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Etnomatemática

Concepção etnoantropológica de matemática

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by Ubiratan D’Ambrosio

It is so common that teachers and the public in general say that mathematics is a cultural endeavor. Indeed, mathematics is part of culture and it is linked to the history of peoples and communities all over the World. Although mathematics has been developed as an academic discipline and it is incorporated in the school programs, it is a very well known fact that mathematics, in everyday life, relate to routine practices and to professions. We have much research to show that even people without schooling deal with numbers and with measurements in their daily life. In many cases, these ways of doing mathematics are not accepted by teachers, since they follow different paths of reasoning. Indeed, these different paths of reasoning reflect cultural roots.

Cultural roots may be understood in different ways. These may be traced back to ethnic background, learnt from parents, grandparents, great-grandparents and thus going back to ancestors. with some characteristics that are related to their everyday practices and to their professions. all over the World. But we may ask in which ways mathematics taught in our schools fits into the history of the people. We see that practically all mathematics in the curriculum can be traced back to Mediterranean traditions and spread throughout the World after the Colonial era. We may ask: in the period of the great navigations, what kind of mathematics was present in the lands conquered by the Europeans? How the existing mathematics of every c, in every were modified? , how and conquest, Much of this mathematics was developed from Antiquity and throughout the Middle Ages and the Renaissance. It has been organized as a school subject since the nineteenth century and well into the twentieth century. But since the sixties we see a growing interest in multicultural education and this affects particularly mathematics.

A question frequently asked by teachers is how to include mathematics in the multicultural trend. A proposal is to bring ethnomathematics into the school practice.

Why ethnomathematics? What is ethnomathematics and how can it help children in schools?

The idea of ethnomathematics came as a broader view on how mathematics relates to the real world. Mathematics is an intellectual instrument created by the human species to describe the real world and to help in solving the problems posed in everyday life.

Like every living individual, humans look for survival. But differently than any other species, humans look also for explanations of facts and phenomena, which can be seen and felt, and thus develop new manners of getting from nature what is needed for survival and pleasure. How this differ from other species? There are many answers, which include the capability of humans developing language, tools, art, music, humor and mathematics.

Indeed, the human species is unique among all the animal species to create agriculture, it is the only one to develop a sense of past and future, that is, to measure time, and the only species that developed language. From prehistoric ages humans have been accumulating knowledge to respond to these drives and needs. Of course, the responses vary from region to region, from culture to culture. It is clear that people living in tropical forests have developed different ways of measuring the lands than those living in a prairie, thus they have different geo [land] - metries [measurement].

Those living near the Equator perceive days and nights elapsing in the same way during the all year, while those living above the tropics recognize how the seasons affect the duration of days and nights. Thus calendrical systems, and consequently means of production and its control and distribution, of organizing labor, and many other practices which occur in daily life, have been developed, since immemorial times, in different ways, related to the natural environment. This builds up into arithmetic, which is different from culture to culture.

In the sixteenth century, European nations, beginning with Portugal and Spain and soon followed by Holland, England and France, conquered practically the entire planet and established colonies all over the World. With the colonial regime the ways and means of production and of commerce were aligned into the European model. Together with this came the mathematics which was developed in the European nations. The ways and means of production and commerce of the conquered people were in most cases ignored, in some cases forbidden. Together with this, traditional ways of doing mathematics, as well as language, religion, medicine and so many other cultural expressions were also ignored, in many cases forbidden. Cultural expressions are the essence of cultural dignity.

The end of the colonial era marked the renaissance of cultures that for centuries have been ignored, in many cases forbidden. As a consequence, we have seen in recent years an explosion of new forms of art, of health care, of religions and of costumes in general. Even languages that have forgotten, sometimes forbidden, are now heard and written.

It is natural to ask: what about Mathematics?

We know that the basic ways of doing mathematics is the result of measuring, counting, comparing, classifying, inferring, and that all this is related to the natural and cultural environment. Although the traditional ways of performing these actions have been ignored, and in many cases forbidden, for centuries, we now see that they have survived. Of course, they went through an evolutionary process as a result of the encounter with other ways of doing. These ways of doing mathematics in specific natural and cultural environments are called Ethnomathematics.

Ethnomathematics is seen in communities and are easily recognized in every day practices, and is particularly noticeable among artisans.

Then we ask: Why to bring this to school practice? Some critics say this is useless, this is more like playing, and there no reason to incorporate these practices in the academic curriculum. It may be true that in looking for jobs, students will be required to know traditional school mathematics. But there is much more in educational goals than merely provide utilitarian instruments. Education must enhance cultural dignity.

To reaffirm and in some cases to restore cultural dignity of children is an important component of mathematics education. Much of the contents of current programs are supported by a tradition alien to the children. On the other hand, children are living in a civilization dominated by mathematically based technology and by unprecedented means of communication.

It is equally important to recognize that improving the opportunities for employment is a real expectation that students and parents have of school. But preparation for the job market is indeed preparation for the capability of dealing with new challenges. There is no point in preparing children for jobs that will probably be extinct when they reach adulthood. To meet the challenges of the new self-esteem is essential. Self-esteem goes together with cultural dignity.

Both to acquire cultural dignity and to be prepared for full participation in society requires more than what is offered in traditional curricula. Particularly grave is the situation of mathematics, which is largely obsolete as present in the programs. Classroom mathematics has practically nothing to do with the world the children are experiencing. The same as literacy nowadays mean much more than reading and writing, mathematics is much more than counting, measuring, sorting, comparing.

I am particularly concerned with the fact that efforts to do better in mathematics education are sometimes interpreted as a reduction of the importance of mathematical contents.

I believe this is a grossly mistaken interpretation. We need more and better mathematical contents, but this does not mean the traditional contents which exhaust current programs. The big mistake is to consider math contents as something final, subordinated to criteria of rigor which are also considered final.

Compromising rigor, in benefit of generating interest and motivation, can not be interpreted as conceptual errors or a relaxation of the importance of serious mathematical contents of a modern nature.

Examples are the use of calculators [in lieu of drill with operations], geometric ratios [not formal operations with fractions] and the resource of paper folding for the teaching of geometry.

Multiplication tables may be important not because of the values associated with two numbers, but rather if one recognizes that the product of two one-digit numbers may result in a two-digit product. In modern terms, when pressing one key times one key you get two digits as a result in the screen. Because our calculators represent the highest level of realizing the positional system.

An exercise for children: with a 8-place calculator, when you press 2 then x then 50000000 an E appears in the screen, pressing 2, x, and 49999999, we read 99999998 in the screen. Why?

But let me focus on how Ethnomathematics can be a strategy to achieve these broader goals of education in the 21^st Century.

There has been an overly simplified view of Ethnomathematics. We have to place our discussions on the nature of Ethnomathematics in a broader reflexion on the nature of knowledge. I see knowledge as something generated and intellectually organized by the individual in response to the social, cultural and natural environment and, after being shared through communication, socially organized, thus becoming something that is part of a community [culture] and essential for dealing, recognizing, explaining facts and phenomena. Observers, chroniclers, theoreticians, sages, academics, professionals, POWER "detainers" expropriate this knowledge, classify and label them, and then transmit and diffuse them. Thus we have structured forms of knowledge: language, religion, culinary, medicine, dressings, values, SCIENCE, MATHEMATICS, all interrelated and responding to the way reality is perceived in that social, cultural and natural environment.

Cultural dynamics increasingly plays a role in "broadening" perceived reality, and as a consequence modify the responses. So, language, religion, culinary, medicine, dressings, values, SCIENCE, MATHEMATICS are always changing.

I use the word "ethno" as a form of recognizing the dynamics of different forms of knowledge, in which there is no freezing processes.

There are different ethnomathematicsES (plural), each one responding to a different cultural, natural, social environment.

When ethnomathematicians say "more than one mathematics" they are recognizing different responses to different natural, social, cultural environments. As more than one religion, more than one systems of values, there may be more than one way of explaining, understanding, coping with reality.

I see the possibility of building up a new civilization, in which inequity, bigotry, intolerance, hatred, discrimination, have no place, as the result of unfreezing the forms of knowledge [that is, removing fundamentalisms] and allowing cultural dynamics to play its role in the evolution of the species.

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

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