Paulus Gerdus, Rector of the Universidade Pedagógica in Mozambique, has been informed that his work entitled "Women and Geometry in Southern Africa. Some Suggestions for Further Research" was selected to receive "Special Commendation" in the 1996 Noma Award for Publishing in Africa competition.
The book was praised by the jury as "combining in an ingenious way the study of geometry with that of the visual arts, presenting an important challenge and stimulant to the future of mathematics education in Africa. It demystifies mathematics in relation to gender and race, and erases the borders between mathematics and popular culture as experienced in the work and crafts of women in southern Africa. The book's importance lies in its prospective impact on the education of African women in mathematics".
If you wish to congratulate Paulus personally, this year he is a Visiting Professor at the University of Georgia, 105 Aderhold Hall, Athens, Georgia 30602-7124, USA, firstname.lastname@example.org.
Minutes of the ISGEm Meeting at ICME 8
Seville, Spain, Wednesday, July 17, 1996, 17:00-18:30
Sunday Ajose (USA) welcomed the approximately 50 people who were present and announced the new officers for ISGEm: Ubiratan D'Ambrosio (Brazil)-President, Maria Luiza Oliveras (Spain)-1st Vice President, Jolene Schillinger (USA)-2nd Vice President, Abdulcarimo Ismael (Mozambique)-3rd Vice President, Gelsa Knijnik (Brazil)-Secretary, Rick Scott (USA)-Newsletter Editor, Jim Barta (USA)-Treasurer, Lawrence Shirley (USA)-NCTM Representative.
Sunday then turned the meeting over to the new president, Ubi, who provided an introduction to ISGEm, including the history of the group. Ubi also discussed the present and future situation of developing regional chapters of ISGEm. Ubi introduced Joanna Masingila (USA) who is the chair of the North American group planning ISGEm activities at the 1997 NCTM meeting.
Luis Ortiz-Franco (USA) was introduced by Ubi and then stated the recently approved constitutional amendment and the group discussed the implications of the amendment. Sunday Ajose was asked to talk briefly about the four special interest groups that have functioned within ISGEm: theoretical issues, curriculum, out-of-school applications, and research.
Following a few announcements about other sessions at ICME that might be of interest to ISGEm members, the group discussed questions that were posed by different persons present. One question that generated a lot of discussion was: What is our response to critics who say we should not pay attention to ethnomathematics?
Some responses to this question were:
unless we present ethnomathematics as not limiting students' mathematical learning, we will be open to critics' erroneous interpretations.
ethnomathematics is appealing to the intimate cultural roots of each individual as an integrated part of the cognitive process. This is analogous to language; in order to interact with the dominant culture we need to speak English. However, no one suggests that we should forget our mother tongue. It is the same with mathematics.
Prepared by Joanna O. Masingila, Syracuse University
Report on Ethnomathematics Research
Joanna O. Masingila, Syracuse University
This column reports on current research in the area of ethnomathematics. If you know of researchers doing ethnomathematics research, please send Joanna Masingila this information: 215 Carnegie, Syracuse, NY 13244-1150 USA (email@example.com).
Karen Fuson, Tamara Perry and Pilar Ron, from Northwestern University, have been investigating the developmental sequence of addition solution procedures among Spanish-speaking children in which the fingers and number words function in ways opposite to that found in English-speaking children. The Spanish-speaking children in these classroom studies are from families that have emigrated from Mexico, Central America or South America. Fuson and her colleagues have found that unlike the unitary English solutions, these Spanish solutions have the potential to support children's finger and mental solutions structured around ten; these methods are efficient and conceptually helpful for multidigit computation.
Franco Favilli and Jama Musse Jama, from Universita di Pisa, are studying the process of creating mathematical terminology in the Somali language. Somali language was developed and transmitted only through oral means until about twenty years ago. Since 1972, when it gained a national orthography using Latin letters and was instituted as the official language of Somalia, it has been the medium of instruction in all pre-university education. To meet the needs of instruction and all the scientific and technological needs, the Somali language has been rapidly modernized. In mathematics, many words in Somali were created by adapting terms from English or Italian mathematical terminology to Somali phonetics. Some of these words were created so artificially that Somali students and mathematicians themselves have difficulty in understanding their meaning. Other mathematical terms were introduced by using words from the Somali culture that refer to aspects from the real world. However, as Favilli and Jama have found, this also causes confusion for students because sometimes the terms that are chosen for plane figures refer to real world three-dimensional objects. For example, the Somali word "Qabaal" has been chosen to mean ellipse. However, in the Somali everyday language a qabaal is a wooden container crafted from tree trunks and used to give water to camels. Favilli and Jama call for revision of the mathematical terminology so that students will be able to create meaning for the mathematical terms that does not conflict with the meaning that they have for these terms from their everyday experiences.
Colleen McMurchy-Pilkington, from Auckland College of Education in New Zealand, has been examining Maori women's everyday mathematical reasoning. Maori women (indigenous people of New Zealand) are seen by others in their society as non-mathematics users. Statistics indicate that they are generally not achieving in mathematics and they do not pass national exams in mathematics, more often leaving school around the age of 15 years old before the examination time. McMurchy-Pilkington found the Maori women to be competent mathematically in using proportional reasoning, negotiating ratios, planning and budgeting skills in preparing large meals (for up to 1,000 people) as part of the tribal customs surrounding a funeral. Although they sometimes use school mathematics to solve problems, she found that the Maori women have developed their own ways of solving problems that involve complex calculations. McMurchy-Pilkington urges more research in this area to help teachers develop ways of helping Maori girls connect their in-school and out-of-school mathematical knowledge and use this as a bridge to further mathematics.
1996 NCTM Delegate Assembly Resolution
Larry Shirley, ISGEm's NCTM Delegate
The following resolution we presented to the NCTM Delegate Assembly last April. It was not approved. I plan to re-submit it for the Delegate Assembly in Minneapolis.
Be it resolved that: the Board of Directors reconstitute a committee to work with international issues of mathematics education.
Rationale: North American mathematics education cannot stand alone in the world. There is much we can learn and much we can contribute by reaching beyond our borders to the world mathematics education community. Already NCTM has thirteen reciprocal relationships with "corresponding societies"-national mathematics education organizations around the world-, and interest has been expressed by organizations in several other countries. Also, there is an appointed international representative of NCTM. An international committee can strengthen such outreach by assisting the International Representative in maintaining the formal links and encouraging increased informal ties to these other mathematics education organizations and to individuals in other countries. This can strengthen the role of NCTM in international committees, encourage exchange of curricular and instructional ideas, assist researchers in gaining a more global view of mathematical experience, and help build a broader viewpoint for North American teachers and students.
Administratively, this committee could also provide a stronger base for affiliates of NCTM which have international links and for continued participation in the International Commission on Mathematical Instruction.
On the ISGEm Membership Form we ask people to describe any projects they are working on related to Ethnomathematics. Below we have reproduced some of that information to encourage communication among individuals with similar interests.
Dr. Indira Chacko, U of Papua New Guinea, PO Box 1078, Goroka, Papua New Guinea.: Traditional counting systems in Papua New Guinea and the uses in the society.
Martha Allexsant-Snider, 107 Layle Lane Watkinsville, GA 30677 USA. I'm working with an NSF funded teacher development project that incorporates ethnomathematics in professional development experiences for elementary teachers.
Maurice Bazin, Ave Edison Passos 15/20520531-070 Rio de Janeiro, BRAZIL. Just published "Math across Cultures".
Bonnie Berken, Math Department, St. Norbert College, 100 Grant Street, De Pere, WI 54115-2099 USA. Strip Symmetry Patterns in Wisconsin Woodland Indian Beadwork, curriculum development in the area of multicultural mathematics.
Mary E. Brenner, Department of Education, University of California, Santa Barbara CA 93106 USA. African mathematical thinking and its relationship to classroom math. Development of pre-algebra curriculum that taps into students' everyday math knowledge.
Anne Carrington, University of South Australia, St. Bernards Rd,, Magill, AUSTRALIA. Creating/teaching a mathematics background for teachers of children up to 8 years old. This is intended to make student teachers explore situational mathematics in dance, sports, driving.
Marta Civil, Mathematics Department, University of Arizona, Tucson, AZ 85721 USA. I work with ethnic minority students (mostly Mexican origin) and their teachers and families trying to develop an approach to math education that reflects their experiences and knowledge as resources for learning. I am interested in aspects of culture and mathematics, particularly as it relates to groups who have not "traditionally done well."
Bill Collins, Syracuse City School District, 312 Oswego St,.Syracuse NY 13204 USA. Classroom (K-12) implications in math.
Ron Eglash, 1133 Highland Street, Columbus OH 43201 USA. African Fractals.
Connye LaCombe, 1284 Smith Ave. SW, St. Paul, MN 55118-2045 USA. Ongoing study of cultural impacts on student understanding.
Paul Laridon, Mathematics Department, University of the Witswatersrand, P.B. 3, Wits, 2050 SOUTH AFRICA. A research project relating Ethnomathematics to the curriculum of South Africa.
Dr. Shirley A. Leali, 4566 South Monroe Blvd., Ogden, Utah 84403 USA. Gender Equity -Math/Sci/Tech.
Jerry Lipka, University of Alaska, School of Education, 7th Floor, Gruewing Building, Fairbanks, AK 99725 USA. We are working with Yupik elders and Yupik teachers in the process of developing Yupik based math and pedagogy.
Karen Dee Michalowicz, 5855 Glen Forest Drive, Falls Church, VA 22041 USA. Native American Mathematics
Clo Mingo, Route 5, Box 297, Sante Fe, NM 87501-9311 USA. Anasazi mathematics, sundials, etc.
Lina Maria Monteiro Vicente, R. Vieira Lusitano, 10 1 E Damaia, 2720 Amadora, PORTUGAL. I work in a project with young people from Africa.
Swapna Mukhopadhyay, 122 Miller Hall, Box 353600, University of Washington, Seattle, WA 98195 USA. Teaching graduate classes entitled "Mathematics as a Cultural Expression", and "Mathematics for the Multicultural Mind". Research on the Hmong community.
Nancy A. Nutting, 7429 - 16th Ave., S. Richfield MN 55423 USA. Multicultural mathematics teaching, especially at the elementary level.
Norma C. Presmeg, Curriculum & Instruction, Florida State University, Box 3032, Tallahassee, FL 32306-3032 USA. Following the principles of the graduate Ethnomath. course I teach, we are involved in research with high schools to investigate optimal ways of introducing ethnomath in high school math classrooms.
Dr. Schindar S. Sachdev, Professor and Chair, Dept. of Math and Computer Science, Elizabeth City State University, Elizabeth City, NC 27909 USA. Writing a book on geometry / Contributions made by African American mathematicians.
Patricia Schmidt, 101 Reilly Hall, Le Moyne College, Syracuse, NY 13214 USA. I teach graduate and undergraduate multicultural ed. course. I am presently gathering data related to cross/cultural analysis.
Joel E. Schneider, Children's Television Workshop, 1 Lincoln Plaza, New York, NY 10023 USA. Our TV math game show is in production in Jakalta, expected to premiere in April. The ?rush? version has been on the air since January 1995 and drawing large audiences.
Dr. Karen Schultz, Georgia State University, COE, Dean's Office, 30 Pryor St. 10th Floor, Atlanta, Georgia 30303 USA. The German Teacher Exchange, The Ivory Coast Project, The Egyptian Teacher Visitor Program, The International Consortium of Urban Teacher Educators.
Frederick L. Uy, 205-14 50th Avenue, Bayside NY 11364-1047 USA. I continue doing lessons in geometry using a multicultural approach.
Betsey S. Whitman, Framingham State College, 100 State Street, Framingham MA 01702 USA. "Gender streaming" mathematics classes in Standard 6, 7, and 8 in Malawi (Central Africa).
Geometry in the Middle Grades: A Multicultural Approach
Frederick Lim Uy
The following is the abstract of dissertation work being done by the author. For further information he can be contacted at 205-14 50th Avenue, Bayside NY 113641047 USA.
After appropriate research, the investigator created 18 geometry lessons using a multicultural approach. The lessons were designed to replace portions of a middle grades geometry curriculum dependent upon standard textbooks and were piloted in an independent New York City school. The study involved 46 students and lasted for six weeks.
The lessons were divided into four units; at the start of each, students were given a mathematical pre-assessment. After the entire unit had been taught, the students completed a post assessment on both the mathematical and the cultural topics. Additionally, students were asked to complete a questionnaire and were interviewed. The investigator maintained a daily log of his observations throughout the field trial. Finally, a five-member jury reviewed the lessons and completed an evaluation form supplied by the investigator.
This study supported the claims that (1) students appreciate the contributions of cultures that are different from their own, and (2) linking the study of mathematics with other disciplines and cultures provides more meaning to the mathematics studied. When students were asked why they enjoyed the multicultural approach, most indicated that they saw uses and applications of mathematics outside the classroom and in other cultures that they had not encountered in previous mathematics classes. Also, the students appeared to realize that certain mathematics topics could be connected to other disciplines.
The results of this study suggested that many students appreciated the mathematics topics because they saw a direct and human way of applying them. The students appeared to be highly motivated and involved with the lessons, and classroom discussions were lively with broad participation.
The jury indicated that (1) there was a nice flow of topics, (2) the sequencing of the lessons was adequate and moved from less difficult to more difficult, and (3) the lessons were appropriate for middle grades. The jury members suggested that there should be more in-depth cultural and historical background for each lesson and agreed that the materials fostered awareness, appreciation, and acknowledgment of other cultures.
Preview of ISGEm Activities at 1997 NCTM Meeting
An ISGEm session for the NCTM 75th Annual Meeting (April 17-21, 1997) in Minneapolis entitled Teaching and Assessing African American Students: Illustrated with African Fractalshas been arranged. This presentation models approaches to teaching and assessment traditionally used in African-American schools and which resulted in the development of strong mathematics students. These strategies will be illustrated using African fractals and technology. The presenters are Gloria Gilmer and Ron Eglash.
As has become a custom, an ISGEm Business Meeting will be held. The main item of business will be discussion and voting on the creation of a North American chapter of ISGEm. If the chapter is approved, officers will be elected.
Below is the Treasurer's Report promised in the last issue of the Newsletter.
Statement of Operations - January 1, 1996 through October 31, 1996
Membership, Compendium, & Contributions $2353.00
Total Income: $2369.98
Newsletter & mailing & supplies $1524.64
NCTM Affiliation Dues $80.00
Returned checks $20.00
Bank Service Fees** $219.00
Federal Tax(Bank deduction) $2.45
Total Expenses: $1846.09
January 1, 1996 Bank Balance: $370.72
Net Income: $523.89
Balance October 31, 1996: $894.61
Program Director Positions
Division of Elementary, Secondary, and Informal Education
National Science Foundation
The Division of Elementary, Secondary, and Informal Education (ESIE) of the National Science Foundation (NSF) seeks qualified applicants for Program Director positions in its Teacher Enhancement, Instructional Materials Development, and Informal Science Education programs. Temporary positions (of one-to-two year duration) will become available starting in late Summer 1997. Applicants must hold a Ph.D. or have equivalent experience in the following disciplinary or related education areas at the grades K-12 level:
Science (elementary grade levels)
Informal Science Education (with expertise in community-based organizations).
Salary range is from $52,867 to $97,366 annually; locality pay adjustments are available. Applicants must submit a resume, current salary information, and up to three letters of recommendation by December 1, 1996 to ATTN: Ms. Nina Beard, National Science Foundation, Division of Human Resource Management, Suite 315, 4201 Wilson Blvd., Arlington, VA 22230. For general information regarding the application process, call Ms. Beard at (703) 306-1185 (x3026). For information about ESIE and its programs, contact Dr. Joseph Stewart, Program Director, at (703) 306-1620. NSF is an equal opportunity employer committed to employing a highly qualified staff that reflects the diversity of our nation.
"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.
Calinger, Ronald. Classics of Mathematics, Prentice Hall, 1995.
This edited volume of readings contains more than 130 selections from eminent mathematicians from A `h-mose' to Hilbert and Noether. The chapter introductions comprise a concise history of mathematics based on critical textual analysis and the latest scholarship. Each reading is preceded by a substantial biography of its author. The publisher suggests that it "takes a multicultural approach and draws on the new field of ethnomathematics, examining topics like mathematical tablets from Old Babylon and papyri from pharaonic Egypt, the rise of theoretical mathematics in classical Greece, and mathematics in medieval Islam, traditional China, India, and Mayan America".
Crump, Thomas (1990). The Anthropology of Numbers. Cambridge University Press, Cambridge.
This book in the Cambridge Studies in Social and Cultural Anthropology is suggested to be of
interest to those in the "adjacent discipline" of "mathematical social science". It includes the
The ontology of number
The cognitive foundations of numeracy
Number and language;
Cosmology and ethnoscience
Economy, society and politics
Measurement, comparison and equivalence
Music, poetry and dance
Games and chance
Art and architecture
The ecology of number.
Oliveras, María Luisa, Etnomatemáticas: Formación de Profesores e Innovación Curricular[Ethno-mathematics: Teacher Preparation and Curricular Innovation], Granada, Spain: Editorial Comares (Polígono Juncaril, Condominio Recife, parcela 121, nave 11, 18210 Peligros, Granada, Spain), 1996.
This is the publication of the work done as a doctoral dissertation in the Department of Mathematics Teaching at the University of Granada. The study establishes the interrelationship between Ethnomathematics, teacher preparation, and school mathematics curriculum. It has an extensive appendix of drawing and photographs of geometric forms found in the work of local artisans.
Rauff, James V. My Brother Does Not Have a Pickup: Ethnomathematics and Mathematics Education. Mathematics and Computer Education, v30 n1 p42-50 Win 1996.
Rauff discusses mathematics education in a cultural context and presents guidelines for mathematics education that values cultural diversity.
Pinxten, Rik. Ethnomathematics and Its Practice. For the Learning of Mathematics, v14 n2 p23-25 Jun 1994.
Pinxten, a Belgium anthropologist, discusses the question of whether to teach traditional school mathematics or develop the mathematics as the set of skills and procedures that a cultural group knows and uses in life. He offers suggestions using examples his from field work with Navajo Indians in the Southwestern United States and Turkish immigrants in Belgium.
Arthur Powell and Marilyn Frankenstein (eds.). Ethnomathematics: Challenging Eurocentrism in Mathematics Education is to be published in April 1997 by The State University of New York Press.
ISGEm Home Page on the World Wide Web
Ron Eglash announces that the ISGEm Home Page is now available for browsing. The URL is
We hope that it will soon have a link to past issues of this Newsletter.
And as long as you are out surfing the Web you might take a look at the following sites:
Symmetry Patterns of
the Wisconsin Woodland Indians
Kim Nishimoto and Bernadette Berken
St. Norbert College
Mathematics is the study of patterns. Patterns abound in nature. Frequently the patterns observed in nature are adapted and utilized by humans in a variety of artistic and creative endeavors. This unit attempts to make connections between the patterns used in strip or border designs by Wisconsin woodland Indians and the mathematics behind these patterns. It focuses on symmetry patterns in strip or border designs and is a result of a project we pursued involving the study and classification of beadwork of Wisconsin woodland Indians. Because of the extensiveness of the beadwork available, we focused on beaded strip designs, the designs that appear in the borders of garments or on belts, garters, necklaces, bracelets, bandolier straps, etc. We wanted to see whether Wisconsin woodland Indians utilized all of the seven mathematically different symmetry patterns in their strip beadwork. In addition, we wanted to see how they utilized the various symmetry patterns.
Mathematicians can describe the balance or symmetry of something by using the idea of rigid motion or isometry. A rigid motion is a transformation in space or in a plane in which the original figure and the image of the original figure are congruent. There are four kinds of rigid motions in the plane. These four rigid motions are a) reflection in a line, b) rotation, c) translation and, d) glide reflection.
The simplest isometry, called bilateral symmetry, or mirror-symmetry, is reflection across a line. A figure with bilateral symmetry looks the same on both sides of a line except that the two sides of the figure are mirror images of each other. Figure 1a shows an example of a figure with a vertical line of symmetry. Figure 1b shows an example of a figure with a horizontal line of symmetry. Figure 1c shows an example of a figure with both vertical and horizontal lines of symmetry.
A second equally simple type of rigid motion is rotation. If a figure has rotational symmetry it will have a center about which it can be rotated by a certain angle without changing its overall appearance. Figure 2 shows an example of a figure with rotational symmetry. For a strip pattern, the only possible angle rotation is through an angle of 180 degrees. Otherwise, the strip pattern will not be preserved.
Translation is the third type of plane isometry. In
this rigid motion, the figure slides a certain
distance in a certain direction. Only an infinite
figure can be translated without undergoing a
change in its appearance. Figure 3 shows a patten
with translational symmetry. Note that the figure
repeats itself indefinitely along the strip.
The last rigid motion, glide reflection, is not as simple or familiar as the first three. It is really a combination of two motions: a glide or translation some particular distance along a line followed by a reflection across that same line. If you were to consider the pattern that your footprints leave in the snow you could see a simple example of a pattern that exhibits glide reflection symmetry.
Because every strip pattern can be constructed from one of these four kinds of rigid motion, a simple system for classifying patterns easily evolves. This method of classification has been used for a long time and in fact was first developed by crystallographers who wanted to classify the three-dimensional patterns that were found in crystals.
Classification of strip patterns in the plane is a simple process requiring no complex tools. There are only seven one-dimensional strip pattern types possible that result from the various rigid motions utilized.
The seven one-dimensional strip pattern types can be classified using a 4-character classification. The first character for a strip pattern is always a "p". The second character indicates whether or not the pattern exhibits vertical symmetry. The second character is an "m" if the pattern has a vertical line of symmetry. Otherwise the second character is a "1". The third character gives information about the horizontal/glide symmetry of the pattern. The third character is an "m" if the pattern exhibits a horizontal line of symmetry. The third character is an "a" if the strip pattern has a glide reflection but not a horizontal line of symmetry. Otherwise the third character is a "1". The fourth character is a "2" if the pattern has a point of 180 rotational symmetry. Otherwise the fourth character is a "1".
These 4-character classification codes thus give complete information about the mathematical symmetry ele-ments of any conceivable strip pattern. Consider the two beadwork patterns below. Although very different to look at, both are mathematically equivalent in terms of the symmetry elements they possess. Both can be classified as pmm2.
A simple flow chart can be used to easily classify
any strip pattern with this 4-character code. This flow chart is presented by Dorothy K. Washburn
and Donald W. Crowe, and is more completely described in Symmetries of Culture: Theory and
Practice of Plane Pattern Analysis, published by the University of Washington Press.
In all, we examined, photographed, and classified 210 Wisconsin woodland Indian specimens from collections of the Neville Public Museum of Brown County and the State Historical Society of Wisconsin. Of these, there were 148 true strip beadwork specimens which represented all major woodland Indian tribes in Wisconsin. We found that Wisconsin woodland Indians utilized all seven of the mathematically different strip symmetries in their beadwork. As we anticipated, patterns having both vertical and horizontal lines of symmetry were most frequently utilized. Nevertheless, it is important to note that all seven types of strip symmetries were utilized. What was most amazing to find were the many unique patterns that all exhibited the same mathematical symmetry.
Table 1 shows the distribution of the strip symmetry patterns that we encountered in our project.
TABLE 1Wisconsin Indian Beadwork Strip Patterns from Collections of Neville Public Museum
of Brown County and The State Historical Society of Wisconsin.
Beauty, art, mathematics: all three interconnected in the beaded strip patterns of woodland
Wisconsin Indians. These beaded treasures represent the blending of culture and knowledge and
provide a glimpse of some of the mathematics of Wisconsin woodland Indians.
Washburn, D.K. and Crowe, D.W. (1988). Symmetries of Culture: Theory and Practice of Plane Pattern Analysis. Seattle and London: University of Washington Press.
Preview of ISGEm Activities at 1997 NCTM Meeting
An ISGEm session for the NCTM 75th Annual Meeting (April 17-21, 1997) in Minneapolis entitled: Teaching and Assessing African American Students: Illustrated with African Fractalshas been arranged. This presentation models approaches to teaching and assessment traditionally used in African-American schools and which resulted in the development of strong mathematics students. These strategies will be illustrated using African fractals and technology. The presenters are Gloria Gilmer and Ron Eglash.
As has become a custom, an ISGEm Business Meeting will be held. The main item of business will be discussion and voting on the creation of a Nortn American chapter of ISGEm. If the chapter is approved, officers will be elected.
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, Fundación Cresinvio, Calle Javier de la Rosa 567, Prov de Santa Fe.
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, Enrique Jemio, UNST-P, Casilla 5747, Cochabamba
BRAZIL, Geraldo Pompeu jr, Depto de Matemática, PUCCAMP, sn 112 km, Rodovia SP 340, 13100 Campinas SP
COSTA RICA, Leslie Villalobos, EARTH, Apartado 4 442-1000, San José
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
NORTHERN IRELAND, School of Psychology, Queens University, Belfast BT7 INN
PERU, Martha Villavicencio, General Varela 598, Depto C, Miraflores, LIMA 18
PORTUGAL, Teresa Vergani, 16 Av. Bombeiros Vol., 2765 Estoril
SOUTH AFRICA, Mogege David Mosimege, University of the North, Private Bag 1106, Sovenga 0727
SPAIN, Maria Oliveras, Depto de Didáctica de Matemáticas, Campus Cartuja, U de Granada, 18071 Granada
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
Maria Luisa Oliveras Contreras, 1st VP, Depto de Didáctica de las Matemáticas, Campus Cartuja, Universidad de Granada, 18071 Granada, SPAIN, firstname.lastname@example.org
Jolene Schillinger, 2nd Vice President, New England College Box 52, Henniker, NH 03242 USA, email@example.com
Abdulcarimo Ismael, 3rd Vice President, Departamento de Matematica, Universidade Pedagogica Nacional, P.O. Box 4040 , Maputo, MOZAMBIQUE
Gelsa Knijnik, Secretary, Rua Prof. Andre Puente 414 ap.301, 90035-150 Porto Alegre, RS, BRAZIL, firstname.lastname@example.org
Jim Barta, Treasurer, Department of Elementary Education, Utah State University, Logan, Utah 84341 USA, Jbarta@cc.usu.edu
Patrick (Rick) Scott, Editor, College of Education, New Mexico State University, Las Cruces,
NM 88003 USA, email@example.com
Lawrence Shirley, NCTM Representative, Dept of Mathematics, Towson State U, Towson, MD 21204-7079 USA, E7M2SHI@TOE.TOWSON.EDU
Gloria Gilmer, Past President, Math Tech, Inc., 9155 North 70 Street, Milwaukee, Wl 53223 USA, firstname.lastname@example.org