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**Shiva Thapa, **

**M.Ed 2 ^{nd} Year, University Campus, Kritipur, Roll .no. 984**

· **Background/Introduction: **

The term ethnomathematics was first coined by Brazilian mathematician Prof. Dr. Ubiratan D’Ambrosio( Sao Paulo, Brazil) however a German historian and philosopher Oswald Spengler (1980-1936) whose interest was also in mathematics and science had tried to write about mathematics in different cultural eras. Later on Prof. Ambrosio led the concept of ethnomathematics in logical end and established as an emerging issue of modern mathematics. Ubiratan D'Ambrosio in 1977 during a presentation for the American Association for the Advancement of Science presented the concept of ethnomathematics. How ever it was established as a valid research program in 1984 in the session of ICME. He presented various document between 1985 and 2001 about ethnomathematics.

· **Meaning of Ethno-mathematics:**

Prof. D'Ambrosio deconstructs the word ethnomathematics as: ethno + mathema + tics (techné) where ethno is natural, social, cultural and imaginary environment, mathema is explaining learning knowledge and tics is models, style, art and techniques. So ethnomathematics is combine form of mathematics, cultural anthropology and mathematical modeling. We know anthropology simply refers the holistic study of human being and cultural anthropology refers cultural variation among all human being of the world.

We know that mathematics is universe. It has its own world and own language. The way of learning mathematics is different in each individual due to their culture, society and environment. Different people of different cultural group have different way of doing simple mathematical operation, counting, estimating, calculation, measurement etc. We know that with out mathematical concept everything remains incomplete. Every social task is going on in the base of mathematics. A carpenter uses mathematics in his own style, a farmer uses mathematics in his farming, and a mechanic uses the mathematics in making and repairing the machine. In the practice of Nepal generally the teacher and student uses the numeration system in base 10 where as some specific cultural group of Nepal as well as some ethnic group of Mexico and United State of America uses the numeration system of base 20. There are various way of measurement used universally. We use Sexagesimal system (English System) measured in degree where as other uses French system called centesimal system measured in grade, and some uses radian or circular system. The rural area's people of Nepal are traditionally using their own tools of measurement called *mana, pathi, dhak, taraju, hat, bitta*, etc. So we can say that ethnomathematics is the mathematics practiced by different cultural group such as urban and rural communities, group of worker, professional classes, children in a given age group, indigenous societies, and so many group of the world. We have accepted Standard Unit in measurement but also we are practicing it in different manner. Such type of mathematical practice is called ethno-mathematics.

"The mathematics which is practiced among identifiable cultural groups such as national-tribe societies, labor groups, children of certain age brackets and professional classes" -D‘Ambrosio, 1985).

Simply we can say the ethnomathematics is:

Ø The way of mathematical representation in cultural aspects.

Ø Mathematical practice in indigenous groups.

Ø Mathematics for non mathematician.

Any concept of ethno-mathematics must eventually meet philosophical debates about the nature of mathematics. For more than two thousand years mathematics has been regarded as the epitome of rational truth, the study of the essential features of quantity, relationships and space. However the concept of ethno-mathematics has broken that conviction. The term ethnomathematics is used to express the relationship between culture and mathematics. The term requires a dynamic interpretation because it describes concepts that are themselves neither rigid nor singular—namely, ethno and mathematics (D’Ambrosio1987). The term ethno describes “all of the ingredients that make up the cultural identity of a group: language, codes, values, jargon, beliefs, food and address, habits, and physical traits.” Mathematics expresses a “broad view of mathematics which includes ciphering, arithmetic, classifying, ordering, inferring, and modeling”.

Prof. D'Ambrosio writes in his article entitled, The Program Ethnomathematics: A Theoretical Basis of the Dynamics of Intra – Cultural Encounters that the word Ethnomathematics may be misleading. It is often confused with ethnic-mathematics. I see ethno is a much broader concept, focusing on cultural and environmental identities.

· **Development of Ethnomathematics as the issue in mathematics Education**

v **Overview of Ethnomathematical Issue from different international Convention: **

ICMI( International Commission of Mathematical Instruction) is an international organization founded in 1908 to foster efforts to improve worldwide the quality of mathematics teaching and learning. Since 1969 it has been organizing the ICME( International Congress of Mathematics Education). It has completed its 11^{th} Congress and 12^{th} will be held on 2012 in Seoul, South Korea and the past conference of ICME are: 1969- France, 1972-UK, 1976-Germany, 1980-USA, 1984-Australiya, 1988-Hungary, 1992-Canada, 1996 Spain, 2000-Tokio, 2004-Copenhegun Denmark, 2008-maxico. From third ICME the issue of Ethnomathematics has been discussing how ever from 5^{th} Congress of ICME has given the shape of Ethomathematics formally.

*How developed the concept of Ethomathematics? *

*Mathematics in culture and society, Why teach mathematics?? -1976 on third ICME, (Ubi D'Ambrosio)*

*Dared use of the word Ethomathematics. If there are ethnobiology, ethnomusicology, ethnopsychiatry, then why not Ethomathematics ? -1977 AAAS*

*Concept of Ethomathematics, Its etymological meaning-1978 ICM*

*Preparation of Backgroud for ethnomathematics/Holistic concept of curriculum, cycle of knowledge from reality to action -1780 ICME *

*Recognition of Ethomathematics as a valid research program-1984 ICME*

ISGEm( International Study Group on Ethnomathematics) was launched at the 1985 meeting of the National Council of Teachers of Mathematics (NCTM) in San Antonio, Texas and ISGEm has been organizing the ICEm(Interantional Conference of Ethnomathemtics) in every four years.

Ø The First International Congress of Ethnomathematics (ICEm-1) took place in Granada, Spain, from 2 to 5 September 1998

Ø The Second international Conference of Ethnomathematics (ICEm-2) took place in Ouro Preto, Brazil.

Ø Third International Conference on Ethnomathematics (ICEm-3) Auckland, New Zealand 12-16 February, 2006.

Ø Forth international Conference of Ethnomathematics (ICEm-4) is going to held on July 25-30, 2010, Maryland USA. *(**http://pages.towson.edu/shirley/ICEM-4.htm**)*

v *How did Prof Ambrosio initiate the concept of ethnomathematics? In his own word: *

* **''I first started to look at mathematics of different cultural environments, back in the mid-seventies, when preparing the essay for ICME 3, on “Why teaches Mathematics?” My main focus was the relations between Mathematics and Society. My view of Mathematics was as the science that emerged from the Mediterranean basin and organized in antiquity, mainly by the Greeks, and of Society as communities, cultures and civilizations organized according to the model of urban, economic and social relations that emerged in post-feudal Europe, since the Late Middle Ages and Renaissance. Both, Mathematics and Society shared this historical background and became prevalent all over the World. In the Age of Enlightenment the philosophical foundations of both Mathematics and Society were well established. This foundation was supposed to guide my paper for ICME 3. But, after much travel in Brazil, in the Americas and Africa, I was, for some time, curious about traditional ways of dealing with numbers and forms, as well as with the presence of traditions in societal arrangements and in religious practices. These recognitions were responsible for the impressive development of anthropology in the 19**th **and 20**th **centuries, particularly of ethnography. Recognition of the possibility of different mathematics in different cultures and the relations of these different approaches to space and time within models of society and education were timidly suggested in the classics of anthropology. Then I came across the precious and pioneering book of Claudia Zaslavsky, Africa Counts. I became very interested in finding something similar in other regions of the World. Many years of working as a consultant with UNESCO and the Organization of American States favored my ideas. Thus I was courageous enough to deal with the theme of “Why Teach Mathematics?” taking into account these very broad factors. The paper was received with mixed feelings. How could someone question the Mathematics that was in curricula all over the World? The answer to “Why Teach Mathematics?” should stress how important was to teach that mathematics. It was correct to discuss new approaches of teaching and learning that mathematics. Cultural roots and social tensions had not much to do with that mathematics. Against the expected, I decided to open up reflections on mathematics education as related to cultural and social issues. It was a very controversial session during ICME 3. **An important issue, in defense of that Mathematics, was, and continues to be, its cognitive value. They claim it is essential in developing cognitive abilities. This privileged position may be a myth, as suggested by current research in Artificial Intelligence, as well as recent advances in studies of the mind and the brain. Of course, traditional mathematics may be a very important intellectual exercise, the same as poetry, music and Ethnomathematics. After ICME 3, I was strongly motivated to find theoretical support for the views I had exposed in my paper. This led me to look for new approaches to the History and Philosophy of Mathematics. To emphasize Mathematics as related to culture and society, during the 1977 annual meeting of the AAAS in a session on Native American Science, I dared to use the word Ethnomathematics. In the meeting, many speakers were talking about Ethnobiology, Ethnopharmacology, Ethnopsychiatry and many others “ethno-disciplines.” Why not Ethnomathematics? I pronounced the word, to the surprise of many, just as a word to design a very broad idea. Obviously, the academic environment attending the meeting identified Ethnomathematics as ethnic-mathematics. Regrettably, many people still react this way. Clearly, this is not what I had in mind when I used the word. What I had in mind, which emerged in preparing the essay for ICME 3, was a broader view of the History and Philosophy of Mathematics, emphasizing its relation to culture and society. Then, during the ICM 78, in Helsinki, came the idea of the etymological exercise that led to ethno-mathema-tics, where the words were used with special meaning. Thus, ethno means cultural environment, mathema means teaching, understanding, explaining, and tics is used as a reminder of techné, the root for arts and techniques. Thus came the word Ethnomathematics, which I claim to be a conceptual word. In the formation of the word resides the concept of Ethnomathematics. Of course, the abusive and imprecise appropriation of etymology was criticized by some. But how can we propose the new, if we are afraid of criticism, even if sometimes acid? At ICME 5, in Adelaide, Australia, in 1984, these ideas were spelled out. Thus Ethnomathematics was recognized as a valid research program, with obvious pedagogical implications. All I reported above happened within the last 30 years. Now, Ethnomathematics is recognized and practiced all over the word. Much research, practical and theoretical, of a methodological or an ethnographic character, is reported. The number of journals, books, associations, congresses is growing. The International Study Group on Ethnomathematics/ISGEm was created in 1985, and later national study groups, such as the pioneering North American Study Group on Ethnomathematics, were created. Many classroom proposals are available, and a number of teacher training programs are offered all over the world. Criticism is still present, which is an indication of the growing presence of Ethnomathematics. Criticism helps ethnomathematicians to reflect upon their work. A question is always present. What about the future of Ethnomathematics? Is it a fading proposal? Is Ethnomathematics to be replaced by the variants Critical Mathematics Education, or Mathematics and Society, History and Pedagogy of Mathematics, or some branches of Psychology of Mathematics Education? Groups are organized with these labels. Ethnomathematics, the way I conceive it, is intrinsic to all of these, as well as to Pure and Applied Mathematics. I insist in claiming that the essence of the Program of Ethnomathematics is to understand how knowledge is generated, how it is organized and how it is diffused in different cultural environments. Once we recognize influence of culture in knowing and doing, we are within the scope of the Program of Ethnomathematics. This is clear when we understanding the etymological construction of the word. It is ethno+mathema+tics. It is much more than ethno+mathematics. This very subtle difference is deep in its meaning.''*

**Ethnomathematics and mathematics education**

The word ethnomathematics is itself mathematics education. It is an absolutely essential key for Mathematics Education. Of course, *"the way of doing"* mathematics, which means the way of teaching and learning, it cannot be reduced unique and universal at least in the very early elementary levels of learning mathematics. In this stage there is no difference between "*using mathematics*" and *"doing mathematics*", in fact what *we do* in the early elementary levels of mathematical education is to explain and to understand *in a mathematical language* those simple operations which *we use* to manage the every-day-live: *counting, estimating, calculating etc.* Needless to say how *native algorithms* to perform these operations are culturally-dependent and, therefore, are different. That is why the (*Ethno*)-Mathematics becomes absolutely essential for mathematics education.

Prof. D'Ambrosio further writes in his article as mentioned above, **The Program Ethnomathematics: A Theoretical Basis of the Dynamics of Intra – Cultural Encounters**, that once he had presented Ethnomathematics as a Research Program in the History and Philosophy of Mathematics with Pedagogical Implications. From it we can conclude that his intention of describing about enthnomathematics was in application of mathematics in teaching field.

The introduction of Ethnomathematical approach by Ubiratan D’ Ambrosio affected and continues to affect in various ways mathematics education. The researchers of Ethnomathematics field, among others, are interested in: the nature of mathematics teaching/ learning, legalization of mathematical cognition, discovering and use of informal mathematics—that are met in everyday contexts—in teaching mathematics. The current trends of Ethnomathematics have categorized, by Renuka Vital and Ole Skovsmose (1997), in four main strands: They are 1) Pure anthropological approach 2) The historical anthropology approach 3) The socio-psychological approach 4) Ethnomathematics and mathematics education.

In this way ethnomathematics has been developed as the emerging issue in the universe of mathematics.

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