Volume 9 Number 2 July 1994
Minutes from the ISGEm Meeting in Indianapolis
Maria Reid, Recording Secretary
The meeting was called to order by President Gloria Gilmer at 4:40 p.m. at Convention Center, Room 143. The topic of the meeting was: "Mathematics in the Cultural Context."
1. Upcoming dialogue with some SIG groups.
2. The celebration of ISGEM's tenth anniversary in 1995.
3. Everyone is invited to contribute to a new publication on the following topics: Curriculum and Classroom Applications, Research in Culturally Diverse Environments, Theoretical Perspectives, and Out of School Applications.
4. Our electronic mail was discontinued from lack of use. Jim Barta volunteered to have it reinstated.
Report of Newsletter Editor
Rick Scott reported that the first newsletter will be sent out sometime in the Spring, and the other sometime in the Fall. Articles on Ethnomathematics are requested He announced the existence of a compilation of past ISGEM newsletter issues at ten dollars for members and fifteen dollars for non-members. He called for a volunteer to work with him.
Alverna Champion announced that any one who would like to pay dues ($10.00 yearly), may do so during the course of the meeting or by writing to the Treasurer, Anna Grosgalvis, 3830 N. Humboldt Blvd., Milwaukee, WI 53212 USA.
Gloria Gilmer stated that a membership committee is needed to launch a campaign to recruit new members. NCTM is willing to help us. There are approximately twenty distributions around the world. The committee will be responsible for obtaining a complete list.
ISGEm Tenth Anniversary
Anniversary issue of the newsletter is needed. A call is made for volunteers to select papers for the compendium with respect to research papers on Culturally Diverse Environments and Curriculum and Classroom Applications.
NCTM Delegate Report
Lawrence Shirley reported that our resolution, which was submitted to the NCTM Delegate Assembly, was passed with the support of other affiliated groups. The resolution stated that meetings of affiliated groups should be announced in the NCTM Program Bulletin.
Recommendations for Nominees
Recommendations for nominees are needed for:
1. NCTM Committees.
2. NCTM Board of Directors.
3. Candidates for ISGEM officers for 1996.
4. ISGEM Nominating Committee. Positions open for nomination are: President, First Vice President, Second Vice President, Third Vice President, Secretary, and Treasurer. Let us know if you are interested.
Research Pre-session Report
Ubiratan D'Ambrosio reported that the research pre-session was held on Tuesday, April 12, 1994. He said that the research in mathematics education with respect to ethnomathematics was good and solid. He commended Jo Anna on her research presentation at the pre-session.
Jolene Schillinger reported on the financial aspect of the association. Total Income from membership and compendium for the year January 1-December 31, 1993 was $1171.35. Total Expenses was $576.60. The Net Income for 1993 was $594.75, and the Total Bank Balance as of December 31, 1993 was $1802.33. The report was prepared by Anna Grosgalvis, Treasurer.
We would like a strong presence in Seville, Spain in 1996. In 1992, we had a Working Group and a Study Group. For 1996, we need to have our own identity. Ideas are needed. Suggestions for ICME 8, 1996 are:
1. A major speech by a well-known mathematician about Ethnomathematics.
2. A session on current research on Ethnomathematics.
3. Speakers from different countries on different aspects of Ethnomathematics.
4. Poster Sessions.
5. Inform Sunday Ajose of your interest to be on the program.
1. The Ninth InterAmerican Conference on Mathematics Education (IACME I) in Santiago de Chile, July 24-28, 1995. The Chair of the Committee is Eduardo Luna, Math Dept, Barry U, Miami Shores, FL, USA..
Speaker Clo Mingo
Clo Mingo of New Mexico Highlands University's Comprehensive Regional Center for Minorities spoke on "Anasazi-North American Indian Natives." She entitled the presentation Historic Spirals and actively involved participants in an exploration of spirals with various manipulative materials and graphing calculators relating it to spirals found in Anasazi ruins in Chaco Canyon.
There being no further business, the meeting was adjourned at 6:30 p.m.
ISGEm Research Pre-Session in Indianapolis:
Connecting Math Practice In and Out of School
What does mathematics practice in everyday situations have to do with teaching anti learning mathematics In the classroom? This question generated quite a discussion at the ISGEm Research Pre-Session in lndianapolis. A study of mathematics practices of carpet layer estimators and installers, a dietician* an interior designer, a retailer, and a restaurant manager were compared and contrasted with corresponding practices of secondary school students working in pairs. Panelists noted that unlike problem solving in-school (1) problems for practitioners are embedded in familiar settings; (2) practitioners use mathematics as a tool; (3) practitioners are driven by a dilemma; (4) the problem solving process for practitioners is goal - directed; and, (5) practitioners use greater flexibility in dealing with constraints.
A problem posed to a restaurant manager was to change a recipe for six servings to one for 20 servings. "Her goal appeared to be to decide the amount of each ingredient needed and give instructions for the cooks - while being efficient." She decided to make enough fruit for 24 portions and divide the remaining four portions among the 20 cups. When asked to change the recipe for exactly 20 portions, she divided 20 by 6 on her calculator and used the resulting factor 3.3 to increase each ingredient. To make the recipe feasible for the cooks, she changed each decimal into a proper fraction and noted that they only work with halves, thirds and fourths. Thus for example, 2 cups of apples became 6.6 cups but six and a half cups would actually be used.
A pair of second year high school students in a geometry course were asked to change the same recipe for ten servings. They first saw the problem as using proportions to find the increased amounts but then realized that they could solve the problem less formally in an out-of-school context. Thus they made the salad for 12 by doubling everything and divided the two extra portions among the ten people.
In the discussion it was pointed out that in the classroom real life problems are not used and more exact solutions are required than in real life. Frank Lester, a discussant, felt that students in the study did quite well in view of the differences in motivation and problem familiarity between them and practitioners.
A model for connecting everyday anti school mathematics was presented. Panelists felt that many differences in mathematics learning and practice, in anti out of school, can be narrowed by creating experiences that engage students in doing mathematics in school in ways similar to mathematics learning and practice outside of school, Teachers can also guide students in reflecting on how in-school learning and practice are used out of school. Teachers should engage student in conversation, listen to them and encourage and observe their informal methods of mathematizing in order to learn more about students' prior understandings. In school activities should make use of cultural artifacts and conventions that students can use to interpret problems and make sense of them. Finally, students should also be encouraged to generate conventions that may be helpful to them in accomplishing their goals.
The session was organized by Joanna Masingila. The panelists were: Joanna Masingila, Susana Davidenko, and Ewa Prus-Wisniowska of Syracuse University. The discussants were Frank. Lester of Indiana University - Bloomington and Ubiratan D'Ambrosio, vice president of ISGEm. Gloria Gilmer, president of ISGEm presided over the session.
ISGEm Organizing Joint Committee on Math and Culture
In Indianapolis, ISGEm convened a meeting to form a joint committee of NCTM affiliates to address issues on math and its cultural contexts. Interested members of the Bannaker Association and the International Study Group on the Relations Between History & Pedagogy of Mathe-matics also attended this meeting. The rationale for considering the cultural context of math in the classroom is to build directly upon: (a) what students in the classroom are willing to invest time in learning; (b) how students learn in the classroom; and, (c) how classroom teachers can assess when learning has actually occurred.
The group discussed the multicultural movement in education today and the variety of ways mathematics and culture are being connected in the classroom. It was felt that the effects on mathematics interest and achievement among culturally different learners will be minimal unless real differences in students are addressed in the classroom. For example, it was emphasized that the curriculum must include content in which students dominate. To do this, much work must be done to know the students we teach!
The meeting was attended by: Gloria Gilmer, Alverna Champion, Beatrice Lumpkin, Erica Voolich, Sunday Ajose, Lawrence Shirley, Jolene Schillinger, Margery Fels Palmer, Karen Michalowicz, Claudia Zaslavsky, Felix Browder and Ubiratan D'Ambrosio. Others interested in joining this group should contact Gloria Gilmer.
2nd Iberoamerican Math Ed Congress Held in Brazil with Much Ethnomath
The Second Ibero-American Congress on Mathematics Education (II CIBEM) was held in Blumenau, Brazil, from July 17 to 22, 1994. Discussions of Ethnomathematics played an important part in the Congress. In a Round Table discussion on Ibero-America in the International Mathematics Education Scene Claude Gaulin of Canada pointed out that one of the areas in which Ibero-America has made important original contributions in mathematics education is specifically in Ethnomathematics.
A Work Session on Mathematics Education, Ethnomathematics and Social Movements meet on each of three days of the Conference. It was coordinated by Geraldo Pompeu Jr. from Brazil, Gelsa Knijnik from Brazil, Isabel Soto of Chile, Marcelo Borba of Brazil, and Marilyn Frankenstein from the USA.
One of the keynote addresses was on Ethnomathematics - Phenomenological Didactics - School by Isabel Soto of Chile.
Among the other presentations related to Ethno-mathematics were The Relationship between School Mathematics and Daily Mathematics from a Historico-Social Perspective by José Roberto Boettger Jardinetti of Brazil, Popular Knowledge and Academic Knowledge in the Fight for Ground: An Ethnomathematical Approach and Culture, Education and Mathematics in the Fight for Ground by Gelsa Knijnik of Brazil, Ethnomathematics and the Classroom by Geraldo Pompeu Jr. of Brazil, Multicultural Mathematics in the Preparation of Teachers by Fernando Castro of Venezuela.
Another Definition of Ethnomathematics?
One of the often stated objectives of this Newsletter is to carry on a dialogue concerning Just What Is Ethnomathematics. It began in the very first issue back in 1985. It has been fruitful eno ugh to spawn an article in the first issue of A Educação Matemática, the official journal of the Brazilian Society of Mathematics Education. In the article, "Ethnomathematics: A Search for a Conceptualization in the Course of the ISGEm Newsletter" Maria Queiroga Amoroso Anastacio suggests that "Certainly it cannot be said that the discussion of the conceptualization of Ethnomathematics has been exhausted by the ISGEm Newsletter. To encourage further discussion the following definition by Geraldo Pompeu, Jr. of the Pontificia Universidade Católica de Campinas, Brazil, is presented:
Ethnomathematics refers to any form of cultural knowledge or social activity characteristic of a social and/or cultural group, that can be recognized by other groups such as "Western" anthropologists, but not necessarily by the group of origin, as mathematical knowledge or mathematical activity.
How Students Can Own Mathematics: Three Tales
James V. Rauff
There is no greater joy in teaching than that we experience when our students make a mathematical idea or result their own. I hope that the following true stories will convey some of the joy that I experienced when my students took ownership of some small corners of mathematics. The students whose stories I relate were eighth and ninth grade African-Americans participating in a summer enrichment program.1
First Tale: Clayton's Theorem
One morning I presented my class with a collection of connected graphs and asked them to reproduce each graph by starting at a vertex of their choice, ending at that same vertex, and without tracing over any line twice.2 They split into groups and began working on the patterns. Before long they were engaged in a spirited competition to be the first to "solve" each pattern. The one pattern I had included which was impossible to trace (although they did not know it was impossible) caused a great deal of difficulty for all of them. Finally, after about ten minutes of invalid solutions, Clayton3 exclaimed, "you can't do this one!" A student from another group retorted, "Maybe you guys can't, but we will!" Clayton's response silenced the room. "No, I mean nobody can," he said, "Not you, not me, not even Dr. Rauff. It is impossible because one of the corners is a dead end."
I tried to remain as non-committal as possible even though I could see that Clayton had discovered Euler's result. "Show us why it can't be done," I asked. Clayton went to the board and pointed to a vertex of degree 3. He said, "If you start tracing here then you've got to leave on one of these lines and come back on another. But then you've got to leave again on this one (the third one). Now you've got no way to come back to where you started." Joyce objected, "But you can start somewhere else." Clayton had considered that possibility. "If you do then you've got to come into this point on one line, go out on another, and then when you come in again you're stuck. It's a dead end."
After Clayton had successfully fended off several more objections, the class collectively arrived at a generalization. They all examined it over night, and the next day refined it some more. Finally, they c reated a cogent proof of
Clayton's Theorem. You can't trace the pattern if any dot has an odd number of lines going into it.
Second Tale: The Turns of Yvonne and Serena
I had spent a few days showing each student how to use the software package DERIVE to graph functions. The day after they had some time to "play" with the package, I gave them all a list of polynomials (degrees 1 to 10), none of which had complex roots. I asked them to graph these polynomials and tell me about them. I was hoping that they would discover the relationship between the degree at the polynomial and the number of its roots. The class period wore on and nothing was happening. Just as I was about to give some very helpful hints, Serena announced, "We've got it."4 "Got what?" I asked. The turns, " she said, "You can tell about the turns from the biggest power on x."
I wrote down an eighth degree polynomial and gave it to Yvonne (Serena's partner).
"How many turns?" I asked. Yvonne answered cautiously, "Seven." By now, the other groups were watching us. So, I gave the polynomial to another group to graph. We all huddled around the computer screen while the polynomial was entered. Then came the graph. We couldn't see it all. They changed the scale. There in living color was a curve with seven turning points- Yvonne and Serena were heroes.
I asked Serena to explain how she deduced her result. Her explanation was elegant. "Every graph crosses the x-axis the same number of times as the highest power at x," she said. So, for like 8, you've got to cro ss 8 times. But, if you start above and cross 8 times then you've got to turn around 7 times." Serena and Yvonne had not only deduced the fundamental theorem of algebra, but, considering it of only incidental importance, went on to develop the theorem about turning points.
Third Tale: The Snows of Summer
It was a beautiful summer's morning. In the classroom we were going through the motions of discussing some detail of the theory of equations I looked out the window at the network of sidewalks overlaying the campus. "That will be a lot of snow shoveling in the winter," I said. "Yeah," said Clayton, "Just like those tracings we did before." "But," Anita added, "You don't need to shovel them all. Just enough to get to each building." Eager to get away from the topic at hand, they all jumped into the problem of shoveling the walks. The whole class was at the window. Anita was drawing maps on the board. The rest of the morning and the next several days were devoted to the problem of Hamiltonian circuits and related problems. My students developed the theory, discovered essential differences between Euler and Hamiltonian circuits, and created questions and conjectures on minimal paths. It was a beautiful stimulating discussion on some real mathematics that the students had discovered a need for without any direction on my part.
Students that empower themselves mathematically see the beauty of mathematics. They are motivated by their own curiosity. They create concepts and results. They develop logical arguments and vivid examples. Best of all, they come to share the exhilaration of mathematical discovery.
1. The principal's scholars program is jointly sponsored by Millikin University and the University of Illinois with
substantial financial assistance from corporate and private donors.
2. The search for, and creation of, patterns that possess Euler circuits is found in many nonwestern cultures. (see Marcia Ascher's wonderful discussion in her book Ethnomathematics: A MulticulturaI View of Mathematics (Wadsworth, 1991).
3. 1 have not used the real names of the students in this article.
4. It has always amazed me that students will invariably view an activity as a puzzle.
Adults Learning Mathematics - ALM Founding Conference
A research forum to be called Adults Learning Mathematics (ALM) had its Founding Conference and Annual General Meeting at Fircroft Adult College in Birmingham, England, from July 22 - 24. The conference was promoted as a unique opportunity to identify research issues, share your research experience, hear about research in progress, find out how to get published and become a founding member of ALM. For further information contact:
Centre for Mathematics Education
Sheffield Hallam University
25 Broomgrove Road
Sheffield, S10 2NA, ENGLAND
Ethnomathematics: Curricula Discussed in Indianapolis
At the Indianapolis meeting, several ISGEm members gathered in the ISGEm suite prior to the General Meeting. The original purpose was a meeting of the Special Interest Group on Curriculum and Classroom Activities, coordinated by Lawrence Shirley. The session began with reports of new publications and curriculum materials of interest. This was followed by open discussion of issues of concern to ISGEm and its members. This is an attempt to report on some of the news and ideas discussed.
Macmillan/McGraw-Hill's text series Mathematics in Action features multicultural activities used to introduce the mathematics of each chapter while promoting the contributions of all cultures to mathematics. The Mimosa publishing company has introduced a set of "big books" for K-3, which include large teacher copies to show to a group and smaller copies for the students. The title of the set is Mathematics from Many Cultures, and it features examples from Native American, Chinese, Incan, Islamic, African, and other cultures, often drawing similar applications and examples from several different cultures. Multicultural Mathematics, by David Nelson, George Gheverghese Joseph, and Julian Williams, was published in the UK but is available in the US. It discusses a rationale for a multicultural approach to mathematics, thoughts on instruction and curriculum, and many practical ideas for teachers. This is not a school text, but valuable reading for teachers or possibly for methodology classes.
It was announced that a comprehensive annotated bibliography of multicultural and gender issues in mathematics and science is available free of charge. Write to Patricia Wilson, University of Georgia, 105 Aderhold Hall, Athens GA 30602. Also, James and Sheri Banks of the University of Washington are editors of a Handbook of Research in Multicultural Education. It is published by Macmillan.
Two other recent publications were also mentioned, but without publication data. While not directly on ethnomathematics, they are related and relevant to Ethnomathematical teaching. They are: Affirming Dive rsity, by Sonia Nieto, and Africanisms in American Culture, by J.A. Holloway.
Finally, it was noted that the 1995 NCTM Yearbook is on Mathematical Connections, and will include an article on Ethnomathematical connections by Lawrence Shirley. Perhaps even more connected to ISGEm will be the 1997 NCTM Yearbook, so far untitled but on the topic of culture and gender issue in mathematics education. Perhaps some ISGEm members will be contributors to that volume.
Norma Presmeg described a graduate-level education course specifically on Ethnomathematics that she is trying to get started at Florida State University. Write to her for copies of her proposed syllabus. Address: Mathematics Education Box 3032, Florida State University, Tallahassee FL 32306-3032 or you can use e-mail to email@example.com. Similarly, Timothy Craine is developing a course called "Math in Diverse Cultures" at Central Connecticut State University. His address is 34 Chestnut Drive, Windsor CT 06095 or e-mail firstname.lastname@example.org.
The meeting continued with wide-ranging discussion on the need to celebrate diversity and at the same time bring us all together. Questions arose about how much to emphasize differences, especially with concern to be careful about potential stereotyping. Can the many contributions of various cultures to mathematics become stepping stones for mutual understanding?_______________________________
Ethnomathematics Curriculum at the College Level: a Query
Towson State University
Many of us who work in ethnomathematics have been concentrating our curricular efforts on work to use Ethnomathematics in the K-12 curriculum. We have found examples from various parts of the world and various occupational groups and other "cultures" which we can fit into the math programs of elementary and middle schools, and sometimes also high school math. However, at the higher levels of math, from the advanced high school courses into those of universities, it may seem trivial to look at non-standard counting systems or unusual measurement units. We are looking for examples appropriate to the level of the content. In my own case, I teach math education and history of math at a university. I have been fairly successful at incorporating Ethnomathematical curricula into elementary methods courses and even better at looking at Ethnomathematical themes in the history of mathematics.
However, I serve on a university committee that hopes to "multiculturalize" the curriculum across all fields and all departments of the university. Note that this effort is separate from other university efforts at recruitment and retention of minorities. The purpose is to broaden the cultural understanding of all the students.
The university's campaign has actually gone quite well in the departments of history, geography, political science, English, art, and music. However, scientists and mathematicians find it harder to "multiculturalize". When I talk to my mathematician colleagues, they ask, "What is there about partial differential equations or group theory that can be multicultural? Isn't mathematics universal??"
There are some answers to this challenge. George Joseph's The Crest of the Peacock: Non-European Roots of Mathematics includes some good discussion of the high level mathematics done by the classical Chinese and Indian civilizations. They used some mathematical ideas such as the binomial theorem and the solution of systems of equations by matrices several hundred years before these ideas emerged in Europe. Similarly, Marcia Ascher's book, Ethnomathematics includes interesting examples of higher mathematics in kinship structures, the Tchokwe drawings, and others. Elsewhere in this newsletter are reports of specific ethnomathematics courses for university students. All of these are valuable, but still do not quite answer the queries of the mathematicians.
Another way of approaching the problem is to note that, following the ideas of Alan Bishop, mathematics arises from the social and cultural activities of all societies. Thus, we should be able to find examples of applications of mathematics, perhaps even from the higher levels of math. However, actually finding usable examples for the classroom remains difficult.
I am now trying to make a collection of any multicultural examples I can find for classes of calculus, discrete math, abstract algebra, differential equations, probability and statistics, and other university level mathematics. Any ideas to help me? Any general thoughts on this problem? If so, please contact me: Lawrence Shirley, Department of Mathematics, Towson State University, Towson MD 21204-7097 or use e-mail to email@example.com. Thanks.
Brazilian Society of Math Education Dedicates First Journal to Ethnomath
The Brazilian Society of Mathematics Education (Sociedade Brasileira de Educação Matemática launched its journal, A Educação Matemática, with a theme issue on Ethnomathematics. The articles published were Ethnomathematics: A Program (Etnomatemática: Um Programa) by Ubiratan D'Ambrosio, Citizenship and Mathematics Education (Cidadania e Educação Matemática) by Eduardo Sebastiani Ferreira, The "Real World" and the Day-to-Day Teaching of Mathematics (O "Mundo-Real" e o Dia-a-Dia no Ensino de Matemática by Luciano Meira, Popular Knowledge and Academic Knowledge in a Fight for Ground (O Saber Popular e o Saber Académico na Luta pela Terra) by Gelsa Knijnik, Ethnomathematics and the Culture of the Classroom (Etnomatemática e a Cultura da Sala de Aula) by Marcelo Borba. The issue also included two summaries. One was entitled Ethnomathematics: A Search for a Conceptualization in the Course of the ISGEm Newsletters (Etnomatemática: a busca de uma conceituração ao longo dos Boletins do ISGEm) by Maria Queiroga Amoroso Anastacio. The other, by Maria Beatriz Ferreira Leite, is a summary of Geraldo Pompeu Jr.'s doctoral dissertation entitled Designing Ethnomathematics for the School Curriculum: An Investigation of Attitudes of Teachers and the Learning of Students (Trazendo a Etnomatemática para o Currículo Escolar: uma Investigação das Atitudes dos Profesores e da Aprendizagem dos Alunos). The issue ends with summaries of Brazilian theses with an Ethnomathematical perspective.
If you would like a copy of this first issue of A Educação Matemática send $5 to Nelson Hein, SBEM - FURB, Rua Braz Wonka 238, Bairro Vila Novo, CP 1507, CEP 89010-971, Blumenau, SC, BRAZIL.
Have You Seen
"Have You Seen" is a regular feature of the ISGEm Newsletter in which works related to Ethnomathematics can be reviewed. We encourage all those interested to contribute to this column.
Appelbaum, Peter M. Popular Culture, Educational Discourse, and Mathematics, State University of New York Press,
This book (due for release in January of 1995) will analyze contemporary education discourse, using sources ranging from academic scholarship to papular magazines, music video, film and television game shows. Mathematics is used as an "extreme case," since it is a discipline so easily accepted as separable from politics, ethics or the social construction of knowledge. Appelbaum's juxtaposition of popular culture, public debate and professional practice enables an examination of the production and mediation of "common sense" distinctions between school mathematics and the world outside of schools. Terrain ordinarily displaced or excluded by traditional education literature becomes the pendulum for a new conversation which merges research and practice while discarding pre-conceived categories of understanding.
The book also serves as an introduction to emerging theories in cultural studies, progressively illustrating the uses of discourse analysis for comprehending ideology, the implications of power/knowledge links, professional practice as a technology of power, and curriculum as at once commodities and cultural resources. In this way, Appelbaum reveals a direction for teachers, students and researchers to form cooperatively a community attentive to the politics of curriculum and popular culture.
A History of Mathematics, an Introduction, by Victor J. Katz. Published by Harper Collins College Publishers, 10 E. 53rd St., New York, N.Y. 10022. 800 pages, hard cover.
This textbook for a college course in the history of mathematics lives up to its opening promise: "A special effort has been made to consider mathematics developed in parts of the world other than Europe." The multicultural material in the book is extensive and presented in a form that is readily available to classroom teachers or undergraduate mathematics majors. A clear writing style and a layout which does not shun white space combine for a very readable product.
A special feature of the book makes it a pleasure to just turn the pages and admire the historic postage stamps which honor great mathematicians around the world. Organization of the content by mathematical topic as well as time periods makes it easier to grasp the sequential development of concepts, also connections to social history. Enough detail is given to allow complete statements of the mathematical principles. The author takes little for granted, and restates the mathematical results in case the reader's memory needs refreshing. This wise practice made the book more interesting and valuable for this reader. Also valuable are the problem sets at the back of each chapter which include problems from original sources. It is interesting to see how far back many of our algebra "word problems" date.
Members of ISGEm will welcome recognition of ethnomathematics as a subject worth special mention in A History of Mathematics. Although only 12 pages of an 800-page book, and called an "interchapter?" rather than a chapter, the section ends with the stirring statement that 'mathematics was, and is, a force in the lives of people in all parts of the globe.". The high quality of this small sample of ethnomathematics makes a strong argument for expanded, regular chapters of ethnomathematics, including extensive problem sections. Included in this interchapter is a very significant Maya painting from a ceramic vessel. Katz informs us that the woman scribe shown in the painting was identified as a mathematician by Michael Closs because a number scroll is under her arm. There are only 1 1/4 pages on Africa.
The three chapters on Medieval Mathematics are strong and contain some material not readily available elsewhere. The chapters on Medieval China and India and the Mathematics of Islam supply multicultural material for much of high school mathematics. The mathematical development is often shown in connection with the "real world" of its time. For example Katz asks why mathematicians in Southern India developed the "Gregory" series for arctangent, 200 years before Gregory. The stimulus came from astronomy, Katz believes. In fact until the modern period, astronomers were mathematicians and vice versa.
On the relationship between Greece and Egypt, Katz tends to stick to what Martin Bernal calls "the Aryan model." This reviewer prefers Struik' s analysis: "The ancient civilization of the Near East never disappeared despite all Hellenistic influence. Both Oriental and Greek influences are clearly revealed in the science of Alexandria (69 Concise History). The "Aryan model" as Bernal called the European re-writing of history, ends all development of Egyptian mathematics and astronomy with the Greek-Macedonian conquest of Egypt. For example, the work of Diophantus of Alexandria, Egypt is described by Katz as "the only example of a genuinely algebraic work surviving from ancient Greece" (172.) Alexandrian mathematics is presented as purely Greek, rather than a fusion of the newer Greek and the older Egyptian and Babylonian.
Katz does open chapter 2 on the "Beginning of Mathematics in Greece," with a quotation from Proclus, that "Thales was the first to go to Egypt and bring back to Greece this study (geometry) " We are told that Plato visited Egypt, and Pythagoras "spent much time in Egypt... also in Babylonia." Archimedes and Appolonius are also reported to have studied and worked in Egypt. The text clearly states that Euclid, Ptolemy, Hero, Diophantus, Pappus, Hypatia were all of Alexandria, Egypt. Many other scholars of this period worked in Asia.
As a relatively complete "History," the book provides much useful information on the mathematics of the 'Hellenistic" period. The task remains for the teacher to use this material in a way that steers clear of Eurocentric bias. it takes nothing away from the important Greek contribution to acknowledge its roots in Egypt and Babylonia, and to acknowledge all the international roots of mathematics, including the contributions of Africa, Asia and the Americas. This is not an easy task, given the centuries of white racism used to justify slavery and imperialism. Teachers will find much useful material in Katz' valuable book to help them carry out this task. (Beatrice Lumpkin)
Zaslavsky, Claudia. Fear of Math: How to Get Over It and Get On with Your Life!, Rutgers University Press, 1994. 800-446-9323, paper $14.95 (0-8135-2099-8), cloth $37.00 (0-8135-2090-8)
In Fear of Math Claudia Zaslavsky sets out to explode the myth that women and minorities are not "good at math". She presents a "math that you really need in life" that is quite different from school math. Not only does her book provide a host of reassuring method for solving real-world math problems (many of which may be important in various careers), it also presents the testimony of many individuals who have overcome their own math anxiety.
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ISGEm Executive Board
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Math Tech, Inc.
9155 North 70 Street
Milwaukee, Wl 53223 USA
Ubi D'Ambrosio, 1st Vice President
Rua Peixoto Gomide 1772 ap. 83
01409-002 São Paulo, SP BRAZIL
Alverna Champion, 2nd Vice President
4335-I Timber Ridge Trail
Wyoming, MI 49509 USA
Luis Ortiz-Franco, 3rd Vice President
Dept of Math, Chapman University
Orange, CA 92666 USA
Maria Reid, Secretary
145-49 225th Stnue #13-1
Rosedale, NY 11413 USA
Anna Grosgalvis, Treasurer
Milwaukee Public Schools
3830 N. Humboldt Blvd.
Milwaukee, WI 53212 USA
Patrick (Rick) Scott, Editor
College of Education, U of New Mexico
Albuquerque, NM 87131 USA
Henry A. Gore, Program Assistant
Dept of Mathematics, Morehouse College
Atlanta, GA 30314 USA
David K. Mtetwa, Member-at-Large
14 Gotley Close
Marlborough, Harare, ZIMBABWE
Lawrence Shirley, Member-at-Large
Dept of Mathematics, Towson State U
Towson, MD 21204-7079 USA