**ISGEm Advisory Board**

Gloria Gilmer, President

Math-Tech, Inc.

9155 North 70th Street

Milwaukee, WI 53223 USA

David Davison, Second Vice President

Dept. of Curriculum & Instruction

Eastern Montana University

1500 N. 30th Street

Billings, MT 49101-0298 USA

Claudia Zaslavsky, Secretary

45 Fairview Avenue, #13-I

New York, NY 10040 USA

Patrick (Rick) Scott, Editor

College of Education

University of New Mexico

Albuquerque, NM 87131 USA

Sau-Lin Tsang, Member-at-Large

Southwest Center for Educational Equity

310 Eighth Street, #305-A

Oakland, CA 94607 USA

Ubiratan D’Ambrosio, First Vice President

Pro-Rector de Desenvolvimiento Univ.

Universidade Estadual de Campinas

Caixa Postal 6063

13081 Campinas, SP BRASIL

Luis Ortiz-Franco, Third Vice President

Department of Mathematics

Chapman College

Orange, CA 92666 USA

Anna Grosgalvis, Treasurer

Milwaukee Public Schools

3830 N. Humboldt Blvd.

Milwaukee, WI 53212 USA

Elisa Bonilla, Assistant Editor

Centro de Investigacion del IPN

Apartado Postal 14-740

Mexico, D.F., C.P. 07000 MEXICO3

**__________________________________________________**

**ISGEm News**

ISGEm will hold a business meeting on Thursday, April 19, from 4:00 – 6:00 PM at the Annual Meeting of the National Council of Teachers of Mathematics (NCTM) in Salt Lake City, Utah, USA. All interested parties are invited to attend. There will also be a discussion of plans for participation at the Seventh International Congress on Mathematics Education (1CME-7). Contact Gloria Gilmer at the above address if you desire more information.

Also at the Salt Lake City NCTM meeting Gloria Gilmer, Ubiratan D’Ambrosio and Jerome Turner will participate in a panel discussion on “Ethnomathematics Coming of Age.” Their presentation will be on Friday, April 20, at 1:30PM in Suite H at the Salt Palace.

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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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Washburn, Dorothy K. and Donald W. Crowe (1988). __Symmetries of__ __Culture: Theory and__ __Practice of__ __Plan Pattern Analysis__, University of Washington Press, P.O. Box 50096, Seattle, WA 98145-5096, USA, $42.

The following review was prepared by:

Dr. Beatriz D’Ambrosio

University of Delaware

Symmetric patterns are an integral part of many cultures and have historically been the object of study of different groups of scholars. The authors begin their work with an historical account of the studies of symmetries in various fields: crystallography, geometry, design, textile physics and archeology. This is followed by an analysis of symmetries from an anthropological perspective. This introduction gives the reader much interesting insight about what one might expect to find in a study of patterns, both from a technical perspective and from the perspective of cultural analysis.

The text is richly illustrated and exemplified. The richness comes mainly from the fact that examples are taken from tapestry designs, in other instances from ceramic designs, and still others from designs obtained through basket weaving.

An interesting aspect of __Symmetries__ __of__ __Cultures__ is the fact that what could be considered mathematically technical for some readers has been simplified by the authors through the use of flow-charts. This technique permits non-mathematicians to categorize and analyze easily one- and two-dimensional patterns.

From a mathematical perspective __Symmetries of__ __Culture__ establishes a very nice link between transformational geometry and the study of tessellations (mosaics and tilings). It consists of an extensive analysis of one- and two~dimensional patterns.

The text can be seen as being useful for many different groups:

- for pre-service or in-service education in mathematics as an example of how to use Ethnomathematics to discuss and illustrate otherwise rigid and formal concepts of transformations on the plane.
- in a mathematics course on Group Theory, as an introduction to the formal study of groups.
- for anthropology students, as an example of how to involve the study of patterns in a cultural analysis of social groups.
- for students of design since the book provides a complete study of one- and two-dimensional patterns.

Finally, __Symmetries__ __of__ __Culture__ will provide most readers with the simple pleasure of discovering and understanding more abouti the naturally fascinating world of patterns.

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__Mathematics. Education and Societv__, 1989, edited by Christine Keitel, Peter Damcrow, Alan Bishop and Paulus Gerdes, Paris: UNESCO Document Series #35.

This document contains the reports and papers presented in the Fifth Day Special Programme on “Mathematics, Education and Society” at the 6th International Congress on Mathematics Education (ICME) in Budapest from July 27 to August 3, 1988.

It is being distributed free of charge by UNESCO. If you have not received a copy or if you need more copies please contact:

Dr. Edward Jacobson

Math Education Programme Specialist

Div. of Science, Tech & Environmental Ed

UNESCO

Place de Fontenoy

F5700 Paris

FRANCE

The editors would now like to propose a new development: As the book is seen to be worthwhile in helping to bring mathematics education to the “Global Village,” they would like to go further with you and draw various practical consequences. They have thought about a worldwide Working Group with the provisional title “Mathematics Education in the Global Village” which aims at :

*initiating and demonstrating realistic alternatives***to**the present Euro-Centrism in mathematics education; and*.providing substantial and materialized support*to curriculum developers, teacher educators and teachers of mathematics education who ask for assistance.

Therefore, they invite you to offer your ideas for conceptualizing its working; they ask mathematics educators from rich countries to think about proposals of financial or any other direct assistance in developing and disseminating materials. They would like to encourage especially our colleagues in non-industrialized countries to name problems, describe needs and any kinds of assistance which could be met in order to build up a network of autonomous educational programs through our mutual cooperation.

Comments and proposals for this project may be sent to:

Dr. Christine Keitel

Technische Universitat Berlin

Fachbereich 3 – Mathematik

Strasse des l7Juni 136

1000 Berlin 12

WEST GERMANY

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Zaslavsky, Claudia (1989, September). People who live in round houses, __Arithmetic Teacher__. 18-21.

In “People Who Live In Round Houses” Claudia Zaslavsky gives rich examples of how to “bring the world into the mathematics classrooms.” Activities that encourage students to think beyond their own rectilinear culture integrate mathematics with social studies, art and other subjects as students explore the concepts of shape, size, area and perimeter.

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The following references appeared in the __Newsletter__ of the African Mathematical Union Commission on the History of Math in Africa (AMUCHMA). If you would like to receive the __AMUCHMA Newsletter__ request it from:

Paulus Gerdes

C.P. 915

Maputo, MOZAMBIQUE

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Kubik, Gerhard (1988). African Graphic Systems, __Muntu__ (Gabon), vol.4-5, 71-135.

In pre-colonial times, a varied range of graphic systems existed in Sub-Saharan Africa. The author presents the results of his own investigations made in Tanzania, Malawi, Gabon, Cameroun, Angola and Zambia between 1962 and 1984. The author also analyzes Tusona-Luchezi ideographs. “The forefathers of the Eastern Angolan peoples discovered higher mathematics and a non-Euclidean geometry on an empirical basis applying their insight to the invention of these (Tusona) unique configurations.”

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Lagercrantz, Sture (1968). African Tally-Strings, __Anthropos__ (__FRG), vol. 63.115-128__.

Gives an overview of the ethnographic literature on mnemonic aids in counting in sub-Saharan Africa. The map on p.126 shows the distribution of tally-strings over the continent. The most important tallies of higher age are the “memorial cairns (i.e. the custom that every one passing a place where someone for instance has suffered a violent death throws down a stone or a stick).”

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Obenga, Theophile (1987). Notes sur les Connaissances Astronomiques Bantu, __Muntu__ (Gabon), vol.6, 63-78.

Reviews the literature on astronomical knowledge in Ancient Egypt, among the Borana (Ethiopia), Dogon, Lobi, Bambara (West Africa), Vili (Congo), Fang (Cameroun, Equatorial Guinea, Gabon) and Mbochi (Congo).

_____________________________________

Schmidl, Marianne (1915). Zahl and Zahlen in Afrika, __Mitteilungen__ __der__ __Anthropologischen__ __Gesselschaft__ __in__ __Wein__ **(Aus**tria), vol.45, 165-209.

In the first part an overview and comparative analysis of counting systems in Sub-Saharan Africa is given. The second part deals with psychological and historical factors that influence the development of counting (systems).

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**Report of Working Group on Mathematics in Different Cultures**

*Popularization of Mathematics Conference*

*Leeds, England*

*September 17-22, 1989*

*Alan J. Bishop, Working Group Chair*

This group felt that although its brief might have appeared limited at first sight, it has important points to make to everyone concerned with popularization. The term “culture” can, and should, be interpreted broadly in order for popularization to stand any chance of success.

The key aim of popularization is to overcome alienation. We identified power imbalance in society as one of the fundamental causes of alienation, with “Western” Mathematics being seen to be a strong part of the “education” system helping to alienate various groups in different societies.

In some countries there are indigenous cultural groups as minorities (e.g. New Zealand, Australia, USA, Canada, Finland) and in the majority (e.g. South Africa) though in all those countries the dominant culture group assumes Western Maths to be the only Mathematics worth knowing.

In Africa and South America there are ex-colonial societies trying to identify their own view of Mathematics, while in Europe, North America and Australia there are new immigrants feeling alienated from the “resident” culture.

In all these situations it is as much the process of cultural alienation which needs to be overcome as the dominant Mathematical view itself. This implies that the following points need particular consideration:

- Who does the popularizing?” is a key question. Basically, “we” can’t do it for “them,” and we need to recognize the need to develop such notions as bilingual/bicultural units, family and community groups and leaders, indigenous leaders and popularizers.
- Most popularization is carried out in the language of the dominant group and this issue needs addressing. Culture and language are intertwined, and language is for many the heart of culture. “Their” language expresses “their” mathematics.
- Everyone in Mathematics and Mathematics Education needs to be aware of the cultural nature of mathematics. Western Mathematics is a particular form of knowledge having a particular cultural history. This fact needs to inform all kinds of popularization.
- Awareness is not enough though, and in the context of this seminar, legitimation is crucial – that is, popularization must legitimize Mathematical ideas which are not in the dominant mainstream. It means legitimizing other forms of Mathematical knowledge and values, and it means legitimizing the activities of those Mathematicians who practice in other cultural groups.
- There are appropriate and inappropriate ways to talk about knowledge and to use knowledge in different cultures. This demands sensitivity within the popularization process, encouraging again the need for other cultural representatives to be engaged in the process.
- The early Mathematical knowledge of the
__dominant__group should not be ignored in any popularization, otherwise there is a danger of other cultural knowledge being projected as primitive and inferior. In other words, old non- Western Mathematical ideas should not be contrasted with new Western ideas. - There are significantly different conceptual frameworks in different cultures and Mathematical ideas will not necessarily be separated from other ideas in the ways that Western Mathematics is.
- Care should be taken not to glorify, or make exotic, other peoples’ culture. One may well be referring to Westerner’s
__historical__version of that other culture which may not coincide with the other person’s__present__views.

Finally, we consider that ICMI (International Congress Mathematical Instruction) has a key role to play in this area in the following ways:

ICMI should encourage any attempts to popularize which are tackling this cultural dimension. It is a relatively unexplored area, it is extremely complex and __urgent__. Cultures are fighting for survival.

ICMI should invite more involvement from alienated cultural groups in its activities.

.Regional meetings would be particularly appropriate for addressing those issues, but the ICMIs are also extremely important events for increasing awareness and sensitivity.

However, the most important role for ICMI is to legitimize other Mathematical activities besides those which are identified with the dominant cultural group. As an international organization ICMI should have a truly multicultural perspective, and this perspective should influence all its activities, its publications and its structure.

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**Member Projects**

On the ISGEm Membership Form we have asked people to “briefly describe any projects with which they 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:

I am doing my doctoral dissertation on secondary school students’ beliefs about mathematics in Zimbabwe. Later, as a mathematics educator living and working in Zimbabwe, I plan to do research aimed at uncovering the Ethnomathematics of various groups in Zimbabwe and bringing it into the classroom. In particular, I wish to study the Ethnomathematics in Zimbabwean traditional medical practice.

*David Kufakwami Mtetwa*

*14 Gotley Close*

*Marlborough, Harare*

*ZIMBABWE*

_______________________________

Mathematics and Astronomy of the Andean region for the period 1500 B.C. to 1480 A.D. Logical and mathematical structure of kipus (quipus). Knowledge of kipucamayocs. In October 1988, I organized an international seminar in Lima, Peru, on “Kipus and Kipucamayocs.”

*Oscar Valdivia*

*Universidad lnteramericana de Puerto Rico *

*Colegio Universitario de Arecibo*

*Call Box UI*

*Arecibo, PR 00612*

___________________________

My research interests related to Ethnomathematics relate to issues revolving around the role that the tool we choose to use creates/influences the culture. My interests come from Vygotsky, Luria, Cole & Scribner’s work chiefly from linguistics. I found that computers do the same things. And presently I am more interested in how to create positive mathematical-cultural climates in classrooms. As well, I noticed children in Central America and Mexico were able to do outstanding informal mathematical tasks, yet in the formal classroom atmosphere, they had great difficulty with the same problems.

*Daniel C. Orey*

*Department of Teacher Education California State University, Sacramento*

*6000 “J” Street*

*Sacramento, CA 9S819-2694, USA*

___________________________

I am busy writing my dissertation entitled “An Ethnographic Study of the Creation, Learning and Teaching of Mathematics among Unschooled Carpenters.” I spent six months in Cape Town, South Africa, working as an apprentice with a group of carpenters and conducting ethnographic research.

*Wendy Millray*

*5243 West 11th St., Apt. 1814
Greeley, CO 80634 USA*

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**Ethnomathematical Perspectives on the NCTM Standards**

Daniel Orey

Sacramento State University

In the United States, the aftermath of the sixties has increased the visibility and participation by many minority group members in the mainstream of daily life. As well, a new understanding has developed; instead of a “melting pot,” the United States had become an enormously diverse “salad bowl.” I believe that the mathematics curriculum offers educators an excellent opportunity to give learning groups with diverse ethnicity the opportunity to experience success. The recent publication, __Curriculum and Evaluation Standards for School Mathematics__ (Commission on Standards for School Mathematics, 1989) has caught the imagination of and been the topic for discussion by many mathematics educators. It is the purpose of this article to offer some ideas about implementing the Standards an ethnically diverse setting.

Those of us nurtured from within the Western cultural tradition tend to think of mathematics as a unique flowering of European culture, and insofar as the history of the subject is taught in schools in the United States, it may appear to be so. However, cultural evidence suggests that mathematics has flourished worldwide and that children benefit by learning how “mathematical practices arose out of the real needs and desires of all societies” (Zaslavsky, 1989). Students should learn that mathematical thinking is part of the basic human endowment. For as Anthropologist Edward T. Hall (1977) stated:

*“Most cultures and the institutions they engender are the result of having to evolve highly specialized solutions to rather specific problems.”*

It is this very universality of mathematics that can become the most obvious contributor to a curriculum that seeks to address any challenges coming from diverse populations. Math developed by many non-European cultures can communicate a recognition and a valuing of the cultural heritage of ethnic minorities present in the classroom, whereas not doing so can communicate the opposite. This perspective can help minority students by increasing their knowledge of and respect for the cultures of their origins, at the same time informing students from the majority culture about the mathematical richness of the various cultures whose people now live alongside them. Additionally, students need to learn to identify, respect and value alternative solutions to problems, as well as the many unique and varied approaches to problem solving.

*“Schools should prepare individuals to take part in the dynamic pluralistic society by teaching respect and value for different positions, by encouraging students to rely on the scientific method of problem solving, and by fostering a commitment to the general welfare of society (Appleton, 1983, p.93).”*

An understanding of minority and learning styles can offer important insight for the development of experiences and problem solving tools relevant to the mathematics classroom. This awareness is important in order to build an understanding of why many minority students experience difficulty in certain contexts. An understanding of differences in learning styles allows the teacher to build upon a student’s strength, instead of considering these differences as a deficit. A particular cognitive style, encompassing “the way one perceives and thinks about the world” including “thinking, perceiving, remembering and problem solving” is culturally determined (Appleton, 1983). Developing a cognitive style in learners that encourages diverse and creative methods, through cross cultural sharing and interchange, should become a vital attribute of any mathematics program.

**Learning and Culture**

Mental activity is part of the overall human endowment, yet at the same time, much of the way it is directed is culturally determined (Appleton, 1983). Cognitive style, or the way in which a person “encounters, orders and thinks about the world” (Appleton, 1983) influences how well a student performs in a given academic environment. Experience in multicultural learning environments, and specifically, experience in dealing with more than your own culture, exposes learners to alternative methods in perceiving the world around them. Hall (1977) has said:

*“The natural act of thinking is greatly modified by culture; Western man uses only a small fraction of his mental capabilities; there are many different and legitimate ways of thinking; we in the West value one of these above all others–the one we call “logic”, a linear system that has been with us since Socrates.*

The “ability to solve problems, or create products, that are valued within one or more cultural settings” (Gardner, 1983) is a valuable asset for all societies. Finding ways to tap into the diverse strategies that exist within any given classroom should become a primary concern. While at the same time, a teacher can encourage those linear/logical methods that connect all students to the dominant culture. The recent call for a redirection in mathematics education (Commission on Standards fpr School Mathematics, 1989) as well as certain computer software activities offer an extraordinary opportunity for educators to accomplish this goal.

Table 1 outlines the following discussion, as gleaned from the literature on culturally determined differences in learning styles for school-aged children. It is understood by this author that not everyone falls into one or the other group. The literature has supported the idea that most children come to school stronger in one or the other style. Presently, the dominant culture stresses, indeed appears to have built its curriculum upon, the majority learning style. “Successful” students, as labeled by the dominant culture, tend to be better at the use of those items that are in the majority category.

Table 1: Learning Styles

Minority |
Majority |

People-oriented | Object-oriented |

Relational | Analytical |

Field Dependent | Field Independent |

Polychronic Time | Monochronic Time |

(P-time) | (M-time) |

While giving many students timed tests, dittos, rote memory work, or works that asks them to copy and answer (often meaningless) problems, is mind-numbing for many children, it is particularly alienating for many minority children who come from cultures where human interaction and cooperation are highly valued. Though there are times when these activities are necessary, it is imperative that teachers in multicultural environments understand that their students may have particular difficulty with these kinds of solo work activities. It is imperative that the teacher in an ethnically diverse environment, use cooperative strategies for problem solving because minority students come from cultures that place value upon interpersonal communication encouraging all students to work together in cooperative groups and gives opportunities to communicate mathematics information (Kantrowitz & Wingert, 1989). As well, learning to work successfully with other people, in a dynamic and complex environment, is vitally important in an information society (Peters, 1988).

The largest single reason employees can lose a job is because they cannot get along with their own fellow workers. Giving students opportunities to learn how to work cooperatively on problems (often with people they may prefer NOT to work with) is an important life skill. Minority students can become important role models for more competitive students in working together cooperatively.

**Relational and Analytical Learning Styles**

Some students will need to see the relationship of what is being newly introduced to what they already know. Many teachers have heard “but WHY do I have to learn this? (Jackson, 1989), and it is precisely this need, that the student may be trying to fulfill. Other students are just as easily overwhelmed by, or see no need to identify, the connections to the past and present, but need to know HOW it works. If we give information to students using only one of these modes, then we miss other students who do not learn well in that mode.

Experiencing concepts in a variety of contexts, or seeing a number of uses of the same skill, not only reinforce the skill in a number of areas, but allow students to make a variety of mental connections with which to remember the concept. A given concept must be taught using as many different styles of communication as is possible.

Using integrated lessons, realistic simulations or projects that show the relationship of mathematics to the real world, are essential for creating an environment for learning, because “a person discovers, or creates knowledge, in the course of some activity having a purpose” (Commission on Standards for School Mathematics, 1989). Learning when to focus energy towards a given type of data, as well as coming to an understanding of why others do not approach a given problem the same as you have is a vital experience in coming to understand our fellow human beings.

**Field Dependent & Independent Learning Styles**

Minority and majority groups have had different backgrounds and experiences that may classify them as either Field Dependent or Field Independent (Jackson, 1989; Appleton, 1983; Lowenfeld & Brittain, *1975; *Witkin, 1962). For example, students from traditional Mexican-American backgrounds tend to be field dependent; they have come to rely on surrounding field or environmental cues or relations in perceiving and interpreting information (Appleton, 1983). Many Anglo students appear to be field independent; they have been trained to focus on specific stimuli or data without regard to the surrounding environment (Appleton, 1983). The distinction is similar to that of relational and analytical styles, yet it is more focused and applies to the ability to take in information. For example, some people are able to spot individuals in a crowd, yet others, seemingly overwhelmed see only the whole group. Some students need to have plenty of stimuli: music, crowds, noise, activity. Others operate at an optimum in a quiet room with orderly plans and activities and relatively little excitement. It is important that we recognize the relationship between environment and learning style.

**Monochronic and Polychronic Time**

Hall (1977) has observed that the world is dominated by at least two different frames of reference as regards usage of time: monochronic and polychronic. Monochronic (M-time) emphasizes schedules, segmentation and promptness. This view of time is found primarily in Anglo America and Western Europe. Polychronic (P-time) is characterized by several things happening at once and is less tangible than M-time. Many people using P-time come from Latin America and the Middle East. Understanding this vital frame of reference is crucial to creating connections for students of different cultural backgrounds.

**Implications for the Mathematics Classroom**

The recent publication, __Curriculum and Evaluation Standards for School Mathematics__, (Commission on Standards for School Mathematics, 1989) encourages the use of teaching strategies that can improve the learning of mathematics for minority students. In the __Standards__, the National Council of Teachers of Mathematics (NCTM) has created a vision of:

- math power for all in a technology society;
- mathematics as something one does–solve problems, communicate, reason;
- a curriculum for all that includes a broad range of content, a variety of contexts and deliberate connections;
- instruction based on real problems; and
- evaluation as a means of improving instruction, learning and programs.

The very core of the __Standards__ addresses equity. By emphasizing how mathematics is really something done to solve problems, communicate and reason; one is reminded how in reality mathematics is tools for communication and interpreting information, and therefore, so much more than the mere arithmetic that has so thoroughly dominated the curriculum. NCTM recommends that teachers develop curriculum that includes a broad range of content in a variety of contexts with deliberate connections. Teacher can use their own particular multi-ethnic classroom realities as a rich resource upon which to build. As well, NCTM calls for instruction to be based on real problems that students themselves create and solve, and whose solutions they discuss. The __Standards__ emphasize that the primary function of evaluation should be as a means of improving instruction, learning and programs. Evaluation should not be used to track students. A consequence of tracking is often walls between culturally diverse groups of people.

**In Conclusion**

A multicultural perspective on mathematical instruction should not become another isolated topic to add to the present curriculum content base. It should be a philosophical perspective that serves as both filter and magnifier. This filter/magnifier should ensure that all students, be they from minority or majority contexts, will receive the best mathematics background possible. Every step a teacher makes in designing, planning and teaching mathematics should be fed through the filter and exposed to the magnifier. It is possible that the most interesting aspect of what NCTM has proposed not only is good for the majority student population, but empowers the minority learner as well.

For educators, these are indeed challenging and exciting times; the face of the classroom one will see tomorrow may well be quite different from that of today. Never before have we known so much about how human beings learn, how they develop and mature. Never before have we had the abundance of materials and ideas that are available in to assist teachers in this process. Never before have we had such a diversity of students in our classrooms. It is time to lend both our spiritual and material resources and rise to the challenge because the image of society in which few have the mathematical knowledge needed for the control of economic and scientific development is not consistent either with the values of a just democratic system or with its economics needs (Commission on Standards for School Mathematics, 1989).

Mathematics is a tool. Being proficient in the use of this tool is important for students if they are to have any input at all as to how their own society can change and evolve to include them.

**References**

Appleton, M. (193). __Cultural Pluralism in Education: Theoretical__ __Foundations__, New York: Longman.

Burke, J. (1985). __The Day the Universe Changed__. London: British Broadcasting Corporation.

Committee on Economic Development (1985). __Investing in our__ __Children:__ __Business__ __and__ __the__ __Public Schools__. New York: Committee for Economic Development.

Commission on Standards in School Mathematics. (1989). __Curriculum and Evaluation Standards for School Mathematics__. Reston, VA: National Council of Teachers of Mathematics.

Gardner, H. (1983). __Frames__ __of__ __Mind: The__ __Theory__ __of__ __Multiple Intelligences__. New York: Basic Books.

Hall, E.T. (1977). __Beyond Culture__. New York: Anchor.

Jackson, 5. (1989, May 9). Presentation at the Excellence in Mathematics and Science Achievement Symposium. San Francisco: Southwest Center for Educational Equity.

Kantrowitz, B. & Wingert, P. (1989, April 17). Special report: How kids learn, __Newsweek.__

Kearns, D.T. (1988,February 17). School reform: Strengthening a weak system, __The Sacramento Bee,__. p. B-5.

Lowenfeld, V. & Britain, WI. (1975). __Creative and Mental Growth.__ __6th__ __ed.__. New York: MacMillan.

Luria, A.R. (1978). __Cognitive development: Its cultural and social foundation__. Cambridge, MA: Harvard University Press.

Peters, T. (1989, June21). Learn, innovate, act–or lose the job, __The Sacramento Bee__, p. E-3.

Witkin, H.A. (1962). __Psychological differentiation__. New York: Wiley.

Zaslavsky, C. (1989), Integrating math with the study of cultural traditions, __Newsletter International__ __Student Group on__ __Ethnomathematics__, 4(2), p.6-9.

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**Making Math Work For Minorities****National Convention****Washingt on, D.C., May 4-5, 1990**

To receive information about the national Convocation, send name, title, affiliation, address and phone number to:

Beverly Anderson, Project Director

Mathematical Sciences Education Board

818 Connecticut Ave., NW, Suite 500

Washington, D.C. 20006, USA

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**8th 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

_______________________________________________

**ICME-7 in 1992**

The Seventh International Congress on Mathematics Education (1CME-7) will be held in Quebec, Canada, in August 1992. In order to make the program of ICME-7 fully representative of developments in mathematics education worldwide, the International Program Committee (IPC) needs your help in reaching the people in our organization who can contribute to the Congress program.

The Committee would particularly like to receive suggestions in the following categories in good time for the next meeting in early June 1990:

- Topics and speakers for lectures.
- Topics and organizers for Topic Groups.
- Members of Advisory Panels for the Working Groups

Please send your suggestions to:

David Wheeler

Chair, PlC for ICME-7

Department of Math & Statistics

Concordia University, Loyola Campus

Montreal, Quebec CANADA H4B 1R6

Components of the program of ICME-7:

__Working Groups__. A list of titles follows. Each group meets for four 90-minute sessions, including time for discussion in smaller subgroups. The detailed planning of each group is delegated to a chief organizer assisted by an advisory panel.__45-minute lectures__. Taken together, the 30-40 lectures should cover many of the issues that are important for mathematics education in the 1990s around the world, and should address all the constituencies with an interest in mathematic education. Prospective lectures may be asked to supply evidence that they know how to speak effectively to a mixed international audience.__Topic Groups__. Each group will be scheduled for one, two or very exceptionally four sessions of 60 or 90 minutes’ duration. Each group must involve a team of people in its planning and execution. Proposals will be judged on the significance of the topic and the strength and representation character of the presenting team.__ICMI Study____Groups__.__Posters and short communications__. Forms for submitting proposals will be included with the Second Announcement of the Congress.__Project and (possible) national presentation__.__Exhibitions and____workshops__.__Opening and closing ceremonies and plenarv addresses__.

**List of Proposed ICME-7 Working Groups**

- Formation of elementary mathematical concepts.
- Students’ misconceptions and inconsistencies of thought.
- Students’ difficulties in calculus.
- Theories of learning mathematics.
- Improving students’ attitudes and motivation.
- Pre- and in-service mathematics teacher education.
- Language and communication in the classroom.
- Innovative assessment of students in the mathematics classroom.
- Differentiation of students within classes and programs.
- Multicultural and multilingual classrooms.
- The role of geometry in general education.
- Probability and statistics for the future citizen.
- The place of algebra in secondary and tertiary education.
- Modeling activities in the classroom.
- Undergraduate mathematics for different groups of students.
- The impact of calculators on the elementary school curriculum.
- Technology in the service of mathematics curriculum.
- Methods for implementing curriculum change.
- Mathematics for early school leavers.
- Mathematics in distance education.
- The public image of mathematics and mathematicians.
- Mathematics education with reduced resources.
- Methodologies for mathematics education research.