Mathematics, Culture, Politics And Ethnomathematics:
By Amrit Thapa
[Reviewed 27th April, 2012]
Fourth Semister 2007
Fourth Semister 2007
Kathmandu University
History of mathematics:
Researches about the history of development of human species (available till the date) suggest that mathematics has been developed initially as guided by the basic requirements for the survival; this includes food habits, climate, space and other natural factors. As mentioned by D’Ambrosio (2001), Homo Sapins have been considered as living on the earth about forty thousand years ago. Australopithecus known as preceding the Homo Sapins lived in or somewhere near today’s Tanzania 5 million years ago and spread all over the world. Due to the power of analyzing, comparing and communication of the knowledge with the experiential world, these species transformed themselves as influenced by the climate, availability of food, available space, growing population and other factors. As these species spread to different places, they encountered new environment, climate, food and spaces. To tackle with new challenges in life they constructed new ideas and techniques. They shared their ideas through symbols, pictures and other forms of languages. This socially accepted knowledge formed a culture which further reconstructed and shared generation to generation.
Study shows that Australopithecus used chiseled stone to clean animal carcasses, it would make possible to scrape the bone, and thus, not only make use of every piece of meet but also extract nutrients from the bone that would not be possible only with teeth. They had to develop this instrument because their most common food was meat of animals and birds. As the population increased, they encountered deficiency of food they had to invent eating plant body parts or the fruits and hence had to develop farming. Thus the need for survival and curiosity for knowing have influenced people for inventing mathematical ideas like counting, measurements, and other systems in mathematics. The culture and religions are the systems of knowledge that we share and accept as common knowledge.
Mathematics, Culture and Politics:
The construction of mathematical or ethnomathematical knowledge has been greatly affected by the political interests. About 2500 years ago (D’Ambrosio, 2001) Greeks and Romans expanded their domain eastward of Mediterranean capturing the thousand-year-old civilizations such as Persia, India. The conquerors destroyed or colonized (or claimed as their own) the knowledge system of the conquered people and imposed their own knowledge system to present themselves as superior. The conquerors not only imposed their system of knowledge but sometimes they tried to destroy the objects representing the original knowledge system or they were eliminated from the territory or punished to death. However, not only the conquered got influenced from the culture of conquerors but sometimes the invaders also got influenced from the local culture and reconstructed their knowledge system to fit the new environment. For example, the black Africans taken to America not only got influenced from the American culture but they brought African culture in U.S and the American ethno-culture got influenced from the culture of the slaves taken from Africa. This has occurred also in the British and other European colonizers. They have reformed their mathematical knowledge after they colonized India, China and other countries in Asia and Africa. But due to lack of acknowledgement of the source of influence the academic mathematics looks different than what practiced in different cultures.
Thus, ethnomathematics values cultural construction of knowledge than universalizing the knowledge. Saying this does not mean to indicate that we need to ignore the important inventions in mathematics; ethnomathematics encourages to research on ethnic groups, identify the mathematical ideas in practice and incorporate them to the curriculum and text books so that these knowledge help learners understand and become comfortable in applying the system of knowledge in their day to day life. Ethnomath does not try to displace the mathematical inventions made earlier in Europe and America but it tries to re-enforce the world of math with further researches of ethnic inventions. It works in widening the field of math. Its emphasis is onto “mathematics for all”. This is more valuable for the country like our which is full of diverse ethnic cultures.
Talking only about ‘western curriculum’ and ‘western occupation’ in our schools and academic institutions will be an injustice and an immature decision. As the issue of large and small culture aroused in the above discussion, it is necessary to define what is meant by large and small culture. Can the knowledge be evaluated with respect to the population? Can it be restricted within the boundaries? So, who is the owner of the knowledge? Is the professor or a researcher who collects knowledge from students or the field of research an inventor of the knowledge? Or the actual inventors of the knowledge are the farmers, carpenters, sailors or other people who actually observe and experience in their day to day life. This is to be made clear before we actually enter into acknowledging the knowledge. In many researches and history books we can read that the mathematical knowledge have been contributed by different cultures like Egyptians, Babylonians, Indians and so and so. But there arise questions, who were Egyptians? Does “Egyptian civilization” represent the people who actually involved in the invention of the mathematical knowledge? Does “Arabian culture” represent the inventors who might have been in a minority ethnic culture within the large boundary of Arab? Will it be fair that all the ethnic communities who contributed in knowledge invention called as the inventions of the Indians? Will it be a justice to the inventors who lived in ethnic minority within the covering of huge population ignored and called their works as the work of the well known cultures and civilizations? Indians invented Number system, where is (the ancient) India and what was its boundary? Which people represent India? Are all the ethnic communities bounded by the boarder lines of India represented by the so called Indian faces? Can we call the inventions of the people living in a remote corner of India in an ethnic minority as the inventors of the so-called Indian Mathematics? What about the people living in different adjacent territories of the Indian subcontinent?
Thus the above discussion arises more questions. Is it possible that the number system as said to be invented in India covers Nepal in the assumption of that historical time? That means is it possible that the number system be developed by a farmer or a shepherd in the remote part of Nepal? So it means we need to find the place in Nepal where, how and in what culture and profession the knowledge was constructed. It may be a Gurung, Rai, Tamang, Chepang, Tharu, Dalits or other Janjatis. So is there any reason to claim that upper casts and people with majority claim themselves as superior of knowledge? Thus, there may evolve innumerable possibilities, besides accepting others’ ideas as the universal truths people around the world need to unearth the history and live with high-esteem.
We really need to thank D’Ambrosio of Brazil who helped us and the people around the world to understand and free ourselves from the intellectual colonization of western and so-called developed cultures. This is the world where many scientists and researchers lost their lives for attempting to disprove or reject the knowledge (as the only truths) established by the western and other powers. History shows that the economic powers have always tried to suppress other’s knowledge in the name of humanity and civilization. There have been attacks to different civilizations for the treasure of knowledge, economically weak civilizations have been destroyed and the knowledge and their recognition swept away. So it can be imagined that there may be hidden powers indirectly working to stop the comrades of ethnomathematics from excavating the hidden realities.
Ethnomatheamtics and Future:
Now to discuss about how the program “ethnomathematics” may contribute to empower ethnic cultures and individuals, it is necessary to know the meaning of the term “ethnomathematics” and its purposes. The prefix ‘ethno’ from ethnography refers to the study of mathematics in relation to culture. According to the proponent D’Ambrosio the term “ethnomathematics” can be defined as the study of mathematics that takes into consideration the culture in which mathematics arises by understanding the reasoning and the mathematical systems that they use. Culture refers to a set of norms, beliefs and values that are common to a group of people who belong to the same ethnicity. The people share a language, a place, traditions, and ways of organizing, interpreting, conceptualizing and giving meaning to their physical and social world (Hammond, 2000).
The people living in different cultures invented different mathematical ideas while attempting to organize, systematize and improve their livelihood with the changing time and world. The raw ideas invented by members of a culture are shared within the periphery of the culture through the language and activities. They are tested and verified or further modified due to change in time and need. This clearly indicates the cultural construction of mathematical knowledge. The evidences of some ethnomathematical researches show that different cultures in different places practiced different forms of mathematical knowledge. However, the western occupation and domination so paralyzed the human life in the third world countries that people considered math as the collection of truths discovered by the power houses of the intelligence which resided in the western culture. It is evident that even in western culture mathematics has been defined in different ways but the so-called intellectuals try to formalize and universalize the definitions and its contents.
From the above arguments it is clear that mathematics is a cultural construct, this helps us to be confident that our culturally rich and diverse society is full of such hidden mathematical treasures which are yet to be uncovered. The externally designed curriculum and the mathematical knowledge imported in the form of text books have brain-washed our children who are the pillar of the future. The foreign structure and hidden interests of designers not only fade the interest of students in mathematical learning but also it helps to produce individuals with low self-esteem and with disrespect to own culture and land. Very poor pass rates in our examinations and failure of individuals produced from the academic institutions in market and work place shows the failure of foreign curriculum (Luitel, 2009). Thus, it is a very immediate requirement of our society, market and the interest of the country to incorporate the practices of different cultures into local and national curriculum. This will definitely help generate interest in learners towards mathematics as they see the application in their day to day life.
Incorporating the ideas and inventions of ethnic groups and people living in minority in the text books will help children understand the value of all the people living in the society. The clashes and dissatisfaction appearing in the recent days in our country and all around the globe suggests the immediate need of an environment where every individual is respected for his/her own culture and given opportunity to enjoy and preserve her/his own identity. This will help establish democratic feelings in the minds of new generation. Ultimately this will help developing a democratic, prosperous, class-free and clash-free society. At the end, as the curriculum focuses on local need and planning for future it will definitely trace a smooth path for the future.
Referrence:
D’Ambrosio, U. (2001). Ethnomathematics. Rotterdam: Sense Publishers.
Hammond, T. (2000). Ethnomathematics: Concept definition and research perspectives. An unpublished master’s thesis, Columbia University, New York.
D’Ambrosio, U. (2001). Ethnomathematics. Rotterdam: Sense Publishers.
Hammond, T. (2000). Ethnomathematics: Concept definition and research perspectives. An unpublished master’s thesis, Columbia University, New York.
Luitel, B. C. (2009). Culture,
worldview and transformative philosophy of mathematics education in Nepal: A
cultural-philosophical inquiry. PhD, Curtin University, Perth.
Ernest, Paul (1994a): Social constructivism and psychology of mathematics education. In P.Ernest (Ed). Constructing mathematical knowledge; Epistemology and mathematics education (pp. 62-72). London: The Falmer Press.Restive, Sal (1994). The social life of mathematics. In P.Ernest (Ed.) Mathematics education and philosophy: An international perspective (pp. 154-161). London: The Falmer Press.
Zaslavsky, C. (1999). Africa Counts: Number and pattern in African cultures (Third ed.) Chicago: Lawarence Hill.
KUMES (28th April, 2012): Mr Amrit B. Thapa is currently working as a visiting faculty at the Kathmandu University, facilitating Masters of Education Classes. He is a full time faculty/coordinator at Rato Bangala School, Patan Dhoka, Lalitpur. He has been working as a Teacher Educator, he is working at RBF (Rato Bangala Foundation) and has conducted numerous (short) Teacher Professional Development Programs in different institutions. He is interested in working for empowering/democratic education for sustainable peace.
