Volume 6 Number 1

November 1990

ISGEm News
NCIM Directors Approve ISGEm for Affiliation
At its September meeting, the NCTM Board of Directors approved ISGEm's application to be an affiliate of NCTM!

'ISGEm Business and Program Meeting In New Orleans
Plan to attend the ISGEm business and program meeting in New Orleans in connection with the 69th Annual Meeting of the National Council of Teachers of Mathematics of the USA. The meeting is scheduled for Thursday. April 18,1991, from 4:30 to 6:30 p.m. Please check your NCTM program booklet for the room number. The program will include a presentation by Lawrence Shirley of the University of Maryland on "Video Games" in the USA and a report by Beatriz D'Ambrosio of the University of Delaware on her trip to Guidea-Bissau to develop curriculum for UNESCO.

€ISGEm Advisory Board Meeting In New Orleans
The ISGEm Advisory Board will meet in New Orleans on Wednesday, April 17,10 am. to noon, and again on Friday, April 19, from 10 am. to noon. Additional details about these meetings will be mailed.

€ISGEm Research Pre-Session in New Orleans
Patrick Scott, editor of the ISGEm Newsletter, has organized a Research Pre-Session in New Orleans. Arthur Powell of Rutgers University and Marilyn Frankenstein of the University of Massachusetts will introduce ideas on how concepts and practices from Critical Fducation Theory, attributable to Paolo Freire and others, connect with and extend our conception of ethnomathematics.

Jerome Turner of St. Francis Xavier University will offer suggestions on how Complimentarity, adapted from work in physics by Neils Bohr, can serve as a theoretical structure for work in ethnomathematics.

The session is scheduled as a work session on Tuesday, April 16. Please check your program booklet for the exact time and place.

€ISGEm Talks In New Orleans on Ethnomathematics and Games Children Play Around the World
Watch your NCTM program booklet for three talks sponsored by ISGEm on Ethnomathematics and Games Children Play Around the World. From 2 to 2:30p.m. on Wednesday, April 17, Jerome Turner will speak on Bhutanese Games. From 2 to 2:30 pm. on Friday, April 19, Claudia Zaslavsky will speak on Three in a Row Games. On Saturday, from 9:30 to 10a.m. Alverna Champion will speak on Games of African Childran. Also look for the Friday session from 9:30 to 10a.m. at which David Davison will speak on Manipulatives and Writings.

Critical Math Network Convenes at Cornell
by Paul Ernest
University of Exeter, United Kingdom
This was a small and friendly but high-level conference at Cornell University, New York, organized by Marilyn Frankenstein, Arthur Powell and John Volmink (with Marty Hoffman). The conference brought together an international collection of scholars from the occupied West Bank, Australia, Tanzania, Great Britain, South Africa, Braitil and the United States.
The format was deliberately informal and dialogical. There were no formal papers, only brief presentations and extensive discussion and debate. The conference considered three broad themes which are repinted below with the associated questions, because of their wider significance.
I. Epistemology and Philosophy of Critical Mathematics Education: How do we see mathematics knowledge itself as problematic? What are the origins of mathematical knowledge? Whose knowledge is it and in whose interest? What meaning does that have for people? For social change? How do we deal with conflicts/contradictions in knowledge?
II. Mathematics In Its Cultural Context: How will we reconceptualize mathematics to incorporate non-Eurocentric viewed and include the historiography of how and why the Eurocentric view became "standard?" How can we begin to speak about mathematics that we cannot recognize through Eurocentric Eyes? What are the effects of culture, language and ideology on the mathematics people develop?
III. Political, Economic and Social Issues in Mathematics Education: How is mathematics knowledge used to understand or obscure political, economic and social issues? What is the relationship between mathematics knowledge and power? What is emancipatory mathematics knowledge? What does it mean to empower students? What are the differences between awareness and indoctrination?
From my perspective, a number of important issues arose and were discussed at length.
(1) The philosophy of mathematics; the need for a radical view of mathematics as a social phenomenon -- not an absolutist body of incorrigible knowledge-- to provide a foundation for a view of mathematics as created by learners and indeed by all peoples.
(2) The nature of ethnomathematics -- is it the study of the mathematical ideas of non-literate peoples, or does it include all socially situated mathematical practices and activities beyond the formal academic discipline of mathematics? In my view, it is the latter, so as to be fully consistent with (1).
(3) Cultural imperialism, Racism and Mathematics. Both Eurocentric histories of mathematics, and the dominance of white academic western mathematics (with the concomitant invalidation of all else) is nothing but cultural imperialism and racist. School practices, whether overt or covert, which reproduce the disadvantages of ethrLic minority students are also racist.
(4) Critical mathematics education. We discussed what this is and practical means of implementing it (not forgetting the powerful reactionary forces it will arouse). Aspects include respect for the learner, aims of intellectual and social empowerment, and critical engagement with social issues and received structures of knowledge and society.
(5) Support for critical math educators. We explored the means of supporting each other personally, via networks, and by the circulation of materials. We also explored the means to further critical mathematics education by publication, the dissemination of exemplary materials and the development of its theoretical basis.
In my view, conference participants left feeling recharged, and ready to do battle with the dragons of reaction, once again.

A Multicultural Mathematics Curriculum
By Beatrice Lumpkin
Chicago, Illinois
Illinois has joined a growing number of states that have mandated the inclusion of multicultural components throughout the public school curriculum, including mathematics. In response, the Bureau of Mathematics of the Chicago Board of Education Curriculum Department has made substantial additions to curriculum materials, beginning with the systemwide objectives.
For each grade level K to 12, the state has grouped specific objectives for mathematics achievement under seven State Goals. Fach group of objectives is introduced with a paragraph citing some multicultural contributions to mathematics. The content varies with grade level and subject. For example, "Measurement" objectives for Algebra I are introduced by:
Students should be able to relate the origin of measurement to real-life situations. For example, the building of the African pyramids required extremely accurate measurement to construct right angles in the base so that any error would be less than one part in 27,000 or 1/ 27000. The unit of measure was the cubit, the length of an early pharaoh's forearm. The idea of a 24-hour day-- 12 hours of day and 12 hours of night--originated in Egypt. The Babylonians of Mesopotamia established the time measures of 60 seconds to 1 minute and 60 minutes to 1 hour. They also created the angle measures of 60 seconds to 1 minute and 60 minutes to 1 degree. Native Americans, especially the Inca, Maya, and Aztec, developed a system of measurement that was so accurate that they were able to lay out miles of direct highways across high mountains and rugged terrain. The Ashanti of Ghana used standard gold weights to calibrate their scales with the accuracy required by their extensive commerce.
For Algebra II (advanced algebra), the introduction to the specific algebra objectives includes the work of Hypatia:
Students should know that the modern algebra developed in Europe is based on the algebra that began in Africa and Asia. Indeed, the word algebra is Arabic in origin; Europe received algebra as a gift from Asia and Africa. Under the influence of the African Moors, algebra spread through Europe from Spain and Italy. Equations were first solved in Africa 4,000 years ago by using proportions. Ancient Egyptians introduced the concept of the unknown or variable, which they called aha, the Egyptian word meaning heap. They also used the first symbols for addition (feet walked toward a number) and subtraction (feet walking
away). Africans were the first to use rectangular coordinates for their Egyptian star-clocks and for their construction plans for large temples. Babylonians (Mesopotamians) developed algorithms to find square and cube roots in the solution of equations. Geometric series, which play an important role in calculus and science, were first explored in Egypt 4,000 years ago. Hypatia, an Egyptian woman, worked with conic sections and indeterminate equations. The matrix method for the solution of systems of equations was pioneered by the Chinese 450 years before Cramer's rule was formulated in England. Chinese mathematicians also used the so-called Horner's method for the solution of higher degree equations long before Horner was born in England.
In addition to Measurement and Algebra, areas covered by the state objectives are Number Concepts, Quantitative Relationships, Geometric Concepts, Data Analysis and applications. The multicultural introduction for 10th grade geometry includes some examples of ethnomathematics:
Students should examine the contributions to geometry made by people all over the world. For example, African mathematicians in ancient Egypt developed formulas for the area of a triangle, a rectangle, a trapezoid, and a circle. Their study of geometry was stimulated by the need to resurvey the fields after the annual Nile River flood had wiped out all farm boundaries. The Ancient Egyptians were also the first to develop the concepts of congruency and similarity of geometric figures. The right triangle theorem was used by the Babylonians 1500 years before Pythagoras was born. Therefore, the Pythagorean theorem is a misnomer. The Egyptian formula for the area of a circle used a value of pi that very closely approximated the known value of pi today. The Egyptian value was 3.16 which was almost equal to the correct value of 3. 14...The first known use of trigonometry was in the application of the cotangent in the construction of pyramids in Africa 4,800 years ago.
Today people throughout the world apply geometry to everyday needs. Eskimos build their dome-topped igloos along the lines of an inverted catenary for greater strength. On Mount Kenya, families lay out the circular base of their homes by using a string attached to a centerpole as the radius. Mozambicans build rectangular houses by using equal- length ropes as the diagonals.
A different challenge was met for the new Algebra Framework now in preparation. Here the challenge was to integrate multicultural materials in the form of real-life examples which could relate to the student's world. Actually, many of the famous problems from the history of mathematics in Africa, Asia and Latin America proved to be quite suitable for 9th grade algebra. The material is now in the process of field testing and initial reactions have proved favorable.

For January 1, 1991 through December 31, 1991

Dues should be paid by January 1,1991 to enable
members to receive both 1991 newsletters from
the International Study Group on Ethnomathematics

Regular Member Dues: $5.00
Contributing Member Dues: $10.00 or more
Honorary Members: No Dues (see ISGEm
Constitution, Article III, Section 2-C)

Contributions are welcome to
fund memberships for those Interested in
ISGEm goals but who are limited by funds.

Proposed Constitution and By-Laws of the ISGEm

The Advisory Board of ISGEm developed the Constitution and By-Laws which appear below. The membership should cut out and mail the absentee ballot on page 7 to Luis Ortiz-Franco by September 1, 1991. Direct all inquiries to Luis Ortiz-Franco, whose address is listed on page 7.

Article I. Name. The name of this organization shall be the Intemational Study Group on Ethnomathematics ([SGEm).
Article II. Purpose. The purpose of the organization shall be to encourage and maintain interest in the teaching and learning of mathematics in cultural contexts and to promote professional growth, fellow- ship and communication among its members.
Article III. Membership.
Section 1. Membership shall be open to all persons interested in ethnomathematics.
Section 2. (A) Members shall pay regular dues and be entitled to all privileges of the organization. (B) The dues shall be set by the Executive Board subject to approval of the membership. (C) At the discretion of the Executive Board, any person shall be granted an honorary membership upon request without payment of dues.
Section 3. The membership period coincides with the calendar year from January 1 to December31.
Section 4. All members shall indicate the region to which they belong. The regions shall be: A. Africa; B. Asia (including the Middle East); C. South Pacific (including Australia and New Zealand); D. Europe; E. The Americas (North, Central, South, and the Caribbean).
Article IV. Executive Board.
Section 1. The Executive Board shall consist of the officers and members-at-large, the NCTM representative, the editor of the newsletter, the immediate Past-President, the President-Elect, the Program Assistant and the Assistant Editor.
Section 2. The Executive Board shall attend to any business of the organization that may require attention in the interval between business meetings.
Article V. Officers. The officers of the organization shall be President, First Vice-President, Second Vice-President, Third Vice President, Recording Secretary, Corresponding Secretary and Treasurer.
Article VI. Duties and Election of Officers.
Section 1. The President shall preside at all meetings of the organization and shall be chairman, ex-officio, of the Executive Board, and shall appoint an NCTM representative, the editor of the newsletter and the Assistant Editor.
Section 2. The First Vice-President shall perform the duties of the President in the absence of the President and shall act as program chairman. The First Vice-President shall appoint as necessary a program committee and a Program Assistant or specity program representatives to promote presentations on Etnno-Mathematics at relevant professional meetings.
Section 3. The Second Vice-President shall perform the duties of the President in the absence of the President and the First Vice-President and shall act as membership officer.
Section 4. The Third Vice-President shall perform the duties of the President in the absence of the President, the First Vice-President and the Second Vice-President and shall act as coordinator of the Special Interest Groups (SIGs) in ISGEm and communicate with members-at- large concerning conferences relevant to ISGEm in their respective regions.
Section 5. The Secretary shall keep the minutes of the business meetings and shall pass these along to the newly elected secretary as a permanent record of the actions of the organization.
Section 6. The Treasurer shall receive and account for all monies of the organization, disburse all sums on order of the President, and render a financial report at the last meeting of the year. A yearly audit must be conducted by two members appointed by the Executive Board.
Article VII. Meetings. At least one business meeting shall be held during each calendar year. The time and place of these meetings shall be set by the Executive Board. All meetings are open to amy member of the Group.
ArtIcle VIII. Rules of Order. The organization shall be governed by Robert's Rules of Order except in matters otherwise provided for by the Constitution.
Article IX. Amendments. This Constitution may be amended at any meeting of the Group by a two-thirds majority vote of the members present and voting, provided notice of the proposed amendment has been given at the previous meeting.
Article X. Dissolution. If at any time the International Study Group on Etunomathematics (ISGEm) shall cease to carry out the purposes herein stated, all assets held by it in trust or otherwise, shall, after the payment of its liabilities, be paid over to an organization selected by the final Executive Board of the International Study Group on Ethnomathematics which has similar purposes and has established its tax-exempt status under Section 501(c)(3) of the Internal Revenue Code of 1954 as now enacted or hereafter amended, and such assets shall be applied exclusively for such charitable, scientific, and educational programs.

Article I - Executive Board.
Section 1. Two of the members-at-large shall be elected from South Pacific, three from Africa, three from Europe, three from Asia (including the Middle East), and three from the Americas (North, Central, South, and Caribbean).
Section 2. Additional members of the Executive Board shall include the Immediate Past-President, the President-Elect, the NCTM Representative, the Editor of the newsletter, the Assistant Editor, the Program Assistant, and the officers.
Article H - Election of Officers and Members-At-Large.
Section 1. The terms of office for all officers and members-at-large shall be four years with half the members-at-large elected every two years.
Section 2. All elections shall be held by ballot prior to the end of each even-numbered calendar year and shall be carried by a plurality vote of the ballots returned. Nominations for the officers and members- at-large shall be made by a Nominating Committee of five members, appointed by the President and approved by the Executive Board. The Nominating Cornmittee shall recommend at least one candidate for each office to be filled. Other nominations shall be received as write-ins on the election ballot at the time of the election. The consent of each candidate, other than write-ins, must be obtained before the name is placed in nomination.
Section 3. Officers shall be elected in years divisible by four.
Section 4. Officers shall begin to serve two years after being elected.
Section 5. Members-at-large shall begin to serve on January 1 of the odd-numbered year immediately following election.
Section 6. Officers shall be elected by the entire membership.
Section 7. Members-at-large shall be elected by the members from their region.
Section 8. All officers and members-at-large can be re-elected.
Article III - Amendments.
These by-laws maybe amended by written ballot by a majority vote of the ballots returned, provided notice of the proposed amendment has been given at the previous meeting.
Excerpts from
World Cultures in the Mathematics Class
HIMED Conference, Leicester, UK
April 7-9, 1990
By Claudia Zaslavsky

The mathematics eduction community in the United States is embarking upon a program to reach all students. As stated in the Curriculum and Evaluation Standards for School Mathematics (NCTM): "It is crucial that conscious efforts be made to encourage all students, especially young women and minorities, to pursue mathematics." (p.68) Recognition is given to the varied backgrounds and interests of the students: "Students should have numerous and varied experiences related to the cultural, historical and scientific evolution of mathematics. (p. 5) Students' cultural backgrounds should be integrated into the learning experiences. (p.68)
"The ethnic groups that have lived longest in the Americas -- and who have been most oppressed -- are the Native peoples and the Africans who were brought to the New World in chains, to serve as slaves to European plantation owners. Now their descendants are determined to reassert their cultural heritage."
It is not only children of "minority" groups who benefit from the inclusion of topics relating to their heritage. Students in our "global village" must learn to respect and appreciate the contributions of peoples in all parts of the world. Educators are beginning to recognize the value of infusing mathematics with the achievements of world cultures, to "multiculturalize the curriculum." (Bishop, D'Ambrosio, Gerdes)
In this presentation I shall describe some of the mathematical practices of African peoples and of the indigenous peoples of the Americas, suitable for incorporation in the curriculum at the primary and middle grade level.
All peoples have developed numeration systems to the extent of their needs. The English language system of numeration and most European systems are based on grouping by tens and powers of ten. Why is ten commonly used as a base? Is it because we have ten fingers (digits)? The peoples of West Africa and Middle America, as well as the Inuit of the far northern group by twenties. In some languages, such as Mende of Sierra leeone, the word for twenty means "a whole person" -- all the fingers and toes.
Children can learn about numeration systems by examining the construction of larger numbers. In the Yoruba (Nigeria) language, for example, the name for 65 means "take five and ten from four twenties," using the operations of multiplication and subtraction, rather than multiplication and addition, as in most European languages. These are different solutions to the same problem, one just as good as the other. (Zaslavsky. Africa Counts, 207)
Finger gestures to express numbers are commonly used by people who do not speak each other's languages. These gestures may be related to the number words, or, again, they may be quite different. When the indigenous peoples of North America were pushed westward by European settlers, tribes speaking different languages were thrown together. Of necessity, they developed systems of finger signs, including signs for numbers. (Zaslavsky, "It's OK")
The peoples of Middle America developed their own systems of written numerals, dating back at least two thousand years in the case of the Maya. The systems were based on twenty and powers of twenty, and included the use of zero,positional notation, addition, and the repetition
of symbols.
Another aspect of number is the ability to do mental arithmetic. The year 1990 marks the 200th anniversary of the death of the slave Thomas Fuller, known as the African Calculator. Shipped to North America in 1724 at the age of fourteen, he developed remarkable powers of calculation, although he was forbidden access to any kind of schooling, as were all slaves, and he could neither read nor write. Late in his life he was used by anti-slavery advocates to demonstrate the mental capacity of Black people. (Fauvel & Gerdes)
Conclusion: The introduction of multicultural, interdisciplinary perspectives into the mathematics curriculum has many points in its favor:
(1) Students become aware of the role of mathematics in all societies. They realize that mathematical practices arose out of a people's real needs and interests.
(2) Students learn to appreciate the contributions of cultures different from their own, and to take pride in their own heritage.
(3) By linking the study of mathematics with history, language arts, fine arts and other subjects, all the disciplines take on more meaning.
(4) The infusion into the curriculum of the cultural heritage of people of color builds their self-esteem and encourages them to become more interested in mathematics. As one eleven-year-old boy wrote in his evaluation of a classroom activity based on African culture, "As you probably don't know I feel very strongly and am in deep thurst (sic) with my black people, and the math has made me feel better." There is little to be added to this heart-felt comment!
Bishop. A.J. Mathematical Enculturation (Dordrecht Kluwer, 1988).
D'Ambrosio, Ubiratan, "A research program and a course in the history of mathematics: Ethnomathematics," Historia Mathernatica 16 (1989), 285-6.
Fauvel, John & Gerdes, Paulus, "African slave and calculating prodigy: Bicentenary of the death of Thomas Fuller," Historia Mathematica 17 (1990) (to appear)
Gerdes, Paulus, "On culture, geometrical thinking and mathematics education," Educational Studies in Mathematics 19(1988), 137-162.
National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, 1989)
Zaslavsky, Claudia, Africa Counts: Number and Pattern in African Culture (Brooklyn: Lawrence Hill Books, 1979).
Zaslavsky, Claudia, "It's OK to count on your fingers," Teacher 96 (1979) 54-56.

Important Directions for Completion
of Your Proxy Vote
€Mark "X" in ink in appropriate box.
€Sign and date your proxy as requested.
'Carefully detach proxy and return by April 1,1991, to Professor Luis Ortiz-Franco, Dept. of Mathematics, Chapman College, Orange, CA 92666 USA.
€Please write suggested amendments on a separate sheet.

Detach here and mail

I Accept the Proposed ISGEm Constitution
I Reject the Proposed ISGEm Constitution
I Accept the Proposed ISGEm By-Laws
I Reject the Proposed ISGEm By-Laws


Letters From Our Readers
Addressed to Dr. Gloria Gilmer:
I am concerned about my students' perceptions of mathematics and of themselves as learners of mathematics. My students are rarely in the mainstream of mathematics. I have met them in many different educational settings: the evening division of a state university, an experimental "free" alternative high school, a special developmental program in a two-year public college, an eighth grade equivalency program at a military base in Germany, college courses inside the walls of the Attica Correctional Facility, and now at a private four-year comprehensive college.
Many of these students have come to believe that the mathematics classroom is not the place for their own ideas, their own insights, or their own questions. They have found, however, that when they reject their own ideas, they must learn to reproduce the ideas of others in a language that is also not their own. Their learning often becomes rote and without meaning. They feel powerless in this situation, choose to be passive in the mathematics classroom, and to leave the study of mathematics at their earliest opportunity
These views of mathematics and mathematics learning are not ones I hold. In fact, if I saw mathematics and mathematics learning as these students tell me that they see it, I would reject the study of mathematics as they do. Mathematics learning requires learners to use their own ideas, insights, thoughts, questions, and strategies as part of the learning process.
The focus of my present work is to help students to learn to listen to their own ideas, to accept them, to share them, to develop them, and to test them within the framework of the mathematical situation on which they are working at a given time. Early in this process I ask students, in a classroom setting, to develop their own metaphors for mathematics. These serve as a prelude to a discussion of mathematics and mathematics learning in which I discuss the important role of intuition in mathematics. All of this is part of a project called, "To Reclaim Intuition in Mathematics," funded by the Exxon Education Foundation. As this project continues I come to believe more strongly that the notion of intuition in mathematics is key to helping students make the transition to active, inquisitive learners.
Dorothy Buerk
Dept. of Mathematics and Computer Science
Ithaca College
Ithaca, NY 14850

Dear Ms. Gilmer:
I liked and valued your "Ethnomath Approach to Curriculum Development" presentation at Salt laake City.
When ISGEm's literature first came my way in the early 80's, I was glad to see the subject's emergence, but angry that they stole my name for it.
I used the term Ethnomathematics as the title of a speech in 1971. It was at MSU, working on my MA in Mathematics and collaborating with Dr. Victor Low,then Director of the African Studies Center. I spoke to Africanists then, Spring 1971, defining Ethnomathematics as the study of pre-Western and non-Westem Mathematics and Logic. My qualifications to do so were years of teaching Mathematics in Africa and then receiving an MA in Africa Studies from UCLA in 1967. It was there and then that I coined the term Ethncmathematics as the focus of a personal quest to merge my two loves, Africa and Mathematics.
Resistance from the Mathematics community was at first polite ridicule; this has waned. It remains for one of us to write THE definitive test, ETHNOMATHEMATICS. It must DEFINE the term with approaches from its many facets, at length, deeply; and it must DESCRIBE EXAMPLES from across time and space; and it must GENERALIZE.
The drift of some writers today is obviously motivated by a political and sociological agenda. This concerns me, as this is not how scholarship works.
I will be honored to correspond with you.

Wilbur Mellema
Mathematics Department
San Jose' City College
San Jose, California

Letters from our readers may be addressed to the editor, Patrick Scott, whose mailing address appears on page 7 of this newsletter.

Assistant Newsletter Editors
If you are interested in joining the Editorial Board of the ISGEm Newsletter please contact our editor, Patrick Scott, whose address is listed on page 7 of this newsletter.

Chair for Out-of-School SIG
As you may know, the Out-of-School SIG is one of four special interest groups in ISGEm that allow for a research focus in a ready-made focus group. We need a volunteer to chair this SIG. Interested parties should contact Gloria Gilmer whose address appears on page 7 of this newsletter.

Members for Membership Committee
David Davidson, our membership chair, wishes to launch a membership drive. To do so, he needs a committee. If you are interested in assisting in expanding our membership, please contact David Davidson. His address appears on page 7 of this newsletter.

Members for Nominating Committee
The president, Gloria Gilmer, will appoint a five-member Nominating Committee in preparation for elections slated for 1992. This committee will nominate officers and members-at-large. Responsibilities of members-at-large include, but are not lirnited to, organizing a working group for copying, translating and disseminating newsletters in or near one's country, encouraging presentations on ethnomathematics at professional meetings (especially those in or near one's country) and recruiting members in or near one's country. Please submit names of nominees for this committee to Gloria Gilmer whose address appears on page 7 of this newsletter.

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 the person involved in order to encourage communication among individuals with similar interests:

Ken Winograd received a three-year gift membership to ISGEm from his professor Fredrick L. Silverman. Professor Silverman reported that Ken did an excellent study of problem posing and problem solving behaviors of 5th graders.
Ken Winograd, 140114th Street, Greeley, CO 80631.

Claire Fenton is a K-12 mathematics consultant with the State Department of Education in Santa Fe, New Mexico.
Claire Fenton, Mathematics Education Consultant, State Department of Education, Education Building, 300 Don Gaspar, Santa Fe, NM

Lynn Hart is the co-principal investigator on the National Science Foundation's Problem Solving and Thinking Project at Georgia State University.

Marie Bryant is a doctoral student at the University of Texas at Austin. Her address is 4021 Steck, #826, Austin, TX 78759.

Michael Smith is a candidate for a master's degree at Curtin University of Western Australia. His thesis concerns difficulties in teaching problem solving to Aboriginal students.
Michael Smith, Box 113, Alice Springs, N.T. 0871, Australia 089 524108.

Tina Tau of Portland State University is interested in family math and informal mathematics education especially for underrepresented groups.
Christine W. Tau, 29300 NE Pendle Hill Rd., Newberg, OR 97132. (503)538-2201.

Pamela Harris is interested in the mathematics of indigenous people who stlll speak their own language at home, but have schooling in English, or in English and their own language in a bilingual education program. "The Northern Territory Department of Education has published four small books I have written on the topics of measurement, space, time and money in tribal aboriginal communities. I plan to do research in 1991 on the mathematical starting point of Pitjantjatjara children on the northwest reserve of South Australia.
Pamela Harris,20 Carville Street, Annerley, Queensland, Australia
(07) 391-6584.

Claudia Henrion is interested in women in math and the history of math. She is currently writing a book on contemporary women in math. She taught a class at Middlebury College in Vermont on the history of mathematics with a focus on the interaction between mathematics and society, hence she has been drawn to ISGEm.
Claudia Herion, Box 203, E. Thetford, VT 05043.

Please note these references to Bishop's work in the transcription of the paper by Gloria Gilmer (on page 4 of the May 1990 issue of the ISGEm Newsletter) entitled "An Ethnomath Approach to Curriculum Development. Alan Bishop. Mathematics Education In its Cultural Contest, Educational Studies in Mathematics. 19(1988)179-181 and Alan Bishop. A Cultural Perspective on Mathematics Education. Kluwer Academy 1988, Hingham, MA.

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. Claudia Zaslavsky prepared "Have You Seen" for this issue.

Cooney, Thomas J., ed. (1990). Teaching and Learning Mathematics in the 1990s. National Council of Teachers of Mathematics, Reston, VA 22091, USA.
The 1990 NCTM Yearbook includes a significant section on "Cultural Factors in Teaching and Learning" ("p 130-173). Articles by Lynn Steen, Walter Secada, Suzanne Damarin, Lee Stiff, Gilbert Cuevas and Brian Donavan consider the vital issues of"mathematics for all" and ways to increase the participation of women, language minority students, and people of color in the study of mathematics, as well as the influence of cultural diversity on the mathematics curriculum and on how mathematics is learned. Also relevant is "Contextualization and Mathematics for All" (pp 183-193), in which Claude Janvier maintains that the ways in which folks apply mathematics depend upon the context; in other words, the very essence of ethnomathematics must be incorporated into the classroom!

Ernest, Paul, ed. (1989). Mathematics Teachings: The State of the Art, Falmer Press, London UK.
Multicultural education has for some years been mandated for teacher education in the United Kingdom. Two chapters deal with this sensitive issue: Derek Woodrow's "Multicultural and Anti-Racist Mathematics Teaching" and Marilyn Nickson's "What Is Multicultural Mathematics?" Nickson concludes that more thought must be given to the social nature of mathematical knowledge and its implications for the curriculum if we are to meet the demands of the multicultural society in which we live. Readers will find other chapters relevant to etlinomathematics, particularly Paul Ernest's "Social and Political Values."

Lave, Jean (1988). Cognition in Practice : Mind, Mathematics and Culture in Evervday Life, Cambridge U.P., New York, NY USA.
Lave analyzes the successful application of mathematics by adults in such everyday activities as grocery shopping and the computation of dietary requirements, as compared with their inadequate attempts to solve similar problems in a school-like paper-and-pencil context.

Research Advisory Committee of the National Teachers of
Mathematics (July 1989). "The Mathematics Education of Underserved and Underrepresented Groups: A Continuing Challenge," Journal for Research in Mathematics Education: (p371-375).
A call to mathematics education researchers to consider the learning of mathematics by women and underrepresented minorities as an "area of high-priority research."

Zaslavsky, Claudia (September 1990). "Symmetry in American Folk Art," Arithmetic Teacher: pp 6-12.
Activities appropriate to middle school students based on symmetry in old American quilt and Navajo rug patterns, integrating mathematics with social studies and art. Full color illustrations include artwork by New York City public school students.

Guest Editor
Gloria Gilmer, ISGEm president, is newsletter editor for this issue of the ISGEm Newsletter. Patrick Scott is on leave in Honduras.

NCTM 69th Annual Meeting
New Orleans, April 17-20, 1991
Wednesday, April 17, 10 a.m. - noon
Meeting of ISGEm Advisory Board and SIG Chairs
Thursday, April 18, 4:30-6:30 p.m.
Open ISGEm Business/Program Meeting

Friday, April, 10 a.m. to noon

Meeting of ISGEm Advisory Board and SIG Chairs.

Conference on Gender/Race/Class Equity
May 9-10, 1991, Toronto, Ontario
Glendon College, York University
For further information contact Marelen Richman,
Room 716, Atkinson College, York University,
4700 Keele St, North
York, Ontario M33 'P3

9th Interamerican Math Ed Conference
Miami, August 3-7, 1991
For further information, write to:
Rick Scott
College of Education
University of New Mexico
Albuquerque, NM 87131 USA

7th International Congress on Math Education
Quebec, CANADA August 1992
For further information write to:
David Wheeler, Chair IPC for ICME-7
Department of Math & Statistics
Concordia University, Loyola Campus
Montreal, Quebec CANADA H4B 1R6

ISGEm Advisory Board
Gloria Gilmer, President
Math-Tech, Inc.
9155 North 70th Street
Milwaukee, WI 53223 USA

Ubiratan D'Ambrosio, First Vice President
Pro-Rector de Desenvolvimiento Univ.
Universidade Estadual de Carnpinas
Caixa Postal 6063
13081 Campinas, SP BRASIL

David Davison, Second Vice President
Dept of Cirruclum & Instruction
1500 N. 30th Street
Billings, MT 59101-0298 USA

Luis Cttiz-Franco,
Third Vice President
Department of Mathematics
Chapman College
Orange, CA 92666 USA

Claudia Zaslavsky, Secretary
45 Fairview Avenue #1 3-I
New York, NY 10040 USA

Anna Grosgalvis, Treasurer
Milwaukee Public Schools
3830 N. Humboldt Blvd.
Milwaukee, WI 53212 USA

Patrick (Rick) Scott, Editor
College of Education
University of New Mexico
Albuquerque, NM 78131 USA

Elisa Bonilla, Assistant Editor
Centro de Investigacion del IPN
Apartado Postal 14-740
Mexico, D.F., CP. 07000 MEXICO

Sau-Lin Tsang, Member-at-L&ge
Southwest Center for Educational Equity
310 Eighth Street #305A
Oakland, CA 94607 USA