interest among the Bushoong and Tschokwe of central Africa for the continuous tracing of figures. She gives some information on the cultural context in which this interest has arisen and flourishes, and demonstrates how geometrical and topological ideas are handled. She uses the formal terminology of Graph Theory to present the complex ideas of these peoples, but embeds her presentation in the cultural context so that their ideas will not be seen as "just a pale reflection of our own".

The Tshokwe appear to deal with more figures than the Bushoong, but only men draw the figures and apparently due to culturally disintegrating outside influences "it is primarily older men who are knowledgeable and proficient in drawing". Some of their drawings (called sona) are related to a rite of passage ceremony (mukanda) of boys into adulthood. One of the simplest, a simple closed curve that shows their topological interests, represents the camp where the rituals take place. The boys and their teachers are inside and the rest of the community is outside.

Ascher states that recognition of the mathematics of the curve tracing among these peoples is "of more than academic interest". It provides another Ethnomathematical example of how the notion of Gerdus of the importance of teaching African students through their own traditions and Zaslavsky's concern "with enlarging the cultural education of Western students of mathematics" can be achieved.

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Frankenstein, Marilyn (1989). Relearning Maths: A Different Third R -- Radical Maths, Free Association Press, 26 Freegrove Rd, London N7 9RQ.

Why do so many people have difficulty learning maths? 'Maths anxiety' describes a situation familiar to many students, but that term locates the problem in the failings of the learner. This textbook. Relearning Maths, breaks new ground by showing how prevalent teaching methods create the anxiety and other obstacles which can be overcome through different methods.

The text invites students to reflect on their maths work and feelings about it: through self-evaluation, evaluation of problems in the text, analysing error patterns and writing a maths journal (diary). Integrating maths knowledge with other disciplines, it encourages students to look for hidden messages in maths exercises: for example, totalling a grocery bill suggests that individual payment for food is the natural way for a society to organize food distribution. This text encourages students to become 'critical co-investigators in dialogue with the teacher' (as Paolo Freire described the relationship in Pedagogy of the Oppressed).

Focusing on maths anxiety, Part I analyses misconceptions that block learning. For example, many students feel that they must be 'slow' or 'thick' if they make a mistake, and that a wrong answer is completely wrong and useless. Students can overcome their anxiety by analysing error patterns for correct (as well as incorrect) reasoning and by discussing how to teach each other about their mistakes.

When faced with a maths problem, students often read it fast, pick out the numbers and perform any operation for the sake of 'doing something'. In Part II they learn not to do so, by first working on problems whose solution requires no operations. Students practice reading, understanding, comparing and rounding numbers -- before they solve any problems involving addition, subtraction, multiplication and division. In this way students learn to approach problems more slowly and carefully.

Relearning Maths is intended mainly for adults who feel they have little knowledge of maths. The book aims:

* to help people realize that they already know some maths and thus are capable of learning any maths they don't already know;

* to provide a survey of basic maths skills, filling in any gaps in students' familiarity;

* to transform people's maths anxiety into anger at a system that leads to the mathematical disempowerment of large numbers of adults;

* to help students to control their own learning; and

* to interest students in some enjoyable aspects of maths.

At a time when some political pressures threaten to narrow maths teaching to mere 'numeracy', this book provides an alternative approach: 'maths literacy', a comprehension of how numbers are selectively used to construct or conceal reality. It sets maths problems in the context of current issues around race, gender and class.

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The following was submitted by Luis Ortiz-Franco of Chapman College.

Saxe, Geoffrey B. (1988), "Candy Selling and Math Learning", Educational Researcher, 17(6), 14-21.

In this article offers evidence that children gain mathematical understanding in out-of-school contexts, but the mathematics may only on occasion resemble that of the classroom. He observed child candy sellers who live in an urban center in northeastern Brazil and noticed that these children construct fairly complex mathematical goals that emerge in practice and that take form in a web of such socio-cultural processes as inflating monetary systems, practice-linked conventions, and patterns of social interactions. He interviewed and administered some tasks to the subjects who ranged in age from 5 to 15 to contrast the mathematical understanding of unschooled sellers and nonsellers, to contrast the mathematics of unschooled sellers at different age levels, and to study the interplay of schooling and selling experience for those candy sellers who attended school. The tasks were designed to generate information on four general areas: 1) representation of large numerical values; 2) arithmetical manipulation of large values; 3) comparison of ratios; and 4) adjustment to inflation in wholesale to retail markups.

One finding was that children growing up in Brazil, with minimal education, regardless of selling experience, develop an understanding of the organization of the currency system to a sufficient extent to use it to represent and compare large numerical values. Another finding was that virtually none of the candy sellers used paper and pencil solution strategies to solve the addition, subtraction, and ratio problems that they confronted. However, young children typically avoid problems of ratio by selling their candy for only one ration (i.e. three candy bars for Cr$1000 bill) while older children sold their candy for more than one pricing ratio and did address ratio comparison problems in their practice. Two other finds are noteworthy: 1) sellers develop a mathematics that is adapted to the practice and, over time, manifest mathematical operations of increasing complexity and powers; and 2) sellers who attended school worked towards adjusting practice-linked regrouping strategies to solve school-linked mathematical problems.

The research reported above is a contribution to the literature on Ethnomathematics related to out-of-school applications and illustrates how the knowledge acquired in a cultural setting outside the classroom can benefit formal school work. Moreover, the results of the study support the notion that mathematical activity outside the school can sometimes be ahead of the formal school curriculum and yet the schools fail to reward that knowledge.

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Profile of COMUN

(reprinted from UME Trends)

Gloria Gilmer

Minority underrepresentation in the mathematical sciences is well-documented as a national problem and a growing concern within the profession. The need for a greater understanding of the nature of the problem and a comprehensive effort to correct it is addressed by the Committee on Opportunities in Mathematics for Underrepresented Minorities (COMUN) - a joint committee of The American Mathematical Society (AMS), The Mathematical Association of America (MAA) and The American Association for the Advancement of Science (AAS).

The charge to the committee is to inform the mathematical community of opportunities available or denied to minorities for the study of, or careers in, mathematics; and, to enlist their cooperation in increasing minority participation and leadership in all categories of mathematical activity.

This committee is a pin-off of the AMS Committee on Opportunities in Mathematics for Disadvantages Groups. The initiative to create a joint committee came from Gloria Gilmer and Lynn Steen in recognition of the fact that support will be needed from the entire professional community in order to reverse the underrepresentation of minorities in mathematics at all levels.

The first major objective of the joint committee is to bring to the attention of the nation what works and what does not work in getting more minorities to pursue studies in mathematics at more advanced levels. In this way, the committee hopes to influence the creation of more effective programs of instruction in mathematics for minorities.

The committee approached the Mathematical Sciences Education Board (MSEB) for support. Subsequently, MSEB obtained funding from the Exxon Foundation to undertake a series of regional workshops beginning in the spring of 1989 and culminating in the spring of 1990 in a Convocation at the National Academy of Sciences (NAS) in Washington, D.C. The MSEB project is called "Making Math Work for Minorities". The following cities are targeted for workshops: Atlanta, Philadelphia, Chicago, San Antonio, Seattle and Irvine. Additional information on these workshops may be obtained by writing to MSEB, 818 Constitution Avenue, N.W., Washington, D.C. 20006.

The joint committee is creating a minority directory. Minorities who wish to be listed in the directory should write to Sylvia Bozeman, Department of Mathematics, Spellman College, Atlanta, GA 30314.

The committee is also calling for papers on equity issues related to: preparation for college mathematics; access to study more advanced courses in mathematics; motivation and support systems; course content; instructional methods; the use of technology in instruction; student evaluation; and student/teacher interactions for inclusion in a publication. Papers may be sent to Gloria Gilmer, Math-Tech, Inc., 2001 West Vliet, Milwaukee, WI 53205.

The committee is chaired by Gloria Gilmer. Its members are Manuel Berriozabal, Sylvia Bozeman, Jim Donaldson, Rogers Newman, and CLarence Stephens. Argella Velez-Rodriguez of the U.S. Department of Education is an advisor to the committee and Shirley Malcolm of the Office of Opportunities of AAAS is an ex-Officio member.

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MEMBERS PROJECTS

On the ISGEm Membership Form we have asked people to "briefly describe any projects with which you are involved that are related to Ethnomathematics." Below we have reproduced a few of the responses with the name and address of person involved in order to encourage communication among individuals with similar interests:

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I hope that ethnomathematics will include mathematics used as tool to understand socio-economic- ecological problems. This is my interest - how mathematics can help to clarify local community issues (housing, garbage/toxic disposal, transportation, use of energy,...), global issues (ecology, use of global natural resources,...), as well as other controversial issues (evolution,...)

Joseph Fishman, 395 Riverside Dr, New York, NY 10025 USA

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I am based in Asia, and am in a good position to collect data on ethnomathematics in this region. If you know people who are interested in collaborating in research projects, I would be interested in assisting, especially if the projects were concerned with language in mathematics education.

Raymond A. Zepp, University of East Asia, P.O. Box 3001, MACAU

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Since we spoke I've been thinking some about the importance of math education for the U.S. and an anthropological approach to the subject. Although I am interested in mathematical type problems, my own formal education in the subject was generally abysmal; the only exception was a year spent in Germany where they taught math as something that you can think about and reason with, rather than something to memorize as a chore.

Ronald H. Berg, LASPAU, 25 Mt. Auburn St., Cambridge, MA 92138 USA

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I work with Northern Canada with Inuit children whose spatial and organizational view of the world often differs from my own rather middle-class Southern Canadian view. Logic and assumption vary, creating real frustrations within the elementary school environment as we press children to define their view within our own.

Jennifer Macpherson, Box 789, Iqaluit, Northwest Territories, XOA OHO CANADA

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This semester in conjunction with a college-wide project to integrate scholarship on gender, race, and class issues across curricula, I am compiling a bibliography of references on ethnomathematics. In particular, I am searching for important, recent scholarly (and pertinent popular) books and articles appropriate for inclusion in an annotated bibliography that is to be useful to colleagues for rethinking and revising courses to incorporate material and perspectives in ethnomathematics. As part of this effort, our library will become a repository for books and articles in the bibliography, relevant journals, and materials in media forms other than print.

Arthur B. Powell, Academic Foundations, Rutgers University, 175 University Ave., Newark, NJ 07102 USA

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Participant in Tri-County Math Project study group re minority issues in mathematics. Ethnographic research on Family Math programs with Hispanic and Hmong families. Research interest in Ethnomathematics and the Cambodian immigrant community in California.

Martha Allerant-Snider, 789 Laurel Walk Apt A, Goleta, CA 93117 USA

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Integrating Math with the Study of Cultural Traditions

(This paper was presented at the ICME VI)

Claudia Zaslavsky

In my talk today I will discuss the multiculturization of the mathematics curriculum, in particular at the elementary and middle grade level. Usually I include slides of beautiful works of art and architecture from many parts of the world and many eras in history. The audience is sure to be captivated by the photographs, if by nothing in my talk. Today there is no time for pictures, and I shall try to win you over with my talk.

All societies have developed mathematical practices appropriate to their daily lives and their cultures, an area of mathematics now known as "ethnomathematics." Yet very little information about these practices has entered the curriculum at any level.

Children tend to view mathematics as a cut-and-dried, esoteric subject that arose full-blown from the minds of a few white men in the past. Small wonder that many students seem to leave behind the mathematics classroom. It should be no surprise that many students find mathematics irrelevant, develop fears and anxiety about the subject, and drop it as soon as possible.

For many years I taught secondary level mathematics in a small school district near New York City, an oasis of integration in the midst of a racially segregated society. The population consisted of profession and other middle class families, mainly white, and working poor, predominantly black families. Known for racial integration of schools and housing, an unusual situation in the 1950s, the district attracted families looking for that environment, including several famous black figures.

Some of our educational practices were innovative for the time, and even for today. Although female students participated in academic mathematics course to the same extent as males, we had found that many of our students were dropping mathematics after fulfilling the minimum requirements. The majority of these dropouts were African-American and working class young people. With the federal funding that was available in the 1960s, several of us in the mathematics department wrote curriculum materials for all high school grades, incorporating hands-on activities and applications that were meaningful to the students. The curriculum included major topics in algebra and geometry, and at the same time afforded students the opportunity to improve their inadequate skills in arithmetic, with topics in statistics, for example. Some topics related to their social studies course, thus making both subjects more meaningful.

The turning point for me came when the district offered a course in African history to the faculty, in response to the growth of African-American interest in exploring their African roots. As my term project I chose to write an essay on the topic I called sociomathematics of Africa. This proved to be a far more ambitious undertaking than I had anticipated. Very little information was available in libraries in any country. Eventually I was able to gather enough material for a book, Africa Counts: Number and Pattern in African Culture [Zaslavsky 1973, 1979, 1984], still the only book of its kind, now available in hardcover and in paperback in English, and in a beautiful Hungarian edition. A tremendous contribution to the book came from University of Wisconsin professor D. W. Crowe, an early participant in the United States-sponsored group organized in the early sixties to fashion a modern mathematics curriculum for African countries. Dr. Crowe had amassed a wealth of mathematical materials based on indigenous African practices--house construction, games, repeated patterns in art, to mention a few. With typical cultural arrogance, the group rejected his contributions. Subsequently I was the fortunate recipient of these materials.

Several years later, E. G. Begle, Chair of the School Mathematics Study Group (SMSG), one of the most prominent and influential new mathematics programs in the United States, wrote [1969]:

The question arises as to what are the effects of the culture in which a student is brought up on his ability to learn and do mathematics. A related question is whether pedagogical procedures that are effective in one culture will be equally effective in another culture... I might also point out that the problem is not one in the United States alone. Many countries are asking for assistance in improving their mathematics education programs. Having looked into a number of attempts to honor these requests, I am convinced that failure to study the cultural milieu of the proposed reforms has often resulted in a serious waste of time, effort, and money.

When I was writing my book, I had in mind an American audience, and I used many of the themes with both teachers and students. But I was amazed and gratified to learn that African scholars were also interested in the book.

Mathematics educators in African and other developing countries now recognize the need to multiculturalize the mathematics curriculum [D'Ambrosio 1985, Gerdes 1985]. But the Third World exists even in the First World, certainly in the United States. Our cities house scores of different ethnic groups, each with its own culture. In the New York public schools are children speaking over fifty different languages, and in Los Angeles the variety is even greater. Black and Hispanic young people, particularly from low income families, take fewer mathematics courses and score far lower on standardized tests, than do white students, although they are just as capable. Witness the recent film "Stand and Deliver," the true story of Garfield High School in East Los Angeles, where more students take college-level calculus than in all but a half-dozen schools in the entire country. Almost 90% of these students are from low-income Hispanic families [Bennett 1987]. So it can happen! But we must find ways to appeal to a diversity of cultural backgrounds and learning styles, rather than to dismiss these students as incapable of learning.

The educational failure of ethnic minority children in the industrialized countries has persuaded some educators of the need to incorporate multicultural perspectives into the mathematics program [Bishop 1987]. Indeed, all children profit from such an expansion of the curriculum. Children learn that mathematical practices arose out of the real needs and desires of all societies. Mathematics comes alive when children study the measurement and numeration systems, the patterns in art and architecture, the games of skill and games of chance of various cultures. Students have the opportunity to learn about mathematical contributions of women and of Third World societies, a generally neglected area of mathematics. They can take pride in their own heritage, and at the same time become familiar with and learn to respect the cultures of other societies.

For the past fifteen years I have been conducting seminars and workshops for teachers on the theme: "Bring the world into the mathematics class" [Zaslavsky 1973, 1985, 1987]. The participants are encouraged to explore the mathematical practices of their own students' cultures, and to integrate these practices into the mathematics curriculum. Wherever feasible, they coordinate mathematics with other subject areas. They develop activities based on real life problems, activities that challenge students' curiosity and reasoning powers. Both teachers and students begin to realize their own power as they work together to organize classroom procedures, control the curriculum, and construct their knowledge.

I will relate a few typical outcomes at different age levels.

1. Language-minority children often feel inferior because of their inability to speak the language of the country. However, given the opportunity to count in their own language, to teach the number words to their classmates and even to the teacher, and perhaps to explain the structure of the numeration system, their self-esteem grows immeasurably.

2. In a session on the topic of mathematical probability, the participants (teachers) discussed the tossing of coins, dice, cowrie shells, half-shells of nuts, and other objects appropriate to various societies. After they had carried out experiments with some of these devices, a first grade teacher in the South Bronx, the poorest and most neglected area of New York City, decided to introduce the subject to her students. According to her plan, she would explain "head" and "tail" of a coin, then toss one coin, and so on. To her surprise, the children, with their streetwise experience, knew all about tossing coins, and entered enthusiastically into the activity.

3. A project dealing with the shape of a house [Zaslavsky, in press] involved finding the area of several different shapes, all having the same perimeter, by sketching the shapes on grid paper and counting squares enclosed by each shape. As an aftermath to this activity, one class, working in small groups, designed, constructed and decorated several African-style compounds of round houses with conical roofs. In the course of this activity they learned that a cylinder is a rectangle whose two opposite edges have been joined, and that a cone is a circle with a sector removed. Another class use rulers, tape measures, and lengths of string to find areas and perimeters of many objects in the classroom.

4. In response to a unit on African sand drawings, an aspect of graph theory, one ninth grade student commented: "I loved the fact that I got a chance to learn some of the math from a completely different country." Another said: "It showed that we shouldn't think our way of doing math is the only way there is." Ironically, the most talented mathematics student in that class wrote: "The traceable networks are nice for recreation, but they aren't real mathematics." To him, real mathematics meant the standard academic curriculum.

5. Several teachers of various grade levels are including mathematics in their study of apartheid in South Africa and racism in the United States [Zaslavsky 1986].

6. An Afro-American teacher wrote a paper about black children's exposure to number concepts through the illegal lottery known as the "numbers game." She described the use of probability, the skill of semi-literate people in recalling and recording numbers, and the system of hand gestures used when the police were on the scene. In conclusion she wrote: "Certainly if teachers could in some way use some of this number logic with the children, or at least recognize their familiarity with numbers when they meet them, perhaps number games based on Playing the Numbers might be substituted for the boring activities now presented to the children" [quoted in Zaslavsky 1975].

Many obstacles block the implementation of multicultural mathematics education, among them a dearth of materials. inadequate teacher training, and the mania for testing that grips the United States. The most daunting impediment is the conception of proper mathematics education held by some educators and school boards. As an example, one referee, in an evaluation of my article, "Symmetry in American Folk Art" [Zaslavsky, to appear], dealing with patterns in quilts and Navajo (Native American) rugs, both traditional women's art forms, crossed out, with no word of explanation, two complete paragraphs and many phrases. These passages dealt with affective aspects of these activities. Apparently this referee believes that students' attitudes to mathematics are of no consequence, that motivation plays no part in the learning of mathematics.

A further deterrent to enriching the mathematics curriculum came with the announcement of the results of the 1986 National Assessment of Educational Progress in mathematics. Commenting on the improvement in scores on basic skills, the president of the Educational Testing Service commented: "Thanks to the back-to-the-basics thrust, we've brought up the students who were at the bottom" [New York Times June 8, 1988:A1]. In other words, children have improved int heir ability to carry out computations, a task that can be performed more quickly and accurately by a calculator. At the same time, the test results showed little or no progress on higher-order reasoning abilities. We must continue to ask "What is mathematics education for?"

References

Bennett, W. J. (1987). James Madison High School: A Curriculum for American Students, Washington D.C.: U.S. Department of Education.

Bishop, A. (1987). The interaction of mathematics education with culture, Cultural Dynamics, 2.

D'Ambrosio, U. (1985). Sociocultural Bases of Mathematics Education, Campinas, Brazil: UNICAMP.

Gerdus, P. (1985). Conditions and strategies for emancipatory mathematics education in underdeveloped countries, For the Learning of Mathematics, 5, p. 15-20.

Zaslavsky, C. (1973). Africa COunts: Number and Pattern in African Culture, Boston: PWS Publishers.

Zaslavsky, C. (1975). What is math for?, Urban Review, 8, 232-240.

Zaslavsky, C. (1985). Bringing the world into the math class, Curriculum Review, 24(3), 63-65.

Zaslavsky, C. (1986). Using Mathematics to Learn about South Africa, Apartheid, and Racism, unpublished manuscript.

Zaslavsky, C. (1987). Math Comes Alive: Activities from Many Cultures, Portland, Maine: J. Weston Walch.

Zaslavsky, C. (in press). People who live in round houses, Arithmetic Teacher.

Zaslavsky, C. (to appear), Symmetry to American folk art, Arithmetic Teacher.

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