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Volume 11 Number 2 June 1996



Minutes of ISGEm Business Meeting
Saturday, April 27, 1996
San Diego, California, USA

Jim Rauff, Ad Hoc Recording Secretary

The meeting was called to order by Gloria Gilmer at 4:30 P.M. 22 people attended. Dues were collected during the meeting by Jolene Schillinger.

I. 1996 Elections

Henry Gore presented the Nominating Committee's slate of candidates for ISGEm officers for the period 1996-2000. The nominees are:

Ubiratan D'Ambrosio (Brazil) for President
Maria Luiza Oliveras (Spain) for 1st Vice President
Jolene Schillinger (USA) for 2nd Vice President
Abdulcarimo Ismael (Mozambique) for 3rd Vice President
Gelsa Knijnik (Brazil) for Secretary
Rick Scott (USA) for Newsletter Editor
Jim Barta (USA) for Treasurer
Lawrence Shirley (USA) for NCTM Representative

The slate was approved by the members present. Dr. Gilmer announced that the ballot containing the names of the people slated to be the new officers of ISGEm will be in the next Newsletter. Members may vote by mail or in person in Seville at ICME-8. Ballots should be sent to Henry Gore.

II. Constitutional Amendment

Luis Ortiz-Franco proposed an amendment to the ISGEm constitution to allow for regional chapters. The major features of the amendment are:

1. To allow each region or sub-region as delineated in the Constitution (Europe, Asia, Australia, Africa, North America, South America) to form a "Chapter" with an organizational structure parallel to that of the ISGEm.
2. Each Chapter so created must abide by the ISGEm Constitution.
3. Each member and officer of the Chapters so created must be members of ISGEm.

4. Each Chapter will set their own local dues structure and coordi nate such with the ISGEm.

Precise wording of the amendment will appear in the next Newsletter. Also, the officer election ballot in that newsletter will contain an item by which members can vote for or against the amendment.



III. Ad Hoc U.S. Program Committee

Dr. Gilmer appointed an Ad Hoc U.S. Program Committee to coordinate ISGEm activities at the 75th NCTM Annual Meeting in Minneapolis. Appointed were Joanna Masingila (Chair), Rick Scott, Lawrence Shirley, Jolene Schillinger, Bill Collins, and Gloria Gilmer (Ex-officio).



IV. ICME-8

It was announced that several ISGEm members will attend ICME-8 in Seville, including Sunday Ajose, Joanna Masingila, Ubiratan D'Ambrosio, and Luis Ortiz-Franco.



V. Treasurers Report

There was no Treasurer's Report. Gloria will get one from Anna Grosgalvis and publish it in the next newsletter. A total of $330.00 was collected in dues. Larry Shirley was reimbursed $40.00 in payment of our delinquent dues to the Delegate Assembly.



VI. Guest Editor

Joanna Masingila will serve as Guest Editor for the June 1996 issue of the ISGEm Newsletter.



VII. ISGEm Directory

An ISGEm e-mail directory will appear in the next Newsletter. A more complete directory was discussed, but no action was taken.



VIII. ISGEm Web Site

Ron Eglash announced that he is looking into the formation of an ISGEm Web site.



IX. NCTM Delegate Assembly

Lawrence Shirley reported on the following resolutions from the NCTM Delegate Assembly.

1. The NCTM should encourage colleges and universities to support testing organizations that follow the Standards. (passed)

2. NCTM should do all that it can to make people aware of the financial crisis that is hurting mathematics education. (passed)

3. The delegate assembly should happen during the conference not the day before. (failed)

4. The NCTM should re-establish its International Affairs Committee. (failed)



Some discussion ensued on this last item as it was sponsored by ISGEm. It was agreed that the External Affairs Committee (as yet rather nebulous) will not be able to address ISGEm's concerns in this area. It was agreed that much political legwork must be done if we hope to get the International Affairs Committee re-established at the 1997 NCTM meeting.



X. Recognition for Gloria Gilmer

Henry Gore moved that a pledge of recognition or an award be given to Gloria Gilmer in appreciation of her 11 years as the President of ISGEm. The motion was seconded by D'Ambrosio and passed unanimously to thunderous applause. Dr. Gilmer appointed Henry Gore to chair a committee to look into the general issue of recognizing contributions to the ISGEm.



Xl. Adjournment

The Meeting adjourned at 5:50 P.M.



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NCTM Delegate Assembly Report

Lawrence Shirley, NCTM Representative



Every year at the annual NCTM meeting, representatives of all the affiliate organizations meet at the Delegate Assembly to consider resolutions to the Board of Directors and other business. ISGEm has been an affiliate for several years, so we participate in the Delegate Assembly. This year, our organizational cousin, the International Study Group on Relations between History and Pedagogy of Mathematics (HPM) received its charter as a new affiliate.

In the business of the Assembly, there were four resolutions for consideration. The first had originally asked that NCTM support the SAT testing program over the ACT, due to the liberal policy on calculator usage of the SAT vs. the ban of calculators on the ACT tests. However, for political etiquette, the wording was modified to the affect that NCTM should generally show favor toward testing organizations and other educational groups that follow more closely to NCTM recommendations. In this form it passed.

The second resolution also had editorial changes, but also passed. It ended up saying that NCTM should work to maintain support for math education from various levels of government, even in these days of cost cutting and tight budgets.

The third resolution pertained to the operation of the Delegate Assembly itself. It asked that the Assembly meeting be held during the NCTM conference rather than the evening before the conference begins. Some delegates said it was difficult to arrive early for the Assembly, but others argued that in the past when the Assembly was held during the conference, they had to miss important sessions. The latter point of view won out and the resolution was defeated.

For the second year in a row, ISGEm had submitted a resolution -- in fact, the same resolution -- that NCTM should re-establish its International Affairs Committee. Last year. the resolution was not accepted for consideration. This year, with the help of the HPM delegate at the afternoon caucus session, the resolution did come to the floor. Delegates from ISGEm, HPM, and the European Council of Teachers of Mathematics (mostly teachers at United States Defense Department schools in Europe) all spoke in favor of the resolution. We argued that NCTM has ties with over a dozen similar organizations in other countries, that many times we have missed news of important developments in math curriculum and instruction from other countries, and generally that we can gain much from a broader view of world math education.

NCTM had earlier suggested that the newly created External Affairs Committee could handle international matters; however, we fear that the External Affairs Committee is a catch-all group in which international matters can easily be ignored.

In response to a query, the NCTM President Jack Price said the External Affairs Committee is newly established and its role is not well defined yet. Based on that, another speaker suggested that we should wait to see how well the External Affairs Committee works out. That seemed to sway opinion and the resolution was defeated. However, the lone NCTM international affairs representative, who supports idea of the resolution, said it was at least good that it was discussed and that we should bring it back to the 1997 Delegate Assembly.

He also recommended more lobbying in the caucus sessions to help delegates better understand the purpose and value of the resolution. (At the ISGEm business meeting, some more suggestions were made on how we can help get the resolution passed -- possible editorial articles, work in our own home geographical affiliates to gain delegate support, etc.).



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Proposed Constitutional Amendment

Luis Ortiz-Franco



In a meeting of the ISGEm Executive Committee held in San Diego, California (USA) on April 26, 1996 during the NCTM National Convention, an amendment to the constitution of our organization was debated extensively. The purpose of the proposed amendment is to allow ISGEm to respond to the increasing frequency and number of activities in ethnomathematics around the world. In view of that growth, the Executive Committee determined that we needed to address the matter of organization of chapters and discuss their relationship to the international structure. Hence, the Executive Committee presented the matter to the general membership present at the business meeting for discussion and comments. The version of the proposed amendment presented to the membership was modified slightly by those present and was then voted on and approved. The membership requested that the amendment be presented to the international membership via the newsletter for adoption consideration. Furthermore, the international membership may vote on the amendment by mall or they can vote on it in the business mzeting at ICME-8 in Seville. The proposed amendment is as follows:



FIRST AMENDMENT

In order to broaden the membership in the International Study Group on Ethnomathematics (ISGEm) and increase the participation in research in ETHNOMATHEMATICS around the world, the following provisions are permitted:

1. ISGEm chapters may be established in each region delineated in this constitution, Article III, Section 4, or in countries within those regions, for the purposes of furthering the aims of ISGEm. Each Chapter so formed must adopt an organizational structure parallel to the structure of ISGEm.

2. Each chapter created under the auspices of this amendment must abide by this constitution. Furthermore, all members and officers of each chapter must be members of that chapter or members at large of ISGEm.

3. Each chapter is permitted to set its own membership dues structure according its own socio-economic conditions. The President of the chapter must communicate to the President, or to the Second Vice President, of ISGEm the membership policies governing her/his chapter.

Please use the ballot at the end of this newsletter to vote on this proposed amendment.

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Fractal Structures in Traditional African Culture
NCTM San Diego April 1996



Ron Eglash presented his studies of African fractals at the NCTM meeting in San Diego. This session was sponsored by ISGEm. Starting with a real-time software demo of "custom-designed' fractals, he then showed how aerial views of African villages, and even individual buildings, can be simulated using fractal algorithms. Eglash cautioned against the erroneous assumption that this implies a "more natural" way of life, and emphasized the intentional aspects of these constructions. From self-organizing patterns in Owari to logarithmic scaling in wind screen fabrication, we find that the mathematical ideas behind fractal geometiy are consciously expressed in a variety of African designs and knowledge systems. He concluded by showing that although four of the five basic components of fractal geometry -- nonlinear scaling, self-similarity, recursion, and infinity -- are found in Africa, there is no indigenous equivalent to a quantitative measure of fractional dimension.

Readers interested in learning more about articles, software and images for African fractals can write to: Dr. Ron Eglash, Comparative Studies, Ohio State University, Columbus, Ohio 43210-1311, USA. Ron's email is: eglasb.1@osu.edu



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Panel Presentation at NCTM Meeting



"Making Connections between Ethnomathematics and the History of Mathematics" was the topic of a panel presentation in San Diego.

Karen Dee Michalowicz, from the Langley School, spoke about "Uses of the Mathematical and Scientific Ideas of Traditional Peoples, Specifically Native Americans, in the Pre-College Classroom." She noted that because Native Americans in the recent past been viewed by many as unsophisticated, heathen peoples, it is important that our students, especially Hispanic and minority students, become aware of and appreciate the cultural and scientific achievement of the people who inhabited the "New World" before the "Age of Discovery". In fact the NCTM Standards lists in its very first goal, "Learning to Value Mathematics:" Students should have numerous and varied experiences related to the cultural, historical and evolution of mathematics... She also provided those who attended the Panel Discussion a bibliography related to the accomplishments of the Anasazi, the Mayans and the Inca.

Jim Rauff, from Millikin University, talked about the "Ethnoalgebra of the Warlpiri" and briefly discussed how the iconography of the Warlpiri of Australia possesses characteristics of modern algebra A set of symbols with defined but variable meaning is used to construct meaningful expressions using specified rules. The expressions in term are abstract models of reality.

Other presentations by panel members included Gloria Gilmer, from Math-Tech, Inc., who discussed "Contemporary Aspects of Ethnomathematics," Jolene Schillinger, from New England College, who spoke about "Women and Ethnomathematics," and Ubiratan D'Ambrosio, from the State University of Campinas, who discussed "Recent Research in Ethnomath:Opening Areas of Action."



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Mathematical Thought and Application in Traditional Seminole Culture

Jim Barta

Utah State University



Author's note: During the past several years, I have been involved with an ethnomathematics research project studying the Seminole tribe of Florida. The project has evolved in two phases. The first phase involved interviewing Seminole elders and others to examine the traditional (historical) daily activities of the Seminole people in which mathematical principles were embedded. This data then (phase two) will be used to collaborative design with teachers at the Ahfachkee Seminole Elementary School on the Big Cypress Reservation culturally inclusive elementary math curriculum. The following describes findings related to the first phase.

The Seminole, a native people whose roots can be traced throughout the southeastern United States came into being during the 18th century (Garbarino, 1988). The name "Seminole" is thought to have originated from the European mispronunciation of the Creek word "simanoli" which meant runaway. The Seminole were comprised of both native and blacks who sought freedom in Florida from persecution and slavery at the hands of the increasing number of settlers in colony of Georgia. They successfully made their homes in the swamps and glades of central and southern Florida where they could freely maintain their traditional ways of life. Several times during a 25 year period ranging from 1817 through 1842, the United States declared war on the Seminole. Many natives resisted with their lives the Government's insistence that they give up their lands and accept relocation out west. Eventually, with numbers estimated to be less than 500, the cavalry grew tired and those natives remaining were left alone. The Seminole are the only native group to have never signed an official "peace treaty" with the United States. Traditional cultural practices are still evident among the people although there is concern among the Seminole that the most recent generation is losing touch with their ancestral culture. Today, a population of nearly two thousand live on several reservations across Florida.

Bishop (1991) has stated that many of the everyday activities of people (past and present) involve a substantial amount of mathematical application. Six "universal" activities that are thought to be practiced by any culture are: counting, measuring, designing, locating, explaining, and playing. These six universal activities (inclusive of D'Ambrosio's broad view of mathematics. 1987) provided the fundamental facets used to probe traditional daily living practices of the Seminole culture. The results of the research have allowed for substantial insight into traditional application of mathematical inventiveness within the Seminole culture. These universals (counting, locating, designing, measuring, explaining, and playing) were inseparably intertwined with other aspects of the Seminole culture. Through a study of these applications, we come to better know the wonder of these people and their early experiences using math. The following examples are outlined.

Counting appears to be predicated on a "Base Ten" system if one examines the numeric names. No written symbols existed, rather physical representations (seeds, pebbles, knots) or finger gestures were used to physically describe quantities when necessary. When gestures have been observed however, counting appears to be done in groups of five (a person will count and touch each digit of one hand while counting from one to five). Counting on from six to ten occurs by retouching digits on the first hand counted. The Seminole referred to zero as "having nothing." Extremely large numbers were not necessary and so no words for them were used. It was culturally inappropriate to have too much of anything. If one did, it meant that they were greedy and that they must share with others in the tribe. Reference was made to these numbers however in other ways. For example, when asked to describe the number of stars in the sky, an Elder stated, "There are so many that I could count for all of my life and never finish counting."

These words listed below are the counting names for the numbers 1-10 and 10-100 (Wilson, 1986).

1 Hum-kin 6 A-pa-kin
2 Ho-ko-lin 7 Ko-lo-pa-kin
3 Too-chin 8 Chin-na-pa-kin
4 Os-tin 9 Os-ta-pa-kin
5 Chaw-kee-bin 10 Pa-lin
20 Pa-lin-ho-ko-lin 60 Pa-lin-a-pa-kin
30 Pa-lin-too-chin 70 Pa-lin-ko-la-pa-kin
40 Pa-lin-os-tin 80 Pa-lin-chin-na-pa-kin
50 Pa-lin-chaw-kee-bin 90 Pa-lin-os-ta-pa-kin
100 Chope-kee-hum-kin

Measurement involved the use of certain "standard units" found in the environment. Parts of the body provide convenience yet suitably standard units of measure. For instance, the distance from the nose to the end of an out stretched arm was used to measure units of cloth. Measurement for construction of their traditional homes known as "Chickees," used the po-cus-wv e-mv-pe (pronounced ba-giz-u-ah e-mobi) which when translated from the Creek language means the "length of an axe handle".

Other "units of measurement" such as the number of paces existing between objects in their environment (distance), the rate one traveled on foot or in a wagon to the trading post (speed), the length of shadow cast by a tree (time) reflect how these people applied their mathematical intelligence to solve relevant problems. It appears the Seminole possess an uncanny ability to measure "by the eye." Exact units were not necessary since minor allowances created few real problems.

Distances, were expressed as a function of the time it took one to travel from Point A to Point B. The speed (or distance) was determined by the mode of travel; walking was the slowest, wagons drawn by cattle was faster. Canoe travel resulted in the greatest speed. The distance from the village to the trading post may be only a half-day travel by canoe. Great distances were described as being so great that a man could walk his entire life and never arrive at the destination.

Seminole located places within their environment by constructing mental maps. Landmarks familiar to most acted as points of reference. Occasionally, maps drawn in the sand were used. Directions used to locate a position were literally named. The cardinal direction "East" for instance was named the place where the sun comes up.

Designs in the Seminole culture were abundantly evident. The patchwork clothing worn by many women and a few of the men resulted from sewing strips of colored fabric into geometric patterns which involved an implicit understanding of transformational geometry. These patterned designs were then stitched onto other clothing such as dresses and shirts.

Math was also used to explain concepts such as age and the time between certain importart events. The year was described as a cycle of two seasons and one's age was calculated by counting how many cycles had occurred since an event happened. Therefore, one might be 21 "summers" old. Age was also relative to those with whom one lived. A person might have lived many winters yet would not be considered an "Elder" if there were others still living who were older.

Playing was an important aspect of the Seminole culture. During the sacred "Green Corn Dance", a celebration welcoming the beginning of a new year, a type of stick ball is played (men against women) and scores are kept. The scoring could be additive (a point for each goal earned) or can be subtractive (a point subtracted from a predetermined originating score). A traditional children's game similar to mumble peg (Appalachian) was played. Children would use a sharpened stick and take turns pitching it into a pile of sand from places on the body. Points were scored when the stick landed vertically and remained upright in the sand. The knee bone of a cow was also used to play a similar game. Certain faces of the bone earned specific points when it landed with that part of the bone face upwards. Children added the combination of numbers earned and played until a predetermined number was reached.

There remains a great deal more to learn about Seminole application of mathematical practices. I feel a sense of great awe to be witness to the culturally-determined mathematics created by these people. Through this ethnomathematical study, we glimpse how math provided them the intellectual tools and language to survive and succeed in the swamps of southern Florida.



References

D'Ambrosio, U. (1987). Reflections on ethnomathematics. International Study Group on Ethnomathematics Newsletter, 3 (September).

Garbarino, M. (1988). The Seminole. New York: Chelsea House Publishers.

Wilson, M. (1986). The Seminoles of Florida. Philadelphia,PA.: American Printing House.



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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 mentioned and/or reviewed. We encourage all those interested to contribute to this column.

Ascher. Marcia (1995, November). Models and maps from the Marshall Islands A case in ethnomathematics. Historia Mathematica, 22, 347-370.

In this article Ascher discusses the stick charts of the Marshall Islanders. The stick charts are planar representations used to teach prospective navigators the unique Marshallese system of "wave piloting." The focus is on the mathematical ideas of modeling and mapping embodied in these charts.

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For the Learning of Mathematics, 14 (2), June 1994, Special Issue on Ethnomathematics, co-edited by Marcia Ascher and Ubiratan D'Ambrosio. It contains the following articles:

"'Africa Counts' and Ethnomathematics" by Claudia Zaslavsky

"Research in Native American Mathematics Education" by Charles G. Moore

"Cultural Conflicts in Mathematics Education: Developing a Research Agenda" by Alan J. Bishop

"Reflections on Ethnomathematics" by Paulus Gerdes

"Ethnomathematics and its Practice" by Rik Pinxten

"Ethnomathematics in the Classroom" by Victor J. Katz

"Modelling as a Teaching-learning Strategy" by Rodney C. Bassanezi

"Ethnomathematics: A Dialogue" by Marcia Ascher and Ubiratan D'Ambrosio

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Lipka. Jerry (1994, Spring). Culturally negotiated schooling: Toward a Yup'ik mathematics. Journal of American Indian Education, 14-20.



This paper describes one aspect of a long-term collaboration between the author and a Yup'ik teachers' research group, Ciulistet, focusing on the processes and development of Yup'ik culturally based mathematics. The premise behind this work is that the Yup'ik language, culture, and worldview, particularly subsistence activities, contain mathematical concepts. These concepts include a number system that is base 20 and sub-base 5, and ways of measuring and visualizing. This has direct applications to school math. However, just as important, the project participants are increasingly realizing the potential of using their culture and language as a means to change the culture of schooling.

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Masingila, Joanna 0. (1995). Carpet laying: An illustration of everyday mathematics. In P. A. House (Ed.), Connecting mathematics across the curriculum (pp. 163-169), 1995 Yearbook of the National Council of Teachers of Mathematics. Reston, VA: National Council of Teachers of Mathematics.

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Masingila, Joanna 0. (1994). Mathematics practice in carpet laying. Anthropology and Education Quarterly, 25 (4), 430-462.



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Zaslavsky, Claudia (1995). LAfrique compte! Nombes, formes et démarches dans Ia culture africaine. Éditions du Choix, 5 rue Jean Grandel, 95103 Argenteuil, France.



Africa Counts is now published in French.

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Zaslavsky, Claudia (1993). Multicultural mathematics: One road to the goal of mathematics for all. In G. Cuevas and M. Driscoll (Eds.), Reaching all students with mathematics (pp. 45-55). Reston, VA: National Council of Teachers of Mathematics.

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Correction: In the last issue of the ISGEm Newsletter we incorrectly listed the name and price of a new book by Claudia Zaslavsky. The correct information is:



Zaslavsky, Claudia (1995). The multicultural math classroom: Bringing in the world. Portsmouth, NH: Heinemann [361 Hanover Street, Portsmouth, NH 03801-3912, USA, $23 .50]

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The Ancient Egyptian Concept of Zero and the Egyptian Symbol for Zero: A Note on a Little Known African Achievement

Beatrice Lumpkin



It is well known that a zero placeholder was not used or needed in Egyptian numerals, a system of numerals without place value. Values were expressed by grouping and addition of repeated ciphers. Still historians such as Boyer (1968) and Gillings (1965) have found examples of the use of the zero concept in ancient Egypt. But Gillings added, "Of course zero, which had not yet been invented, was not written down by the scribe or clerk; in the papyri, a blank space indicates zero." However, some Egyptologists did know that the ancient Egyptians used a zero symbol, but it may have been missed by historians of mathematics because the symbol did not appear in the surviving mathematical papyri.

The Egyptian zero symbol was a triliteral hieroglyph, with consonant sounds nfr (Gardner, 1978). This was the same hieroglyph used to represent beauty, goodness, or completion (Faulkner, 1976). There are two major sources of evidence for an Egyptian zero symbol:

1. Zero Reference Level for Construction Guidelines

Massive stone structures such as the ancient Egyptian pyramids required deep foundations and careful leveling of the courses of stone. Horizontal leveling lines were used to guide the construction. One of these lines, often at pavement level, was used as a reference and was labeled nfr, or zero. Other horizontal leveling lines wcre spaced 1 cubit apart and labeled as 1 cubit above nfr, 2 cubits above nfr, or 1 cubit, 2 cubits, 3 cubits, and so forth, below nfr (Arnold, 1991).

In 1931, George Reisner described zero leveling lines at the Mycerinus (Menkure) pyramid at Giza built c. 2600 BCE. He gave the following list collected earlier at Borchardt and Petrie from their study of Old Kingdom pyramids (Reisner, 1931).

nfrw zero (Note the w suffix added to nfr for grammatical reasons.)
m tp n nfrw zero line
hr nfrw above zero
md hr n nfrw below zero

2. Bookkeeping, Zero remainders

A bookkeeper's record from the 13th dynasty c 1700 BCE shows a monthly balance sheet for items received and disbursed by the royal court during its travels. On subtracting total disbursements from total income, a zero remainder was left in several columns. This zero remainder was represented with th same symbol, nfr, as used for the zero reference line in construction (Reisner, 1931).

These practical applications of a zero symbol in ancient Egypt, a society that conventional wisdom believed did not have a zero, may encourage historians to re-examine the everyday records of ancient cultures for mathematical ideas that have been overlooked.

References

Arnold, D. (1991). Building in Egypt. New York Oxford University Press.

Boyer, C. B. (1968). A history of mathematics. New York Wiley.

Faulkner, R. O. (1976). A concise dictionary of middle Egyptian. Oxford Griffith Institute.

Gardner, Sir A. A. (1978). Egyptian grammar. Oxford: Griffith Institute.

Gillings, R. J. (1965). Mathematics in the time of the pharaohs. Cam bridge, MA: MIT Press.

Reisner, G. A. (1931). Mycerinus: The temples of the third pyramid at Giza. Cambridge, MA: Harvard University Press.



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ISGEm Newsletter Distributors

The following individuals print and distribute the ISGEm Newsletter in their region. If you are 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, VIC 3011

AUSTRALIA, Leigh Wood, P.O. Box 123, Broadway NSW 2007

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

GUATEMALA, Leonel Morales AIdaña, 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



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ISGEm Executive Board

Gloria Gilmer, President
Math Tech, Inc.
9155 North 70 Street
Milwaukee, WI 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 VP
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
ortiz@chapman.edu

Maria Reid, Secretary
145-49 225th Street
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 Rep.
Dept of Mathematics
Towson State U
Towson, MD 21204-7079 USA
e7m2shi@toe.towson.edu

Guest Editor, June 1996 Newsletter

Joanna Masingila
Dept of Mathematics
Syracuse University
Syracuse, NY 13244-1150
jomasing@sued.syr.edu