Ethnomathematics: My Personal View

by Ubiratan D’Ambrosio

It is important to clarify, from this very beginning, about my career and how I arrived to Mathematics Education. I was born in 1932. In 1949 I was already giving private tutoring classes for people preparing to enter public service (mainly tutoring Financial Mathematics). I graduated 1954, with a major in Mathematics (Pure) and taught, for some years, in high-schools. In 1958 I was hired as a full time instructor and graduate student at the University of São Paulo (USP) and received my Doctorate in 1963, with a thesis on Calculus of Variations and Measure Theory (very pure!). In 1964, I went to the USA as a Research Associate at Brown on a year leave, but due to the political events in Brazil, I stayed there and became a tenured faculty at the State University of New York at Buffalo. My first PhD student wrote his thesis on Stability of Differential Equations. During this time, my interest in Education was occasional and minimal. In 1972, I returned to Brazil and became the Director of the Institute of Mathematics, Statistics and Computer Science of the State University of Campinas (UNICAMP), which grew as a major research institution. My first Brazilian doctoral student in Campinas wrote a thesis on Measure Theory and Minimal Surfaces. From this period I realized that Mathematics Education was priority for Brazil, mainly motivated by the cultural and social barriers which were so responsible for failing and dropping out of children coming form marginalized groups. They could not compete with children coming from families with some scholarity. At the same time, I developed an interest in History of Mathematics and on broad (trancultural and transdisciplinarian) theories of knowledge. This is my background.

My current concerns about research and practice in math education fit into my broad interest in the human condition as related to the history of natural evolution (from the Cosmos to the future of the human species) and to the history of ideas. Particularly, the history of explanations of the creation and the natural evolution.

In the last years (surely much before the last five), my motivation has been the pursuit of peace (in all four dimensions: individual, social, environmental and military). I attribute the violations of peace, in all these four dimensions, to the mistaken course of the Western civilization. I try to understand the founding myths of Western civilization, and this links to my research on the history of monotheistic religions (Judaism, Christianity, Islamism), of techniques, of arts and how mathematics permeates all this. A great support is gained by looking into non-Western civilizations. I base my research on established forms of knowledge (communications, languages, religions, arts, techniques, sciences, mathematics) and in a theory of knowledge and behaviour which I call the "cycle of knowledge". This theoretical approach recognizes the cultural dynamics of the encounters, based on what I call the "basin metaphor". All this links to the historical and epistemological dimensions of the Program Ethnomathematics, which can bring new light into our understanding of how mathematical ideas are generated and how they evolved through the history of mankind. It is fundamental to recognize the contributions of other cultures and the importance of the dynamics of cultural encounters. Culture is understood in its widest form, and includes art, history, languages, literature, medicine, music, philosophy, religion and science. Research in ethnomathematics is necessarily transcultural and transdisciplinarian. The encounters are examined in its widest form, to permit exploration of more indirect interactions and influences, and to permit examination of subjects on a comparative basis. Although academic mathematics developed in the Mediterranean basin, expanded to Northern Europe and later to other parts of the World, it is difficult to deny that the codes and techniques to express and communicate the reflections on space, time, classifying, comparing, which are is proper to the human species, are contextual. Among these codes are measuring, quantifying, inferring and the emergence of abstract thinking.

At this moment, it is important to clarify that my view of ethnomathematics should not be confused with ethnic-mathematics, as it is understood by many. This is the reason why I insist in using Program Ethnomathematics. This program tries to explain mathematics, as it tries to explain religion, culinary, dressing, football and several other practical and abstract manifestations of the human species. Of course, the Program Ethnomathematics was initially inspired by recognizing ideas and ways of doing that reminds us of Western mathematics. What we call mathematics in the academia is a Western construct. Although dealing with space, time, classifying, comparing, which are is proper to the human species, the codes and techniques to express and communicate the reflections on these behaviors is undeniably contextual. I got an insight into this general approach while visiting other cultural environments, during my work in Africa, in practically all the countries of continental America and the Caribbean, and in some European environments. Later, I tried to understand the situation in Asia and Oceania, although with no field work. Thus came my approach to Cultural Anthropology (curiously, my first book on Ethnomathematics was placed by the publishers in a collection of Anthropology).

To express these ideas, which I call a research program (maybe inspired by Lakatos?), I created a neologism, ethno-mathema-tics. This caused much criticism, because does not reflect the etymology of "mathematics". Indeed, the mathema root in the word ethnomathematics has little to do with "mathematics" (which is a neologism introduced in the XIV century). The idea of organizing these reflections occurred to me while attending ICM 78, in Helsinki. I played with Finnish dictionaries and was tempted to write alustapasivistykselitys for the research program. Bizarre! I believed Ethnomathematics would be more palatable.

I understand that there are immediate questions facing World societies and education, particularly mathematics education. As a mathematics educator, I address these questions, thus my links to the study of curriculum, and my proposal for a modern trivium: literacy, matheracy and technoracy. This is one of main lines of work in mathematics education.

The pursuit of Peace (in all four dimensions mentioned above), is an urgent need. This explain my works in Mathematics and Peace, Mathematics and Ethics, Mathematics and Citizenship. This is the theme of several lectures and courses for in-service teachers. I have published studies on curriculum and oriented several doctoral theses with this focus.

These two lines of my current work in mathematics education link, naturally, to the pedagogical and social dimensions of the Program Ethnomathematics.

It is important to insist that the Program Ethnomathematics is not ethnic mathematics, as some commentators interpret it. Of course, I work with different cultural environments and work, as an ethnographer, trying to describe mathematical ideas and practices of other cultures. This is a style of doing ethnomathematics, which is absolutely necessary. But these cultural environments include indigenous populations, labour and artisan groups, periphery communities in urban environment, farms, professional groups. They develop their own practices, have specific jargons and theorize on their ideas. This is an important element for the development of the Program Ethnomathematics, as important as the cycle of knowledge and the recognition of the cultural encounters.

More recently, I have worked with the preparation of teachers for indigenous communities in the State of São Paulo. Altogether, there are about 100 small tribes (some with different languages), totalising about only 8,000 individuals. We are now starting a project on the ethnomathematics of the "quilombolas", which are small communities originated from slaves who fled in the XVII and XVIII centuries, and established themselves as small republics in the hinterland of Brazil. The research resulting from all these projects feeds the Program Ethnomathematics.

Besides these more immediate concerns, there are long term concerns. Of course, they are related. Thus my links with Future Studies. I have been active, publishing and lecturing, on history and philosophy focusing future.

I see the special role of technology in the human species and the implications of this for science and mathematics. Thus I focus history of science (and, of course, of mathematics) trying to understand the role of technology as a consequence of science, but also as an essential element for furthering scientific ideas and theories. Basically, I guide much of my investigation on three basic questions:.

How are ad hoc practices and solution of problems developed into methods?

How are methods developed into theories?

How are theories developed into scientific invention?

Once recognized the role of technology in the development of mathematics, reflections about the future of mathematics propose important questions about the role of technology in mathematics education. Hence, my line of work in distance education.

Reflections about the presence of technology in modern civilization leads, naturally, to question about the future of our species. My growing interest in the emerging fields of Primatology and Artificial Intelligence, lead to a reflection about the future of the human species. Cybernetics and human consciousness lead, naturally, to reflections about fyborgs (a kind of "new" species, i.e., humans with enormous inbuilt technological dependence). Our children will be fyborgs when, around 2025, they become decision makers and take charge of all societal affairs. Educating these future fyborgs calls, necessarily, for much broader concepts of learning and teaching. The role of mathematics in the future is undeniable. But what kind of mathematics? Once again, I look for explanations in history.

To understand how, historically, societies absorb innovation, is greatly aided by my involvement with world fiction literature (from iconography to written fiction, music and cinema). I feel it is important to understand the way material and intellectual innovation permeates the thinking and the myths, and the ways of knowing and doing of non-initiated people. In a sense, how new ideas vulgarise, understanding vulgarise as making abstruse theories and artifacts easier to understand in a popular way. This places me on the side of "post-modernists" in the current science wars.

Although this is a difficult position to defend in academics, particularly as a math educator and historian, this summarizes my involvement with current philosophy.

How communities deal with space and time, mainly the sacralization of chronology and topology in history, is central in my thinking. A recent doctoral student of mine worked on concepts of space and time in a modern popular urbanization in the Amazon basin. Another doctoral student deals on how the concept of space permeates the medieval emergence of non-euclidean geometry. And another student looks into modern art and mathematics.

I am now working on a paper dealing with the relations of ethnomathematics, ethnomethodology and phenomenology. I look into their evolution and try to identify a common underlying philosophical framework, through a transcultural and transdisciplinarian lecture.

Let me comment, now, how does these ideas relate to mathematics education, particularly in Brazil, where the situation does not differ much of many other countries which have an intense population dynamics, as for example the USA. These are countries were much progress is noticed. Never in Brazil the publishing houses flourished so much, and never the industrial and agricultural production was so intense. This contradicts official assertion, based on the results of tests and national exams, that the school system is a great failure. According to official sources, Brazil is in a terrible shape in reading, writing and mathematics. Any system, with such results, would have been declared irremediably bankrupt.

I am much worried with the cultural dynamics of the encounter of generations (parents and teachers and youth). This encounter is dominated by mistrust and cooptation, reflected in testing and evaluation practices, which dominate our civilization. In mathematics education, this is particularly disastrous. Paradoxically, the voices of individual math educators are against this, but the practice of the totality insists in sameness. The result is teaching mathematics in an uninteresting, obsolete and useless way.

Resources to testing is the main argument to justify current math curricula. The claims of importance of current math curricula are fragile. Myths surround these claims. These have been, since the 60s, my main motivation for my thoughts about math education. In the last years, this has been intensified by my analysis of results of testing in Brazil and elsewhere in the World.

I try to understand children and youth behaviour and their expectations. History gives us hints on how periods of great changes affect the relations between generations. Most interesting is the analysis of movements after WWII and Viet Nam War.

Synthesizing, there is more concern with mathematics than with our children. In general, education is dominated by a kind of "corporatist" expectations for the future [this is why education leads to the reemergence of fundamentalism and fascism] and, regrettably, mathematics and mathematics education have everything to do with this. Test may be the best instruments to allow this.

I believe that the work done by me and by my colleagues had, or is going to have even more, an actual impact on the practice of mathematics education. The research done by all of us, have a high academic level, leading to different approaches to math education and touch important social issues. But it is a slow process, with many reactions.

I learned from a colleague Science Educator in the early 70s, that changes in education occur by "stealth". I have confirmation of this. When I visit schools, invited by colleagues and former students, and I have an opportunity to talk with students, I see how effective is the "stealth approach".

Although unwritten, unreported, unnoticed by the political and academic authorities, the innovation benefit enormously some students, while other students not even notice this, and prepare for testing. What is wrong with testing? Basically, because they penalize the former, which are creative, and favour the later, which are cooptable and amenable to sameness. Although homogeneous behavior and results are unnatural in the human species, this is the supporting argument for stardardized testing, which prevails in evaluation, although it is denied by the theoreticians who support current testing.