Página do site oficial de Ubiratan D`Ambrosio

Etnomatemática

Concepção etnoantropológica de matemática

E-mail  Ubiratan

Novos textos

ALUSTAPASIVISTYKSELITYS

or

THE NAME ETHNOMATHEMATICS:

MY PERSONAL VIEW

by Ubiratan D’Ambrosio

Ethnomathematics is an emergent research area. The Mathematics Subject Classification 2000, sponsored by the Mathematical Reviews and the Zentralblatt für Mathematik, lists Ethnomathematics as sub-area 01A07 of the research area "History and biography". And the growing number of books and papers published in several languages and the number pf dissertations and theses submitted in several universities of the World are indicators of the vitality of this new research area.

But Ethnomathematics, particularly the way I conceptualize it, and the research program that I propose, and its pedagogical implications, have been challenged by many.

There has been much talking about the word Ethnomathematics. I will elaborate on how I did start using this word and how it developed into the meaning I give to it.

I never claimed that no one else has used this word before, although I had never seen it. I recently learned from Claudia Zaslawsky that Otto Raum wrote, in a review of her book, published in African Studies(1976): "(This Mathematics) might perhaps be most suitably called ethno-maths on the analogy of ethno-music, ethno-semantics, etc.". Wilbur Mellerna, in a letter to Gloria Gilmer, published in the NEWSLETTER of the ISGEM (vol.6, n.1, November 1990), says that he had invented the word ethnomathematics in 1967 and that he gave a talk in 1971 using it. But I had never seen it in print before I started using it. I am sure that a search in the literature, mainly in Anthropology, may reveal other users of the word ethnomathematics. No surprise.

I was aware that the word ethnohistory had been introduced in the 1940s, as the history of non-literate people, and that in 1955, an International Society of Ethnomusicology was founded. Also I knew the field of ethnopsychiatry, focusing on "exotic societies". When I lectured at the Linguistic Institute at SUNY at Buffalo, in the Summer of 1971, the word ethnolinguistics was current. Ethnopsychology, ethnobotany, ethnomedicine were also frequent to refer to the study of practices of different racial groups. And the sociologist Harold Garfinkel coined the word ethnomethodology in 1967 to express his interest in how social interactions and practices are related.

But my use of the word ethnomathematics and the Program Ethnomathematics, have a history of its own. Surely, it should not be confused with the ethnographic approach or, with we might call an ethnic mathematics. Although relying on much of its results, the Program Ethnomathematics has a broader scope.

In 1976, I was invited to organize and preside the section "Why Teach Mathematics?" in the 3rd International Congress of Mathematics Education/ICME 3, in Karlsruhe, Germany. There I proposed a broader view of mathematics and how it should be to taught in schools. I suggested a discussion of the nature of mathematical knowledge, with special attention given to History, Philosophy and Cognition in a broader sense, not restricted specifically to the philosophy and the history of mathematics and the theories about learning mathematics.

Why this? Because I see much of the history and philosophy of mathematics, as well as of mathematical cognition, redundant and biased. The essence of the proposal was to look into different ways of doing mathematics, taking into account the appropriation of academic mathematics by different sectors of society and the way different cultures deal with mathematical ideas. The appropriation frequently leads to imprecise and mathematically unsatisfactory uses of it. And mathematical ideas in some cultures are sometimes seen as ad hoc knowledge, without an underlying structure. Thus, I decided to look into the ways different cultural groups develop ways of doing and knowing through comparing, evaluating, classifying, quantifying, counting, measuring, representing, inferring. These are the grounding bases for mathematical ideas.

It is important to clarify that I consider cultural groups in a broader sense than looking into levels of homogeneity in racial patterns, in languages, in the set of values, in myths and religions. I understand as cultural groups families, friends, communities, professionals, nations, and try to identify ways of doing and knowing of these groups. Although this approach had been growing in importance in the academy, it was practically ignored and, indeed, sometimes rejected in the mathematics circles in 1976. My proposal is a transcultural perception of the nature of mathematical knowledge, which demands a transdisciplinarian approach to knowledge in general.

I insisted on the fact that there are other ways of doing mathematics, proper to different cultures. I found the reference to the pioneer book of Claudia Zaslavsky Africa Counts very important. Much to the surprise of my colleagues, I proposed an unusual bibliography, including Nietsche and Spengler, classics of Anthropology and an historiography in the line of the proposals of the Annales. The expanded version of my talk gave origin to a booklet published soon after.

It did not occur to me then that ethnomathematics would be a good name for the mathematics of other cultural environments, although I was familiar with ethnobotany, ethnomusicology, ethnopsychiatry, ethnolinguistics and other ethno-knowledges. It is easy to understand why I did not use the "ethno" prefix. The work of botanists, musicians, psychiatrists, linguists and others are, basically, ethnographical studies of these disciplines. This research is, no doubt, very important, and there is a great need of more of such studies focusing mathematics. In other words, there always much need for this kind of ethnomathematics, and several important works are available. Much research on the ways of doing mathematics in other cultural environments is available from a long time. Mainly anthropologists and some learning psychologists have published very important research in this approach. Many are concerned with how the number system was incorporated to human cultures. Different ways of comparing, evaluating, classifying, quantifying, counting, measuring, representing, inferring, have been observed in several cultural environments, throughout history, even before anthropology was defined as such. In our days, much research of primatologists focus on these capacities.

We have to learn the mathematics of other cultural environments. Indeed, this has been very interesting and helpful in classrooms. Not only in multicultural education, which is a modern trend in education. But also in culturally homogeneous groups. But this sort of ethnic mathematics, even when relying on rigorous ethnographic studies, can easily lead to a folkloristic view of how other cultures do counting, measuring, etc., with total disregard for the complexity of their cultural specificity. I still see this as an equivocated approach to ethnomathematics, particularly when utilized as a pedagogical resource. It relies on curiosities and anecdotes, dealing with number and figures. Unless properly situated in an ample cultural scenario, this approach to ethnomathematics is prone to reinforce eurocentrism.

Much of the motivation behind these views can be traced back to the 60s and 70s, are present in my paper for the Karlsruhe conference. They emerged from my work with minorities while in the faculty of S.U.N.Y at Buffalo, from my work in Africa, in the UNESCO project called "CPS Bamako" and by coordinating the interdisciplinarian Multinational Project of Science Education of the Organization of the American States. In all these socio-cultural environments, the USA, Africa, Latin America and the Caribbean. I was strongly motivated to understand how knowledge, particularly mathematical knowledge, was generated, intellectually and socially organized, and diffused. This research program depends on studies of the mind and cognition, anthropology, linguistics, history, epistemology, politics, education, as well as some interdisciplines.

My interest was – and continues to be – to understand the nature of knowledge, in particular of mathematical knowledge. I relied on the recognition that mathematics is part of broad cultural contexts, having everything to do with religion, the arts, economics, politics and the social organization of society. I had not yet formulated the research program focused on the generation, the intellectual and social organization, and the diffusion of knowledge, which became the backbone of the Program Ethnomathematics.

The major breakthrough for establishing Ethnomathematics as a research field on its own came after the 5th International Congress of Mathematics Education/ICME 5, in Adelaide, Australia, in 1984. There I gave the opening plenary conference on "Socio-cultural bases of mathematics education."

The reaction to the conference was not different from what happened in 1976, in Karlsruhe. Reactions were mixed, polarized in a group in full agreement with my views and proposal, and another group of those who entirely rejected it. The scenario is not significantly different from what happens nowadays.

The trajectory of these ideas from 1976 through 1984 deserves an explication. Soon after ICME 3 I had several opportunities to expand the ideas outlined in Karlsruhe.

In 1977, during the Annual Meeting of the American Association for the Advancement of Science, Rayna Green organized a section on "Native American Science". I gave a paper and I used the word ethnomathematics, to designate the mathematics of the native cultures, similarly to what other participants were doing with their disciplines. But the use of the word ethnomathematics was always focused on the description of the mathematics of other cultures, mainly those without writing and those marginalized by the colonial process.

In 1978, Bernhelm Booss and Mogens Niss organized a meeting on "Mathematics and the Real World", followed soon after by a memorable satellite conference on "Mathematics and Society", preceding the International Congress of Mathematicians/ICM 78, in Helsinki. Many requests to the IPC of the congress to include this conference as part of the program met with an incredulous reaction. The argument was, as obviously expected, that this theme had nothing to do with mathematics as such. But the concession of a space for a satellite conference and the large number of attendants were big achievements. This was important in drawing the interest of the mathematical establishment to broader societal issues. Soon after, in 1978, Mohamed El-Tom organized an important meeting in Khartoum, sponsored by UNESCO, on "Developing Mathematics in Third World countries".

In those days I was building-up my views on mathematical knowledge. Why did our species develop such a thing as mathematics? And how does mathematics evolve?

My interest in the history of the evolution of academic mathematics in Europe led me into examining the cultural dynamics in the development of Mediterranean civilizations and in the expansion of Christianity. Particularly interesting is the role of paganism in this process.

In the visits to Denmark and Finland, I got very much impressed by the Pagan cultures of Scandinavia. The Vikings, with their ship-building, their navigation instruments and their symbols were, and still are, intriguing. I was impressed by the long length of the days and by the fact that in the Northern part of the region, which I visited later, the days lasted six months! How was the cosmovision of these cultures? Considering that time and cosmography have such an important role in the development of mathematical ideas, how could these people make sense of their own experiences and of the cultural interactions during the almost thousand years of conquest of Southern Europe? The conqueror absorbed the culture of the conquered. This was a dual situation of what I had seen in the cultural dynamics which occurred in the Americas and in Africa during the conquest and colonial era.

The crux was to understand how individuals and cultural groups respond to the drives for survival [proper of every living structure] and transcendence [specific of human beings], which are intrinsic to human nature. These drives lead to actions performed incessantly, in a symbiotic way, by living beings. In response to the needs of survival and transcendence, knowledge is generated, shared by the cultural group, and organized in ways, styles and techniques of doing and of explaining, understanding and learning. Systems of knowledge are the complexes of these responses, given by distinct cultural groups, to the drives for survival and transcendence.

I like to play with dictionaries. When going to different countries, I usually buy a small dictionary and use much of my leisure time in browsing through it. While in Finland, it was a good exercise to understand how would the Finns express their ways of satisfying their needs of explaining, understanding, learning, intrinsic to the human drives toward survival and transcendence. Browsing through an English-Finnish-English dictionary, I made a "good" word the Finns might use to express this: alusta-sivistyksellinen-tapas-selitys! Or making it a little less frightening, alustapasivistykselitys. Free time in congresses is always stimulating. But this was nonsense playing and lots of fantasy!

Maybe the word would be less shocking if it were expressed using Greek roots. Why not ethno[for a group with compatible behavior]-techné[for ways, arts, techniques]-mathemata[for explaining, understanding, learning] or, as it would sound much better, ethno-mathema-tics?

Each culture developed ways, styles and techniques of doing, and responses to the search of explanations, understanding and learning. These are the systems of knowledge. All these systems use comparing, evaluating, classifying, quantifying, counting, measuring, representing, inferring. Of course, Western mathematics is such a system of knowledge, as a broad view of its history shows. But other cultures developed, also, other systems of knowledge with the same aims. That is, other "mathematics", using different ways of comparing, evaluating, classifying, quantifying, counting, measuring, representing, inferring. All these systems of knowledge might well be called ethnomathematics. They are "mathematics" of different natural and cultural environments, all motivated by the drives for survival and transcendence. Mathematics basically respond both to "How" and "Why".

I had already used ethnomathematics in the narrower sense of representing real facts and phenomena, of comparing, evaluating, classifying, quantifying, counting, measuring, inferring, etc., in different cultural environments. But an understanding of the nature of these ethnomathematics was still a challenge for me.

Thus I decided to analyze the development of Western Mathematics, in the broader sense of responses to the needs of survival and transcendence, taking into account the practical and mystic motivations present in this development. I was then led to the study of systems of knowledge in general, looking into the full cycle of the generation, the intellectual and social organization, and the diffusion of knowledge, and the subsequent changes in the systems as results of the cultural dynamics in the encounters. I understand encounters in two senses, which we may call vertical (as different generations in the same cultural environment) and horizontal (mutual exposition of different cultures). Vertical encounters are typical of education, while horizontal encounters are present in visitors exchanges or the conquest/colonial process.

The so-called "externalist" History of Mathematics, focusing on anthropological, social, political and religious issues, among others, is a very clear illustration of the full cycle of knowledge. It looks into how the processes of comparing, evaluating, classifying, quantifying, counting, measuring, representing, inferring have originated, with more or less emphasis of one or another, in different cultures, and how cultural dynamics played an important role in the development of these forms of knowledge, leading to the institutionalization of the ways of thinking and doing which resulted.

Geopolitics determined a marked influence of Greek language and philosophy in Mediterranean Antiquity. The word Mathematics, in the several versions present in Classical Greek and its use in Latin, have different meanings. Only in early Renaissance the word Mathematics came into use with meaning similar to what it is today: a Science in its own, detached from philosophy and the other sciences, which appropriated concepts and techniques from various branches of philosophy, from earlier times and from many different cultures. Thus, Ethnic Mathematics, the same as Non-Western Mathematics, are clearly equivocated.

I sometimes have indulged in the use of such terminology. It is clear to me, examining several different cultures, that the word ethno-mathema-tics, which was the result of an etymological playing, carried in it the synthesis of the research program which I call Ethnomathematics. Summing-up, "Ethnomathematics is the art or technique of explaining and knowing, in different cultural environments".

This is how the name Ethnomathematics came into being in my thinking.

Movimento

Etnopedagogia

 1 Concepção

Célestin Freinet 7

 2 Pensamento

Paulo Freire 8

 3 Estruturação

Ubiratan D`Ambrosio 9

 4 Paradigmas

Edgar Morin 10

 5 Vivências

Pessoas & Livros 11

 6 Processo

E-pombo @ Correio 12

Página inicial