__Volume 13 Number 1 November 1997 __

**Report on Ethnomathematics Research**

**Joanna O. Masingila, Syracuse University
**jomasing@sued.syr.edu

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 (jomasing@sued.syr.edu).

Judit Moschkovich, from the Institute for Research on Learning, and colleagues have been investigating the mathematical activity of people in a variety of work situations. One recent study involved the mathematical activities in the work of insurance agents. Moschkovich and her colleagues found that these practices do not involve only arithmetic computation but also estimating, using heuristics, explaining complex relationships between quantities, and describing diagrams.

Jack Smith, from Michigan State University, is examining the mathematical demands of "blue collar" work in various workplaces involved in automobile manufacturing. His work has been oriented by current concerns that U.S. high school graduates are often ill-prepared for high-skill, high-wage work in a variety of industries. Smith has studied what sort of mathematical knowledge and skills high school graduates need to perform competently in the automobile industry. Two main findings emerged from this research: (1) the demands of high-volume assembly work appear well within the current content of the K-12 curriculum, while (2) more challenging and rewarding work, like computer-mediated machine tool operation, requires extensive spatial and geometric competence that the U.S. curriculum does not strongly support.

Norma Presmeg, from Florida State University, is working on developing a theoretical framework, drawing on literature from semiotics and Ethnomathematics, to address the ways in which real experiences and cultural practices of students may be connected with mathematics classroom pedagogy.

José Fonseca, from the University of Arizona, is involved in a project that is using children's out-of-school knowledge to teach school mathematics. As part of an earlier study, Fonseca and colleagues found that 60% of the students at a bilingual middle school had some knowledge of and skills related to construction. Fonseca designed an instructional unit in which students develop model houses (designing, drawing, and constructing) and learn mathematical concepts and process through this context. He is examining how the students' out-of-school experiences were connected to learning academic mathematics.

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**ISGEm at NCTM in Washington**

**Larry Shirley**

ISGEm's NCTM Delegate

I have had a reply from my request for room, time, and program listing for the NCTM April Conference in Washington. They confirmed that they will list us in the program, and that we will get a room that Saturday evening. However, since the conference is not going on into Sunday, the regular sessions may run later into Saturday evening. We probably will have to start about 5:00 or 5:30, after the last Saturday afternoon sessions are over. They could not confirm an exact room or time yet and probably won't until January. Hence, at the time all we can report is that we will be meeting that Saturday evening, and tell readers to check in the NCTM program book for the exact time and place.

Meanwhile, they have noted that our resolution has been received. The committee will be looking at all of the submitted resolutions over the next month or so, to determine their status.

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** Special Meeting to Honor Ubiratan D'Ambrosio**

The International Study Group on the Relations between History and Pedagogy of Mathematics (HPM) and the International Study Group on Ethnomathematics (ISGEm) will jointly sponsor a conference in the honor of the 65th birthday of Ubiratan D'Ambrosio, professor of mathematics emeritus at the University of Campinas in Brazil, to take place on Tuesday, January 6, l998 at the Omni Hotel in Baltimore, Md. USA. This is the day preceding the opening of the annual joint meeting of the American Mathematical Society and the Mathematical Association of America. We welcome the attendance of all mathematicians and mathematics educators who wish to honor Professor D'Ambrosio. Most of us are aware of Professor D'Ambrosio's influence in the areas of Ethnomathematics, the history of mathematics and mathematics education.

To register for the conference, send your name, addresses (mail and e-mail) and phone numbers, along with a check for US$50 to Karen Dee Michalowicz, Treasurer Americas Section, 5855 Glen Forest Drive, Falls Church, VA 22041 USA.

The check should be payable to HPM. The fee is to primarily cover the cost of a festive birthday dinner in the evening.

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**An Investigation of Muskogee Creek Indian Counting Words**

**Richard DeCesare
**Southern Connecticut State University

**About the Source**

Except where noted, the main source for this paper was a Muskogee Creek Indian named Cheneya. She provided historical information about her tribe, as well as comments about their language. Cheneya provided me with a lengthy list of Muskogee Creek counting words, which we analyzed together.

This paper was originally prepared as part of the *World Counts* symposium that was organized at
Teachers College, Columbia University by Joel Schneider.

**Background of the Tribe and Language**

The Muskogee Creek Indians originated in Georgia and Alabama, and are related to the
Seminoles. Approximately 30,000 are listed on the tribal rolls, including those who are not
full-blooded Creek. Less than 7,000 still speak the language (Census Bureau, 1990), which
contains dialects and a ceremonial language as well. The written language was developed in 1853.
Prior to that, pictures were used to express words. Seven letters are not used in their alphabet: b,
d, g, j, q, x and z. The Creek use the letters 'k' and 'v' frequently; 'v' sounds like 'u' in 'put'. Hence,
one spelling of the tribe would be *Mvskogee*, but there are others. In this paper, we will use
'Muskogee' for simplicity, but all other words will be spelled as they appear in the language.

**Forms of the First 10 Counting Words**

In 1775, James Adair published his *History of the American Indians*, in which he lists the first ten
counting words in the Muskogee Creek language. Below we compare them with the modern list
supplied by Cheneya :

Adair (1775) | Cheneya (1997) | |

1 | hommai |
hvmken |

2 | hokkóle |
hokkolen |

3 | tootchena |
tutcenen |

4 | ohsta |
osten |

5 | chakápe |
cahkepen |

6 | eepáhge |
epaken |

7 | hoolapháge |
kulvpaken |

8 | cheenépa |
cenvpaken |

9 | ohstápe |
ostvpaken |

10 | pokóle |
palen |

There are similarities between most of the words. Of course, we must remember Adair wrote
down what he *heard*, not what he *read*.

"I am sorry that I have not sufficient skill in the Mushohge dialect, to make up useful observations on this head," Adair wrote (Williams, 1986)

**Building Numbers**

The Muskogee employ a base ten counting system, as can be seen by examining numbers above
ten. For example, 'eleven' is *palen-hvmken-tvlaken* (hyphens are mine). The words for 'ten' and
'one' are clearly evident. *Tvlaken* is a form of 'great', hence 'eleven' is translated as 'one greater
than ten'. Interestingly, the idea of 'greater than' is discontinued with numbers from 'twelve' to
'nineteen', and a more colorful expression is used. 'Twelve' is *palen-hokkol-ohkaken*, which
contains the words for 'ten' and 'two', and thirteen is *palen-tutcen-ohkaken*, which contains the
words for 'ten' and 'three'. All the words from 'twelve' to 'nineteen' end with *oskaken*, which means
'sit upon'. Hence, thirteen is translated as 'three sit upon ten'.

Multiples of ten are formed by using *pale* with the appropriate counting word from 'one' to 'nine',
hence, 'twenty' becomes *pale-hokkolen*, or literally, 'two tens', as the words are read from right to
left. 'Thirty' is *pale-tutcenen*, and so on. 'Twenty-two' becomes *pale-hokkolen-hokkol-ohkaken*, or
literally, 'two sit upon two tens'.

The word for 'one hundred' is *cukpe-hvmken*. Since *cukpe* means 'a hundred' and *hvmken* means
'one', the complete word is translated as 'one a hundred'. Similarly, 'two hundred' is written and
translated as 'two a hundred'.

For 'one thousand', *cukpe-rakko-hvmken*, a new root word is introduced. The words for 'one
hundred' and 'one' are evident, but I wondered if *rakko* had some significance. Cheneya supplied
the answer, translating *rakko* as 'large'; hence, 'one thousand' is essentially 'one large hundred'.
'Ten thousand' is *cukpe-rakko-palen*, that is, 'ten large hundreds'. 'One hundred thousand' is
*cukpe-rakko-cukpe-hvmken*, which is 'one hundred large hundreds'.

When we reach 'one million', which is *cukpe-rakko-vcule-hvmken*, we can see 'one hundred', 'large'
and 'one'. Again, Cheneya provided a translation for the word *vcule*: 'old' or 'aged'. Thus 'one
million' is translated as 'one old large hundred'. Using the word 'old' or 'aged' to amplify the size of
a number is not unique: in the Cherokee language, Adair translated 'one thousand' as 'the old one's
hundred' (Williams, 1986).

**Unanswered Questions and Conclusions**

The words 'six' through 'nine' contain *paken*, which could suggest a form of counting up from 'five'
or down from 'ten'. I asked Cheneya if the word had some significance (since it is similar to 'ten',
*palen*), but she had no idea. Also, it was not clear to Cheneya why the word for 'eleven' uses the
idea of 'one greater than' while 'twelve' through 'nineteen' use the idea of 'sit upon'.

This was an interesting collaboration between two cultures. As I looked for patterns in the number words, Cheneya reflected on her own language and was able to view her words in a different light often mentioning she had never thought of the words 'that way' before. Without her help, I would not have been able to give the appropriate meaning to many of the number words.

**Reference**

Williams, S. (ed.). (1986). *Adair's History of the American Indians*, New York: Promontory
Press.

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**Mathematics and Crafts in Andalusia: An Anthropological-Didactic Study**

**María Luisa Oliveras Contreras
**Granada University

**Introduction**

In this paper I shall attempt to set out the work plan and the methodology from an anthropological study in which I explored the uses of concepts, properties, theorems, etc. of different aspects of Mathematics in performing typical crafts in Andalusia, Spain. I used an ethnomathematical approach for the theoretical foundations, and an interpretative-qualitative methodology.

From the point of view of positivist research, it is very difficult to try to explain the plan of work, the methodology, and the results of any ethnographical research on the Didactics of Mathematics. Positivist research presupposes a structured design in which the hypotheses and techniques are determined a priori. This is in contrast to the flexibility which is appropriate for an interpretative and qualitative methodology which proceeds with very open and interactive plans, and emerges as the first phase of the field work is being carried out.

I shall attempt to set out the general questions which motivated me to start this work, as well as the characteristics of the field work and the scenarios which form it. The origin of this work was my desire to discover the degree of the social use of concepts, properties, relationships, theorems, etc. corresponding to intuitive Geometry in the performance of the tasks which constitute the production process of certain hand-made products which have been in Andalusia in a traditional way for many centuries. This curiosity was inspired by my personal involvement with Didactics of Mathematics from my work on methodology, as well as from my interest in the social and cultural manifestations in the environment in which I live.

**Objectives and Scenarios for the Research**

It is clear that the "*teaching* of Mathematics" should give way to "mathematical *education* or
*enculturation*", because it does not merely involve isolated cognitive variables, but the intricate
reality of a human being. A person's education is completed within a society, in the different
institutions which form that society: school, family, etc. These subgroups which make up a
person's environment may have a defined curriculum or may have aims and messages which
emanate from the cultural heritage. Many of the conflicts within teaching arise from the conflict
between planned studies and real life experiences.

Also, in Mathematics, it may be stated that there are specific creations in each cultural environment, within the generalization that belongs to scientific truths, in spite of the fact that the process of "removing facts from their original context" (abstraction), makes us forget the social and cultural bases which precede abstract ideas. When we delve into the processes which surround personal construction of mathematical knowledge, we have no options but to go back to the cultural roots of the social groups of which that person is the result. To a large extent we must accept an approach to these didactical questions that is much more anthropological than psychological.

Therefore, I am attempting to shed some light onto the unclear relationship between school mathematics education and popular mathematics culture in Andalusia. In order to accomplish that, the general objectives of this work are:

A. To discover the mathematics contained within the context of certain cultural products, which have been kept alive up to our days, handed down orally and by experience. Accomplishment of this first objective should contribute to the knowledge of the:

a-1 most hidden facts of our popular culture, and

a-2 social requirements for a mathematical preparation suitable for certain fields of work.

B. Explore the various didactic implications of this knowledge through an analysis of:

b-1 the relationship between the school curriculum and popular knowledge and awareness of the divergence between culture and education related to Mathematics,

b-2 the didactic relationship underlying the learning process,

b-3 the sources of information and the utility of education, using case studies of the professional histories of the informants, and

b-4 the learning involved and its application to the preparation of teachers and resultant models of teacher preparation.

The field to be studied is made up of a selection of "scenarios" or craft work which I considered to be representative of our culture and which will allow us, a priori, to select those processes in which mathematics is applied. Table 1 contains a list of the crafts that were considered.

**Table 1**

**Crafts that Were Studied**

1. Marquetry (inlaid work)

2. Musical instruments, particularly guitars

3. Landscaping, particularly with stone laying

4. Granada pottery

5. Carpentry, particularly hand-made and designer furniture (*bargueños, jamudas*)

6. Dressmaking, preparation of patterns

7. Sculpting and carving in marble and wood

8. Hand-woven carpets

9. Stained glass and lamps

10. Crochet work, lacemaking

11. Bronze and glass craftsmanship, specifically in Granada lamps

12. Iron and copper forging, railings and decorations

13. Hand-made Alpujarra textiles, design and production

14. Goldsmithing and jewelry making

15. Embroidery using tule and gold

16. Graphics arts, sign painting, illustrations, design

17. Other products of construction work: plastering, from carpentry

This list, although it is not totally exhaustive, is a good representation of the work and cultural traditions which were at their cultural zenith during our parents' generation and are much less evident today.

By way of an hypothesis, with respect to objective A, it was expected that we would observe geometrical, topological and measurement therein. With respect to objective B, it was expected that there would be little influence of the school curriculum on their mathematical knowledge prior to specific training or apprenticeship.

**Theoretical Foundations and Work Plan**

I had a firm conviction that the interpretative methodological approach involved a paradigm that was suitable for many studies in the Didactics of Mathematics and that it cast doubt on the relevance of the positivist approach for explaining current problems. Consequently, this research has emerged from a "context" or natural situation, i.e. the performance of everyday tasks by craftsman when they make their products. The researcher and her collaborators collected the data with the intention of perceiving meaning and widespread relationships in the observed phenomena. This approach, according to Lincoln and Guba (1985), has the advantages of adaptability, immediate processing, holistic capacity, and possibilities for clarifying responses and detecting those which have unusual or idiosyncratic characteristics.

I used direct qualitative techniques for collecting data: *participatory and non-participatory
observation, interviews,* and *abbreviated professional case studies*. I began by working out an
outline of the aspects to be borne in mind during the observation and for predicting the contents to
be included, worked out on the basis of the theoretical knowledge of the scenarios to be observed.
The *semi-structured interviews* of the informants, who were the most expert or experienced
craftsmen, contained the request that they should tell their own *professional story*, emphasizing
the initial training period and the stages of greatest difficulty. The final interviews, since there
were initially informal contacts, were audio or video recorded, so that they could be later
analyzed. These audiovisual techniques may be considered to be included under the heading of
direct techniques, since they were obtained directly by the researcher. The work plan covered two
phases, which were developed over four academic years (1989-1993), according to a qualitative
*time series design*. The sample was divided into two smaller samples, the first in those professions
numbered 1 to 10 in Table 1, and the second involved those numbered 11 to 17, and 1, 3 and 8 for
more profound study.

The inductive analysis of the data, as a first step in processing, was by means of a plan suggested by Miles and Huberman (1984).

The next, highly time consuming step, was that of reducing these in accordance with the most important objectives of the study. The third step was the display of the abridged or simplified data.

In order to break down the data I chose to select and simplify them by making the initial reduction
by centering my attention on one topic: mathematics. Therefore, all other information was
ignored. The relationships between the different sequences of the whole process, as well as the
processing of the data are *cyclical* and not linear as in positivist frameworks, which causes a
partial advance in aspects which at the same time shall reinforce those that follow.

There may be many ways of displaying the information: matrices, double entry tables, diagrams,

etc. I chose double entry tables as most appropriate in this case.

**A Presentation of Some Results**

For reasons of space, I cannot go into detailed descriptions of each of the crafts that was analyzed. I shall present a table (Table 2) with the relationships between the mathematical contents discovered and the craft from the first phase of the study, using for this the numbers from Table 1. The mathematical contents discovered are labeled as follows:

- A. Shapes: interior, exterior and borders
- B. Angles and movements, symmetry, translations, turns. Axes, planes, centers of symmetry, guide vectors.
- C. Tessellations of the plane and space
- D. Similarities and dilations. Thales' Theorem
- E. Measurement and units. Optimization of amounts under given conditions. Relationships between length, surface area and volume.
- F. Two-dimensional portrayal of three-dimensional space. Making flat designs in space. Maps and graphs. Surface areas of turns.
- G. Theorem of Pythagoras. Applications.
- H. Specific and incorporated symbols, graphic languages.

**Table 2**

**Relationship between the Crafts and the Mathematical Content**

A |
B |
C |
D |
E |
F |
G |
H | |

1 |
x | x | x | x | x | |||

2 |
x | x | x | x | ||||

3 |
x | x | x | x | x | x | ||

4 |
x | x | x | |||||

5 |
x | x | x | x | ||||

6 |
x | x | x | x | x | |||

7 |
x | x | x | x | ||||

8 |
x | x | x | x | ||||

9 |
x | x | x | |||||

10 |
x | x | x | x |

It may be observed that craft No. 3, landscaping and stone laying, is the one which has the highest number of relationships with the mathematical contents. No. 6, dressmaking, follows it with five. As may be observed, the geometrical shapes and symmetry are concepts applied in all the crafts, whereas only in crafts 1 and 10 is there any specific symbolization. However, the most interesting point is hidden when the summarized data is presented. For example, the different uses of symmetry and tessellation which include an incredible scope, ranging from the designs and patterns for stonework and sculptures to controlling the weaving process for carpets, which is carried out by means of copying the work of another more experienced person, who follows the design. The inlays for the inlaid work, using millimetric measurements, are astounding given their great accuracy, whereas in stonework the mastering of large areas is required.

The use of symbolization by means of areas with different designs and the interpretation of plans, as well as the creations of designs, used in landscaping, carpentry and brickwork, are crafts with a symbolization and interpretation which I consider to be a form of Ethnomathematics. About 90% of the craftsmen were not aware of their use of geometrical elements or of calculations and measurements which are related to Mathematics. They think that they do not need any training in this field and believe that they only need practical training with a master craftsman. The teaching relationship involved is based on authority and uses as its principal teaching techniques simple observation and the copying of actions.

**References**

Lincoln, V. and Guba, E. (1985). *Naturalistic Inquiry*. Beverly Hills: Sage.

Miles, M. and Huberman, A. (1984). Drawing valid meaning from qualitative data: Toward a
shared craft. *Educational Researcher*, 13, pp. 20-30.

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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.

Barton, Bill. (1996) **Making Sense of Ethno-mathematics: Ethnomathematics Is Making
Sense**. *Educational Studies in Mathematics*; v31 n1-2 p201-33.

Proposes a framework to review the literature of the culture of mathematics, specifically in the use of the term Ethnomathematics. Derives a definition of Ethnomathematics; reviews two examples as a test of the power of the definition and the resultant description of Ethnomathematics.

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Moore, Charles. (1994)** Research in Native American Mathematics Education**. *For the
Learning of Mathematics;* v14 n2 p9-14.

Discusses past research involving Piagetian conservation concepts in Native American students; the relation of language to mathematics education; holism in mathematics learning; mathematics and culture; the Outdoor World Science and Mathematics Project, which developed learning modules involving Native Americans; and mentorship in an atmosphere of cultural diversity.

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Ferreira, Mariana K. L. (1997). **When 1+12. Making Mathematics in Central Brazil. ***American
Ethnologist*, 24 (1): 132-147.

This ethnographic account of mathematical activity among the Juruna, Kayabi, and Suya of Central Brazil shows arithmetic practices being fashioned in specific social setting. Values and symbolic properties of both the gift exchange and capitalist economics structure arithmetic dilemmas in the Xingu Indian Park. Within a broad social field that transcends the boundaries of the park to include prospecting sites and cattle ranches, economic calculations are extended to all kinds of goods, material and symbolic. The distribution and circulation of these different forms of capital are discussed in view of the constitution of particular arenas of exchange. Practice theories (Bourdieu, 1991; Lave, 1988) highlight the ways in which mathematical knowledge is constituted in everyday activities, challenging functional assumptions about cognition and schooling. By articulating principles of the gift with those of capitalist exchanges, mathematics is construed by the Juruna, Kayabi and Suya as a product of social work and symbolic fashioning.

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Ascher, Marcia and Ascher, Robert. (1997).** Mathematics of the Incas: Code of the Quipu,** New
York: Dover Publications.

This is a new edition and retitling of the now classic 1981 *Code of the Quipu: A Study in Media,
Mathematics, and Culture*.

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Sebastiani Ferreira, Eduardo. (1997) ** Etnomatemática: Uma Proposta Metodológica
(Ethnomathematics: **A Methodological Proposal, Rio de Janeiro: Mestrado en Educação/
Universidade Santa Ursula.

Sebastiani has perhaps been most well known for his ethnomathematical work with indigenous groups of Northern and Northeastern Brazil. This current volume, available only in Portuguese, is part of the Series on Reflections in Mathematics Education published by Santa Ursula University in Rio de Janeiro. It is the result of the discussions in a seminar on Ethnomathematics held at that university. Sebastiani outlines a course in Ethnomathematics, gives some of the background of Ethnomathematics, and presents Ethnomathematics as a pedagogical model. The volume also includes summaries of student projects, and an appendix with three additional papers by Sebastiani:

O professor de matemática como pesquisador

(*The teacher as researcher)*

Da oralidade a numeramento

*(From "Orality" to "Numeracy")*

A importância do conocimento etnomatemático indígena na escola dos não-indios

*(The importance of indigenous ethnomathematical knowledge in schools for non-Indians)*

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**Have You Seen on The Web?**

**www.mts.net/~lsisco/#Rationale**

Lesley Sisco, a High School teacher in Winnipeg, Manitoba, in an effort to "value her students
interests and also connect them to ideas and traditions growing out of centuries of mathematical
exploration and invention" has developed a web page that includes lesson plans on area
measurement that use, among other units for area, the Aztec quahuitl.

**cs.beloit.edu/~chavey/M103/EthnoMath%20Bibliography.html**

A bibliography on Ethnomathematics is maintained at Beloit College's Department of Mathematics
and Computer Science. The following criteria were used to sort the bibliography:

1) If a source is about one region of the world, it is put in that sub-heading.

2) Within world regions, references are grouped by topic (corresponding largely to the chapters of
the text) where possible. Sources in that region that cannot be easily classified are then grouped in
that region, sub-heading "Other".

3) After the "Regions" headings, additional sources are grouped according to the mathematical
topic; again by chapters of the text.

4) Finally, other sources that cannot be classified easily (general, unclear, or where I cannot be
sure of the English translation) are collected at the end as "Unclassified".

**curry.edschool.Virginia.EDU/~tls9h/Ethnoweb.htm**

Another Ethnomathematics bibliography is maintained by Todd Shockey at the University of
Virginia.

**jwilson.coe.uga.edu/DEPT/Multicultural/MEBib94.htm**

Yet another useful bibliography available on line is *The Annotated Bibliography of Multicultural
Issues in Mathematics Education*, which is the product of work at the University of Georgia
directed by Patricia Wilson.

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**ISGEm Home Page on "Top 10 List"**

The "International Study Group on Ethnomathematics" site is featured in the November issue of the "Top 10 Educational Sites on the World-Wide Web." Learning in Motion" publishes the Monthly Top 10 List for educators and students who are interested in integrating the Internet with their schoolwork.

Ron Eglash, who maintains the ISGEm Home Page, encourages you to browse it at:

**www.cohums.ohio-state.edu/comp/isgem.htm**

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**New Journal on Multicultural Math** **to Be Published in Brazil**

Mariana K. Leal Ferreira is currently editing a volume on multicultural mathematics in Portuguese,
** Matemática na Aldeia**, featuring experiences with the teaching of mathematics among native
populations. She will consider proposals for the publication of articles and review articles on
books and other materials that would be translated into Portuguese by either herself or one of her
colleagues at the Department of Anthropology, Universidade de São Paulo, Brasil. Proposals can
be sent to:

Mariana K. Leal Ferreira

MARI-Grupo de Educação Indigena

Departamento de Antropologia-FFLCH

USP-C.P. 8105

05508-900 São Paulo, S.P.

BRASIL

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**Ethnomathematics Conference and** **Speaker Series at U-mass**

**Gloria Gilmer**

On November 3rd and 4th , the College of Public and Community Service (CPCS) at the
University of Massachusetts-Boston sponsored an Ethnomathematics conference as part of its
25th anniversary celebration. To add to the celebration, there was also a book party for the new
book *Ethnomathematics: Challenging Eurocentrism in Mathematics Education* edited by Arthur
B. Powell and Marilyn Frankenstein.

The keynote speakers were Dirk Struik and Lee Lorch both of whom are internationally acclaimed mathematicians. Both were cited as scholar-activists whose work exemplifies the commitment of CPCS to unite theory and practice in the struggle for justice. Dirk Struik spoke on Ethnomathematics in the History of Mathematics and Lee Lorch spoke on The Painful Path Toward Inclusiveness: The Struggle Against Racism in Mathematical Circles. On the first day, Dirk Struik's talk was followed by a panel which included, Paulus Gerdes, Munir Fasheh, Gloria Gilmer, Arthur Powell and Marilyn Frankenstein all of whom were contributors to the new publication.

On January 12, Gelsa Knijnik will speak on Mathematics Education and the Landless People Movement's Struggle for Justice. In April, Martin Bernal will speak on Ancient Egyptian Science: Fact or Fabrication?

For more information on the speaker series, contact Marilyn Frankenstein at 617-287-7144 or e-mail:frankie@umbsky.cc.umb.edu

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**ISGEm's Tribute to Dr. Gloria Gilmer**

In a very beautiful setting of candle light, flowers and dinner music at the Minneapolis Marriott Center City Hotel, officers and members of the ISGEm paid a tribute to Dr. Gloria Gilmer, their president of 11 years. Patrick Scott, newsletter editor, presided over the program. Maria Reid gave the Occasion. Tributes were presented by Lawrence Shirley, Luis Ortiz-Franco, and Jolene Schillinger, read a letter from Claudia Zaslavsky, who could not attend. Ubiratan A'mbrosio, the new president of ISGEm, presented a plaque to Dr. Gilmer on behalf of the Study Group and a special gift of a book on Brazil. The arrangements committee was Henry Gore and Maria Reid. Others in attendance included: Jim Barta, Ron Eglash, Marilyn Frankenstein, Ed Jacobsen, Gelsa Knijnik, Beatrice Lumpkin, Joanne Masingila, Clo Mingo, María Luisa Oliveras, Marjorie Palmer and Norma Presmeg.

_____________________

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**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

**ISGEm Executive Board**

Ubi D'Ambrosio, President

Rua Peixoto Gomide 1772 ap. 83

01409-002 São Paulo, SP BRAZIL

ubi@usp.br

Maria Luisa Oliveras Contreras, 1st VP

Depto de Didáctica de las Matemáticas

Campus Cartuja, Universidad de Granada

18071 Granada, SPAIN

oliveras@platon.ugr.es

Jolene Schillinger, 2nd Vice President

New England College BX 52

Henniker, NH 03242 USA

jus@nec2.nec.edu

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

gelsa@portoweb.com.br

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

pscott@nmsu.edu

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

gilmer@cs.uwp.edu