**Mathematics Pedagogy in the 3rd World: The Case of a Guatemalan Teacher**

**Richard Kitchen
University of Wisconsin – Madison**

**Introduction**

This article is based on interviews and observations conducted in June of 1994 with one secondary mathematics teacher who works in a public, secondary school in Guatemala City, Central America. The teacher, Señor Chávez has over 20 years of experience working at his school (referred to as the “Gymnasium”). As a senior member of the Gymnasium faculty, Sr. Chávez is knowledgeable about incidents that have occurred at the Gymnasium over the years and has much to share about his pedagogy and the context of his work.

The interviews and observations were carried out as part of a pilot study for my doctoral dissertation. The purpose of this exploratory study was to begin a chain of inquiry, with the specific goal of commencing to answer the following constellation of questions: What goals does a mathematics teacher working in an authoritarian Third World country hope to achieve through his mathematics pedagogy? What sorts of classroom routines characterize the pedagogical practices of the mathematics teacher?

In general terms, this project hopes to provide a teacher from the “Third World” opportunities to speak to us so that we can understand his work, its situatedness, and some of the social and political conditions that impact his practices. The need for a Third World perspective on mathematics pedagogy is based, primarily, on the lack of Third World participation in deciding the models of mathematics pedagogy that are most appropriate for their purposes.

Altbach, Arnove, and Kelly (1992), Carnoy (1974), and Zachariah and Silva (1980) have all argued that national school systems are situated within the context of unequal power relations among nations. Through design, historical circumstances, and the unequal distribution of material and intellectual resources, the Western industrialized countries have and continue to dominate the economic and educational systems of the less industrialized nations. The historical roots of this unequal relationship date back to colonial times when many Third World countries adopted transplanted educational models from industrialized countries that usually “grotesquely misfit the countries’ actual needs, circumstances, and resources” (Coombs, 1985, p. 33).

Moreover, the network of international and national aid agencies linked to, and located in the industrialized nations, have been an important means by which First World countries have controlled education in developing nations (Berman, 1992). Critics of the educational assistance offered by First World donor agencies and the interests that they represent argue that these organizations adhere to conservative Western ideologies, leading to their funding inappropriate and ineffective field projects that are irrelevant to the needs of the recipient nations (See, for example, Carnoy, 1982; Klees, 1986; Zachariah, 1985). Berman (1992) argues for a model proposed by Swedish aid agencies that encourages international donor agencies to actively foster locally-controlled, nongovernmental organizations (NGOs) as the primary means for Third World nations to develop their educational systems in line with their educational needs.

**Why it is Important to Study Mathematics Pedagogy in the Third World?**

Greater involvement by NGOs in the educational planning process necessitates the emergence of more scholarship about the Third World that provides information about the unique educational requirements of these nations, in general, and the needs of teachers, in particular. Constructing educational systems that are responsive to local needs entails people defining “their own issues in their own ways, from their own perspectives, using their own terms” (Secada, 1995). The intent of voice scholarship is specifically to provide an avenue to hear from those people who traditionally have not been heard from in the past. Such scholarship can also contribute to an improved understanding of what knowledge has been imported from the First World and consequently valued in unindustrialized nations, while simultaneously suggesting possible alternative models of mathematics pedagogy that may be more appropriate in the developing world.

Voice scholarship also affords a way to hear from teachers working in places that have so little of even the basic amenities that First World teachers take for granted (e.g., blackboards, chalk, books, and paper). My review of the literature has revealed very little research that allow actual mathematics teachers working in peripheral nations to describe the context of their working conditions in their own words. This should be problematic to anyone interested in education in the Third World.

Another important reason to study mathematics pedagogy from a Third World perspective is simply to support teachers working in difficult conditions. One means to back our Third World colleagues is to study their work, and to share with others the battles that they have fought and the struggles that they have endured. This study can serve the purpose of demonstrating to others working in similar working conditions that they are not alone, that there are others struggling to provide their students future opportunities in conditions that few of us in the First World could tolerate.

Finally, by studying another country’s educational system through the voices of teachers, I hope to provide US educators insights into the realities of our own educational system. By learning about the conditions of teachers working in difficult circumstances with few resources and little support, the study provides US educators with an example from which to compare their work conditions and practices.

**Mathematics Pedagogy in the Third World**

Munir Fasheh (1989), a Palestinian mathematician, has written extensively about the “alien, dry, and abstract” mathematics that is valued in Palestine. Fasheh’s work is unique precisely because it is situated in a Third World context, and provides as an example of the role of mathematics education in an underdeveloped nation. He has advocated ethnomathematics as an approach to mathematics pedagogy that may be more appropriate for the needs of his students. Ethnomathematics acknowledges that mathematics is itself a product of culture and is affected by cultural forces (D’Ambrosio, 1985; Bishop, 1988).

Fasheh discusses the difference between the mathematics that he has studied and teaches, and the mathematics that his mother uses on a daily basis to argue for a more culturally situated approach to mathematics pedagogy:

My math had no power connected with anything in the community and no power connection with the Western hegemonic culture which had engendered it. It was connected solely to symbolic power without the official ideological support system, no one would have ‘needed’ my math; its value was derived from a set of symbols created by hegemony and the world of education. . .

Math was necessary for her (his mother) in a much more profound and real sense than it was for me. My illiterate mother routinely took rectangles of fabric and, with few measurements and no patterns, cut them and turned them into beautiful, perfectly fitted clothing for people. In 1976 it struck me that the math she was using was beyond my comprehension; Moreover, while math for me was a subject matter I studied and taught, for her it was basic to the operation of her understanding. In addition, mistakes in her work entailed practical consequences completely different from mistakes in my math (Fasheh, 1989, pp. 84-5).

Fasheh’s words provide a powerful critique of the abstract, symbolic mathematics that he studied in school. As a member of a developing nation with a unique history, his advocacy for the study of ethnomathematics in his homeland is highly credible.

**Research Findings**

I begin by providing some background information on Sr. Chávez, his students, and the Gymnasium. I proceed by summarizing some of my findings from the pilot study that are relevant in answering the questions that I originally posed: What are some of the pedagogical goals of a mathematics teacher working in an authoritarian, Third World country? What sorts of classroom routines characterize the pedagogical practices of the mathematics teacher?

Sr. Chávez comes from a family of teachers. He has taught at the Gymnasium for more than 20 years, and also has experience teaching at the primary and university levels. He earns approximately $280 a month as a part-time instructor at the Gymnasium. As do many Guatemalan teachers, Sr. Chávez supplements his income by working at a second job that has nothing to do with education.

Because the Gymnasium is public and in the city, the student population there is quite unique. Students come from remote rural regions to study at the school since public secondary schools are relatively scarce in Guatemala. Many of the students are Indians who conceal their ethnic origins to enhance their prospects. According to Sr. Chávez, approximately 30% of the students at the Gymnasium are exclusively of Indian ancestry. In addition, he estimates that about 5% of his students have had at least one parent killed during the war that has plagued Guatemala for more than 30 years, and that only about 25% of the students live in two parent households. A few of the students live in orphanages, and approximately 10% live with relatives other than a parent.

Sr. Chávez and Mari (a Guatemalan woman who assisted me) both emphasized that the students at the Gymnasium are relatively privileged because they can afford to attend classes, at least part-time. In a country where 79% of the population lives in poverty and less than 50% of the population is literate (Simon, 1987), few people, especially few indigenous people, have the opportunity to pursue schooling beyond the primary school level.

According to Sr. Chávez, approximately 20% of the students have a family member who is working in the US. Many of the students have part-time jobs to supplement their families income such as selling things on the city streets, working in shoe factories, selling shoes, and doing restaurant work. Nevertheless, Sr. Chávez stressed that the students and their parents have a difficult time affording the expenses involved in attending the Gymnasium. For example, parents must buy their kids’ school uniforms that includes slacks, shirts, shoes, and a jacket for the boys and skirts, blouses, shoes, and a jacket for the girls. One uniform may cost upwards of $15-$20 (many days pay for the typical Guatemalan worker accustomed to wages as low as $1.50/day).

At the Gymnasium, the salaries of the teachers and director, the salary of one secretary, lights, water, telephone, and a few typewriting machines are paid by the government. Often, the government must take out loans from the state bank to meet its financial obligations to state workers. The science lab is poorly stocked. The school library is stocked with old, dust covered books, many of which look like they have not been opened for years. It is usually closed, books cannot be checked out over-night, and the library can be used only by groups of students who are accompanied by a teacher.

**Sr. Chávez’ Pedagogical Goals**

No curricula framework or guidelines are available in Guatemala to assist mathematics teachers in the classroom. Furthermore, administrative support is minimal, and at times completely nonexistent. Sr. Chávez said that as a rule, mathematics teachers are poorly educated and have few inservice opportunities. In a teaching environment that is as void of basic resources and support as in the school where Sr. Chávez works, it is interesting to ask what types of goals he may have as a mathematics teacher. Has he continued to teach in such poor conditions because he believes in what he is doing, and believes that he is making a difference in his students’ lives? At this point, I am only prepared to summarize what he has identified as some of his goals in the initial stages of the research project.

According to Sr. Chávez, his primary pedagogical goal is to adequately prepare his students for entrance into the university. Though there is not a formal entrance examination in mathematics at Guatemala City’s large public university, Universidad de San Carlos, students must be well-prepared in mathematics to pursue many of the degrees offered at the university.

It appears that Sr. Chávez has control over what mathematics he teaches, how he teaches it, and how he assesses his students’ progress. He told me that he has the syllabi of several mathematics courses offered at the university to assist him in establishing what mathematics is important to teach his students to be successful in mathematics in the future.

Sr. Chávez works hard to develop what he characterized as his students’ “reasoning and deduction capabilities.” He believes that one of the reasons for teaching mathematics is to foster his students’ reasoning skills. In addition, Sr. Chávez believes that the study of mathematics can assist people in a variety of ways, such as advancing a person’s creativity and ability to think abstractly. His primary goal is to advance his students’ conceptual understanding of mathematical topics. He stressed that to enter the university, his students will need to be able to solve a variety of algebraic equations, and to do so, they will need to be able to think abstractly and understand the mathematics conceptually.

Sr. Chávez also discussed how in Guatemala, children cannot begin to think abstractly until between 14-16 years of age, in opposition to Piaget’s theories about development. He believes that the principal reason for this is that Guatemalans have been poorly fed for generations which has led to biological deficiencies. These problems are magnified by poor nutrition, and instruction that does not stimulate development. In fact, Sr. Chávez emphasized that mathematics instruction in Guatemala focuses on the teaching of the basic math facts, and is disconnected and unintegrated.

**Pedagogical Practices and Classroom Routines**

The first and most obvious aspect of Sr. Chávez’ work is the lack of resources available to him to perform his job. Sr. Chávez teaches without textbooks, and has no access to materials to facilitate the instruction of mathematics in his classrooms. He literally photocopies exercises from his textbook to sell to his students for a small fee when he assigns homework. In addition, the textbook in use is more than 30 years old and is one of the few mathematics textbooks available in Guatemala. In effect, the book is the de facto secondary mathematics curriculum. In addition, Sr. Chávez has short class periods of only 35 minutes, and teaches in poorly lit, graffiti-ridden classrooms. So, not only does Sr. Chávez have few resources available to aid his instruction, he also has little time to teach in a poorly maintained facility.

Report cards are distributed every two months. Sr. Chávez bases 50% of his grades on 5 or 6 examinations, and the other 50% on an examination given at the end of the two month period. Students must earn a cumulative average of 60% or higher to pass his classes. There is no final examination at the end of the school year.

One day, Mari and I observed several of Sr. Chávez’ *básico* classes (Middle School classes). Students were in straight rows facing the front of the classroom where Sr. Chávez stood and delivered the lesson in the form of a lecture. In both classes that we observed, almost all of the desks were occupied. Generally, the students were attentive during lectures and on task while working practice problems.

Sr. Chávez began each class by reviewing a factoring problem that the class had been assigned for homework. He was very careful to explain how to solve the problem in a systematic, step-by-step manner. Sr. Chávez then asked his students to solve another problem alone at their desks. What stood out at this point in the lesson to both Mari and I was how willing Sr. Chávez was to help his students. In addition, his students seemed to genuinely respect him. In one class, the bell rang while he was completing an example on the board. Unlike US classrooms, none of the students budged until Sr. Chávez finished his lecture.

**Conclusion**

The research findings at this point demonstrate that Sr. Chávez has little access to new information about alternative models of mathematics pedagogy. I still have much to learn about the Gymnasium, and Sr. Chávez’ goals and pedagogical practices. I plan to return to Guatemala in the summer of 1995 to continue the study.

An auxiliary aspect of this project that has emerged is that Sr. Chávez values my expertise as a mathematics educator. By serving in the dual capacity of researcher and consultant, I can “give something back” to Sr. Chávez throughout the course of this project and provide him with alternative conceptions of mathematics such as those advanced by scholars of ethnomathematics. Without being overly romantic, however, I acknowledge that there are many barriers to ethnomathematics being accepted in developing nations as an appropriate alternative to the highly symbolic and abstract mathematics imported from the First World.

Finally, I cannot stress enough how deeply I respect the work of Sr. Chávez and his colleagues. In light of the difficult conditions at the Gymnasium, Sr. Chávez’ dedicated service of more than 20 years there must be appreciated as a form of professional survival.

Despite the many problems that plague the school, Sr. Chávez continues to attempt to teach his students some mathematics and prepare them for future opportunities.

**References**

Aidoo, A.A. (1991). Critical fictions: *The politics of imaginative writing*. Seattle, WA: Bay Press.

Altbach, P.G., Arnove, R.F., & Kelly, G.P. (1992). *Comparative education*. New York: Macmillan.

Berman, E.H. (1992). Donor agencies and Third World educational development, 1945-1985. In Arnove, R.F., Altbach, P.G., & Kelly, G.P. (Eds.), *Emergent issues in education: Comparative perspectives*. Albany: State University of New York Press.

Bishop, A. (1988). Mathematics education in its cultural context. *Educational Studies in Mathematics*, 19: 179-91.

Carnoy, M. (1974). *Education as cultural imperialism*. New York: McKay.

Carnoy, M. (1982). Education for alternative development. *Comparative education review*, 26, 2, 160-177.

Coombs, P.H. (1985). *The world crisis in education: The view from the eighties*. New York/Oxford: Oxford University Press.

D’Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. *For the Learning of Mathematics*, 5(1), 44-48.

Fasheh, M. (1989). Mathematics in a social context: Math within education as praxis versus within education as hegemony. *Mathematics, education, and society*: Reports and papers presented in the fifth day special programme on “Mathematics, education, and society” at the 6th International Congress on Mathematics Education. Paris: UNESCO.

Klees, S.J. (1986). Planning and policy analysis in education: What can economics tell us? *Comparative education review*, 30, 574-607.

Secada, W.G. (1995). Social and critical dimensions for equity in mathematics education. In W.G. Secada, E. Fennema, & L. Byrd (Eds.), *New directions in equity for mathematics education*. New York: Cambridge University Press.

Simon, J.M. (1987). *Guatemala, eternal spring: Eternal tyranny*. New York/London: W.W. Norton & Company.

Zachariah, M., & Silva, E.T. (1980). Cultural autonomy and ideas in transit: Notes from the Canadian case. *Comparative education review*, 24, 63-72.

Zachariah, M. (1985). Lumps of clay and growing plants: Dominant metaphors of the role of education in the Third World, 1950-1980. *Comparative education review*, 29, 1-21.

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**Report on Ethnomathematics Research**

**Joanna O. Masingila, Syracuse University**

jomasing@sued.syr.edu

There are a variety of researchers doing research work in the area of ethnomathematics. In this article I will describe some current research by several researchers in North America. In future articles in this column, I will report on research in the area of ethnomathematics by researchers in various countries. If you know of researchers doing ethnomathematics research, please send me this information either by mail (215 Carnegie, Syracuse, NY 13244-1150 USA) or by email (jomasing@sued.syr.edu).

Mary (Betsy) Brenner, from the University of California, Santa Barbara, is exploring the distinction between everyday problem solving and mathematicians’ problem solving practices by examining how students use the two modes of problem solving in the context of small group discussions. For this study, she and her colleagues are working with students in two seventh-grade classrooms that are using a curriculum unit that was designed to introduce mathematical concepts involving variables and equations in the context of a thematic problem solving unit.

Marta Civil, from the University of Arizona, is working with colleagues to try to develop mathematics classroom communities in predominantly minority classrooms. In these communities, they are engaging children in doing mathematics (like mathematicians) by working on open ended, investigative situations, sharing ideas and strategies, and jointly negotiating meanings. Civil and her colleagues also are working to have these communities develop from the students’ backgrounds and their experiences with everyday mathematics in an effort to bridge the gap between outside and inside school experiences. Data about the students’ everyday mathematics experiences are collected through household visits.

Sabrina Hancock, from the University of Georgia, recently examined the mathematics practices of four seamstresses. Her research study describes the mathematics she recognized in the skills, thinking, and strategies of the seamstresses as well as documents the skills, thinking, and strategies that they attribute to mathematics. She also compares the mathematics practice of the seamstresses with the mathematics practices of other tradespersons.

Steven Guberman, from the University of Colorado at Boulder, is examining how students understand and transform school mathematics as influenced by their intuitive mathematical knowledge. He has been working with students in three elementary school classrooms by observing during mathematics lessons and then interviewing students about the content and goals of the lessons and how the lessons were related to their intuitive mathematics and its everyday uses.

Jon Rahn Manon, from the University of Delaware, is studying the ethnomathematics of upper elementary North American school children. He is seeking to identify children’s out-of-school mathematics practice and to describe how this lived mathematics interacts with the reified mathematics of the school curriculum. He will also be examining implications for a reformed pedagogy that takes into account this out-of-school practice of children.

Joanna Masingila, from Syracuse University, is examining middle school students’ perceptions of how they use mathematics outside the classroom in an attempt to learn more about and build on students’ everyday mathematics practice in the classroom. Data were collected by interviews, logs, and follow-up interviews. She found that the mathematics that the students perceived that they used outside the classroom could be classified as one of the six activities that Bishop has called the six fundamental mathematical activities. She is also examining the influence of the students’ perceptions of what is mathematics on their perceptions of how they use mathematics.

Michelle McGinn, from Simon Fraser University in Burnaby, British Columbia, recently completed a case study investigating the mathematical activity of two elementary school teachers in different contexts of their everyday lives, inside and outside their classrooms. She found that the teachers’ everyday mathematics practice revealed a marked contrast from mathematics practice legitimated in classrooms, including their own classrooms.

Judit Moschkovich, from the Institute for Research on Learning in Palo Alto, California, has been working on examining the theoretical assumptions underlying two perspectives of mathematics practice: everyday mathematics and mathematician’s mathematics. She has been examining in detail which aspects of school mathematics are compatible with different aspects of everyday mathematics and mathematician’s mathematics with the goal of building a coherent conceptual framework for understanding mathematical practices in different communities and for designing classroom environments.

Andee Rubin and Andrew Boyd, from TERC in Cambridge, Massachusetts, are doing research in a setting where they think it is possible for everyday mathematics and mathematician’s mathematics to coexist in a natural and important interdependence. Their research is part of the VIEW project at TERC (Video for Exploring the World) and they are studying how learners make mathematical sense of motion phenomena in a Video Based Laboratory setting in which their own movements become mathematical data through computer and video technology.

Jim Barta, from Georgia Southern University, will be starting a two phase project with the Seminole people (Florida) to examine from an ethnomathematical perspective, traditional (historical) daily activities in which mathematical principles were embedded. Phase I will be to interview a number of Seminole tribal members, beginning with three well-placed tribal cultural/educational directors and representatives who have knowledge of the daily living practices of their ancestors. They have agreed to facilitate additional contact and interviews with a number of other tribal members (Cultural Center Site Directors, Seminole School Administrators, craftspeople, and elders). The accounts and descriptions they provide will be examined to identify mathematical knowledge and principles necessary to complete such activities. Phase II (to be carried out at a later date) will be predicated on the knowledge base developed resulting from Phase I. Its focus will be to design culturally inclusive mathematics curriculum in collaboration with teachers at the Ahfachkee (Seminole) Elementary School in Clewiston, Florida for their elementary students. Ultimately, the research will impact 72 Ahfachkee Seminole Elementary students.

If readers are interested in contacting any of the researchers listed above, contact me and I will provide you this information.

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**Special Interest Group (SIG) Curriculum & Classroom Activities Meeting in Boston**

The Special Interest Group on Curriculum and Classroom Activities met in Boston prior to the general ISGEm meeting and had a lively and interesting discussion.

It was noted that there are now many publications with multicultural themes for classroom use, but now there is a concern about the quality and relevance of some of these materials. Teachers need to select such materials with care, looking for accuracy, watching out for stereotypical images, and making sure the materials are indeed relevant to the class culture and the mathematical content. It was suggested that we write to publishers, asking “what do you have?” in multicultural mathematics materials; then perhaps we could offer some assessments of the various offerings.

Three members reported activities related to ethnomathematics. Luis Ortiz-Franco has written a report for the Portland Public Schools on “Latinos in Mathematics” and the materials have also been used in some classrooms in southern California quite successfully. Lawrence Shirley continues to chair a Multicultural

Task Force for the College of Natural and Mathematics Sciences at Towson State University; the group is currently planning to analyze general and introductory courses in math and science, to see current and possible use of multicultural curriculum. Also, Shirley went to Cameroon in January to evaluate a secondary math/science education project of the Peace Corps. One of his recommendations was that Peace Corps trainees learn more about ethnomathematics to use in their teaching and curriculum development. Claudia Zaslavsky distributed notices of her two new books, *Multicultural Math: Hands-On Activities from Around the World*, published by Scholastic Professional Books, and *Fear of Math: How to Get Over It and Get On with Your Life!*, published by Rutgers University Press. She is currently working on another book.

The SIG is being asked to gather a ten-year survey of literature on its own particular area of ethnomath. Shirley will coordinate this but will seek input from members. Part will be based on a review of articles in the Newsletters of the past ten years.

There was an open discussion on the question: What is the difference between “multicultural math” and “ethnomathematics”? Many seemed to feel that for several reasons, “multicultural math” is a subset of “ethnomath”. Ethnomath was seen as a basis for multicultural math, a more theoretical foundation. Also, it seems that multicultural math is usually seen as a pedagogical aspect or a school application of the much broader domain of ethnomath. In the school context, especially judging from the curricular materials available, it seems that multicultural math refers mainly to the ethnic aspects of mathematics, while ethnomathematics looks at math in a more general definition of culture, including ethnic culture, but also occupational, age, and other characteristics that can define a culture. In fact, there are particular culture OF mathematics: a varied community/culture/collegiality of pure mathematicians, statisticians, mathematical physicists, economists, etc., as well as teachers and students at all levels. Members of each subgroup may have different views of mathematics and its role in their lives.

A related issue also generated comment: the role of multiculturalism and ethnomathematics in empowering learners by offering mathematics as a tool for their advancement. Where is the line between teaching mathematics for empowerment and teaching political values through mathematics? This is an issue where ISGEm and the CriticalMath group overlap. It is an issue that needs more discussion.

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**Notes from the NCTM Delegate Assembly**

The NCTM Delegate Assembly consists of representatives from every affiliated group of NCTM, including the International Study Group on Ethnomathematics.

Several months ago, ISGEm had proposed two resolutions (which were reported in last fall’s *Newsletter*) for the Delegate Assembly. One was to establish an NCTM Committee on Math and Culture. However, the board considering resolutions noted that NCTM was already working in this area and in particular said that some of the areas of concern of such a committee were being handled by the Committee for a Comprehensive Mathematics Education of Every Child. Although ISGEm really had a different idea for a Math and Culture committee, this resolution made no progress.

The second resolution from ISGEm was to reconstitute the International Affairs Committee. The Board’s response was that the duties of such a committee were being handled by one person, called the International Representative, appointed for a three-year term. The current representative is Jerry Becker of Illinois. We also learned that NCTM has a relationship with math education organizations in thirteen other countries, and interest in similar relationships has been expressed by representatives of groups in several other countries. Hence this resolution also was not recommended for consideration, though it did at least appear on the agenda. After the Assembly, discussion with the current International Representative, Jerry Becker, yielded two important points: first, he would indeed like to have a full committee to assist him with his duties; and second, the NCTM President, in plans to rearrange the committee structure, favors the re-establishment of the International Affairs Committee. Hence, Becker urged ISGEm to submit the proposal again next year, aided in preparing its rationale by this additional information.

Several of the other resolutions of the Delegate Assembly related to administrative details, especially those involved with hosting the national and regional conferences. Another urged greater contacts between NCTM and various organizations of school boards, superintendents, and principals. Another resolution was to require NCTM conference presenters who feature materials from commercially available programs to identify the programs in their session titles. This passed after some discussion. Another, which would have established a new scholarship program named after retired Executive Director Jim Gates, failed to pass, mainly because there was much confusion about how it would be administered (even Jim Gates opposed it!).

Prior to the formal Assembly, affiliated groups met in caucus sessions according to geographic regions. ISGEm, not associated with a geographic region, joined other similar groups in the Non-Regional Caucus. Other member groups included Women in Math Education, the Banneker Society, the group on Logo and technology, and some groups of math supervisors. This allowed discussion of common problems, notably the difficulties of scheduling and announcing meetings and group sessions which are held during the national NCTM meeting. Also, the affiliated groups were reminded that NCTM would provide support to groups which held a joint campaign for group and NCTM membership, and that funds may also be available for special projects of the groups.

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**Adults Learning Maths: A Research Forum (ALM)**

**Diana Coben
Goldsmiths College, University of London
**aea01dcc@gold.ac.uk

What is ALM?

Adults Learning Maths: A Research Forum (ALM) is a new international research forum bringing together researchers and practitioners in adult mathematics/numeracy teaching and learning to share ideas, information and research findings in order to promote the learning of mathematics by adults. ALM now has members in the USA, Australia and continental Europe as well as the UK.

What has ALM got to do with ethnomathematics?

Ethnomathematics focusses on mathematics cultures in context, whether that context is the street, the workplace or anywhere else where people function mathematically – all of which is of vital interest to adult mathematics educators and researchers. We welcome members who are involved in ethnomathematical research and we are keen to network with ISGEm and other organisations which share our interest in research on adults learning mathematics.

Where can I find out more about ALM?

Details of ALM are in the ALM Newsletter, on the Internet on <numeracy@world.std.com>; copies of the ALM Newsletter, are also available from Diana Coben at the address below. Copies of ALM-1 1994. Proceedings of the Inaugural Conference of Adults Learning Maths: A Research Forum (1995) ISBN: 0 901 542 78 4 are now available – one copy will be sent free to current ALM Individual members and everyone who attended the ALM-1 conference. Individual membership is 10 sterling per year, ALM-1 costs 5 sterling per copy including postage and packing (please make cheques out to Goldsmiths College). Contact: Dr Diana Coben, Department of Educational Studies, Goldsmiths College, University of London, New Cross, London SE14 6NW, UK, fax: +44 (0)171 919 7313, Email: aea01dcc@gold.ac.uk. *You may pay in US dollars as follows: Individual member: $16; ALM-1 Conference Proceedings: $8. Please send your order with a US$ check (made out to Kathy Safford) to Kathy Safford, Graduate School of Education, Rutgers State University of New Jersey, 10 Seminary Place, New Brunswick, NJ 08903, USA. Thanks.

What next for ALM?

ALM continues to expand and ALM-2, the second ALM conference, will be held July 7-9 1995 at the University of Exeter, Exeter, UK. The provisional programme includes:

Keynote Address – *Images of Mathematics, Values and Gender* Paul Ernest

*Mathematics: Certainty in an Uncertain World?* Roseanne Benn

*Knitting Tensions: the Prescriptive Versus the Visual* Sandy Black

*Maths Life History: A Case Study* Diana Coben and Gillian Thumpston

*Mathematics in Women’s Work: Making it Visible* Mary Harris

*Trying to Understand Their Thinking* Janet Duffin and Adrian Simpson

*Tutors and Students Muddling Through Together – Why Do Two Minuses Make a Plus?* Joan O’Hagan

*Algebra for Adults: The Voices of the Students* Kathy Safford

*Adults Learn Maths in Austria* Jurgen Maa and Wolfgang Schliglmann

*Technological Competence and Mathematics* Tine Wedege

*The Adult Numeracy Teacher Research Project in Massachusetts* Mary Jane Schmitt.

All are welcome, reductions for ALM Individual members. For details and to book your place, please contact: Anne Chammings, CET Division, DCAE, University of Exeter, Cotley, Streatham Rise, Exeter, Devon EX4 4PE, UK. tel. +44 (0)1392-411906, fax. +44 (0)1392-436082

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**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.

Millroy, Wendy Lesley, ** An Ethnographic Study of the Mathematical Ideas of a Group of Carpenters**, Cornell University, doctoral dissertation, 1990. (Also published by NCTM as

*Journal of Research in Mathematics Education Monograph No. 5*, 1992.)

An example of research on how mathematics is learned and used within cultures on an everyday basis. The carpenters involved in this study represent a “diverse spectrum of South African cultural backgrounds and language groups”.

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Brenner, Mary E., ** Arithmetic and Classroom Interaction as Cultural Practices Among the Vai of Liberia, **University of California-Irvine, doctoral dissertation, 1985.

Brenner, Mary E., **“The Practice of Arithmetic in Liberian Schools”**, *Anthropology and Education Quarterly*, 16, 1985, p. 177-186

Another example of ethnomathematical work on a dissertation. This research shows not only the traditional mathematical practices of the Vai of Liberia, but how elementary students reconcile those practices in the school setting.

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Gerdes, Paulus (ed.). ** Explorations in Ethnomathematics and Ethnoscience in Mozambique**, Instituto Superior Pedagógico, 1994.

Among the articles in this edited volume are:

*On the Origin of the Concepts of “Even” and “Odd” in Makhuwa Culture*, Abdulcarimo Ismael

*Mathematical-educational exploration of traditional basket weaving techniques in a Children’s “Circle of Interest”*, Marcos Cherinda

*Popular counting methods in Mozambique*, Daniel Soares & Abdulcarimo Ismael

*How to handle the theorem 8+5=13 in (teacher) education?*, Jan Draisma

*Symmetries and metal grates in Maputo – Didactic experimentation*, Abílio Mapapá

_______________________________

**ICME-8**

**Seville, Spain, July 14-21, 1996**

The 8th International on Mathematics Education will be held in Seville, Spain, July 14-21, 1996. For more information write:

ICME-8

Apartado de Correos 4172

E-41080 Sevilla

SPAIN

e-mail: icme8@obelix.cica.es

_______________________________

**ISGEm Distributors**

The following individuals print and distribute the *ISGEm Newsletter* in their region. If you would be willing to distribute the *ISGEm Newsletter* please contact the Editor.

**ARGENTINA**, María Victoria Ponza, San Juan 195, 5111 Río Ceballos, Provincia de Córdoba

**AUSTRALIA**, Jan Thomas, Teacher Education, Victoria University of Technology, P.O. Box 64, Footscray, VIC3011

**AUSTRALIA**, Leigh Wood, PO Box 123, Broadway NSW 2007

**BOLIVIA**, Eduardo Wismeyer, Consulado de Holanda, Casilla 1243, Cochabamba

**BRAZIL**, Geraldo Pompeu jr, Depto de Matemática, PUCCAMP, sn 112 km, Rodovia SP 340, 13100 Campinas SP

**FRANCE**, Frédéric Métin, IREM, Moulin de la Housse, 51100 Reims

**GUADALOUPE**, Jean Bichara, IREM Antilles – Guyane, BP 588, 97167 Pointe a Pitre, CEDEX

**GUATEMALA**, Leonel Morales Aldaña, 13 Avenida 5-43, Guatemala, Zona 2

**ITALY**, Franco Favilli, Dipartimento di Matematica, Universita di Pisa, 56100 Pisa

**MEXICO**, Elisa Bonilla, San Jerónimo 750-4, México DF 10200

**NEW ZEALAND**, Andy Begg, Centre for Science & Math Ed Research, U of Waikato, Private Bag 3105, Hamilton

**NIGERIA**, Caleb Bolaji, Institute of Education, Ahmadu Bello University, Zaria

**PERU**, Martha Villavicencio, General Varela 598, Depto C, Miraflores, LIMA 18

**PORTUGAL**, Teresa Vergani, 16 Av. Bombeiros Vol., 2765 Estoril

**SOUTH AFRICA**, Adele Gordon, Box 32410, Braam Fontein 2017

**SOUTH AFRICA**, Mathume Bopape, Box 131, SESHESO, 0742 Pietersburg

**UNITED KINGDOM**, John Fauvel, Faculty of Math, The Open University, Walton Hall, Milton Keynes MK7 6AA

**VENEZUELA**, Julio Mosquera, CENAMEC, Arichuna con Cumaco, Edif. SVCN, El Marques – Caracas

**ZIMBABWE**, David Mtetwa, 14 Gotley Close, Marlborough, Harare

**ISGEm Executive Board**

Gloria Gilmer, President

Math Tech, Inc.

9155 North 70 Street

Milwaukee, Wl 53223 USA

gilmer@cs.uwp.edu

Ubi D’Ambrosio, 1st Vice President

Rua Peixoto Gomide 1772 ap. 83

01409-002 São Paulo, SP BRAZIL

ubi@usp.br

Alverna Champion, 2nd Vice President

4335-I Timber Ridge Trail

Wyoming, MI 49509 USA

champioa@GVSU.EDU

Luis Ortiz-Franco, 3rd Vice President

Dept of Math, Chapman University

Orange, CA 92666 USA

Maria Reid, Secretary

145-49 225th St

Rosedale, NY 11413 USA

marbm@cunyvm.cuny.edu

Anna Grosgalvis, Treasurer

Milwaukee Public Schools

3830 N. Humboldt Blvd.

Milwaukee, WI 53212 USA

Grosgalvis@aol.com

Patrick (Rick) Scott, Editor

College of Education

U of New Mexico

Albuquerque, NM 87131 USA

scott@unm.edu

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, NCTM Representative

Dept of Mathematics

Towson State U

Towson, MD 21204-7079 USA

E7M2SHI@TOE.TOWSON.EDU