Nepali Ethnomath

KATHMANDU UNIVERSITY
SCHOOL OF EDUCATION
ETHNOMATHEMATICS
Gorakh Chand
Q. Write paragraphs elucidating the Various Dimensions of Ethnomathematics.
The Conceptual Dimension.
Knowledge for Existential Qnowledge for Existential question for the Human Speciesuestion for the Human Species
What knowledge is required for the human species to exist? They are in possession of fundamental questions like-who are we? How can we better survive? How to struggle in difficulties? Human species always tried to find answers to those questions. Consequently, the answers to those questions enabled them to construct knowledge which eased them exist in the nature.

Drive for Survival and Transcendence
Among the organisms in the nature human species were able to construct their knowledge beyond the nature. Human species can think more than physical world and beyond the reality. This is called transcendence. Every body wants to survive. They need food, clothing, and shelter to survive.

Relationship of Behaviour and Knowledge
Human species cooperate each other for their survival. Knowledge serves behaviour and new behaviour adds to their knowledge. They have curiosity to learn more things and keep on constructing their knowledge with change in actions. Interdependences among the human species enabled them to survive more safely and live congenial lives, termed as symbiosis. D’Ambrosio (2001) says in the chapter of the various dimensions of ethnomathematics that “This symbiosis of behaviour and knowledge is what we refer to as instinct, which resolves the question of survival of the individual and the species” (p.17).

Transcendence of Space and Time
Human species thought beyond the reality
They imagine about the unknown places. They thought about religious places like hell, heaven, and earth. They did not think of only the present. Slowly and steadily they started to relate present to the past and future even after their death. They started inquiring where they go after their death. When did world start? How it exist? When and how does it end? Such thinking gave rise to various mathematical ideas, and thus D’ Ambriosio thought of how mathematical ideas started.

What is the Beginning in Space and Time?
Through the civilization of human species, humans started to think very seriously, where other animals do not. D’Ambrasio has raised questions how this world began, and they could find the mystery of the nature.

Reality, Artifacts and Mentifacts
Artifacts were the source of knowledge that the human species possessed. Those artifacts resemblance the culture of those species. Mentifacts were those imagination of believes on the design of artifacts. Scientists who studied those artifact and mentifacts carefully acknowledged that how D’Ambriosio had highly emphasized by artifacts and mentifacts of those human species. Thus the reality perceived by each individual of the human species is the natural reality, together with the total of artifacts and mentifacts (experiences and ways of thinking) accumulated by him and by the species (culture).

Informing the Reality to Generations
Communications were the source of means to pass information among them. Only human beings can do this. This led them to accumulate more and more knowledge for the subsequent generations and helps them to survive more comfortably. It is the powerful tool among them to be different fr4om other species. With such means of communications they used their knowledge as shared knowledge.

Compatibilization of Behaviour
People raised questions and developed their knowledge which helped them to adopt in the environment and their behavior certainly brought some comparison. They found the knowledge based on values and utility. Values were based on ethics. Gradually, with the civilization of human species they found the existence of the whole, not as an individual. They started to sacrifice for others. Such mode of life developed among them created congenial environment for the survival, certainly uplifted their life more happily. They started to struggle for the common goal for the survival. Compromises and accommodations were their main agendas which soothe for the compatalization of their behaviours. D’Ambrosio (2001) quoted “The accumulation of knowledge shared by the individuals of a group has the consequences of making the behaviour of these individuals compatible, and, accumulated, this shared knowledge and ‘compartibilized’ behaviour constitute the culture of the group”(p. 18).Hence these phenomena gave rise to the development of Ethnomathematics as stated by D’Ambrosio.




The Historical Dimension.
Imposition of Modern Scientific Knowledge to the Whole Planet
When modern scientific knowledge gained more popularity more emphasis was given to techniques and skills but de-emphasized on from whose culture that knowledge had transcended. Such scientific knowledge came from Euro-centric knowledge and more or less more objective. Consequent of the development of scientific knowledge human species were victimized because of the mechanistic lives and they were refrained from the joy of nature.
Rapid Development of Modern Science and other Areas of Knowledge
After the Medieval age there was a rapid development of modern Science.20th century we marked as the boom of modern science knowledge. Modern science had complicated the society. Life was not linear. People were not in a position to forecast what would happen tomorrow. The world became more complicated after the invention of ICT. World had become like a village. More and more opportunities and challenges could come up. People struggled for the survival of the fittest. Development of modern science and technology had brought chaos, catestrophe, calamity and havoc. No peace of mind prevailed in human beings. To highlight this point I would like to highlight what D’Ambrosio had written in 2001, “Without a doubt, as has always happened with other systems of knowledge, modern science itself will develop the intellectual instruments to criticize and to incorporate elements of other systems of knowledge”(p.18). As such the post modern perspectives of curricululum brought into the light which incorporated Ethnomathematics as the source of learning mathematics through cultural practices.

Intellectual instruments and history of civilization
Modern science and technology brought hues and cries among human species. Owing to the disadvantages of modern science and technology D’Ambrosio had written many articles addressing the shortcomings of development of science and technology, but he was criticized very sternly. Later, notion of Ethnomathematics was appreciated by the world wide people and thought inclusion of this bin the curriculum would make inclusive mathematics. Through this, enculturation would take place and more peace and harmony would be expected.
Qualitative and quantitative reasoning of Babylonians and Greeks
To develop their culture and civilization people used qualitative and quantitative reasoning. They started quantifying every problem geometrically. Babylonian used Arithmetic and Geometry for quantifying and measurement. This sort of reasoning was found more comfortable to resolve many conflicts in their daily lives.
Modernity and quantitative reasoning
Later on when Babylonian heavily used quantitative reasoning it became more popular and convincing to other civilization. Modernity was heavily dominated by scientific reasoning and which was possible only through quantitative reasoning.
Advancement of Arithmetic. Qualitative reasoning gave rise to the development of Arithmetic. People contributed a lot to the development of Arithmetic and it was possible only through qualitative reasoning. Slowly, such type of reasoning gave rise to the development of calculators and computers. But all the problems could not be solved using quantitative reasoning, and thus gave rise to interpretative paradigm and qualitative reasoning.
Ethnomathematics and its Characters
Ethnomathematics was developed more highly in socio-cultural dimension and based on qualitative reasoning. It values the cultural practices that have long historical roots. When we talk about gender equity, disparity, biasness and racial disparity the role of qualitative reasoning is of paramount importance. satisfaction, anger, life style of people, cultural practicese to qualitative reasoningparity e reasoning. it interpretative paradigm and qualit and many other attributions gave rise to qualitative reasoning. Ethnomathematics is thus embedded in socio and cultural phenomena are analogous to qualitative reasoning. As cited in the text written by D’Ambrosio (2001) - “More recently, we see an intense search for qualitative reasoning, particularly through artificial intelligence. This trend is in step with the intensification of interest in ethnomathematics, whose qualitative character is strongly predominant” (p.19).
Rene Descartes Organization of Discipline
Rene Descartes studied objective nature of Mathematics. It was his positivist ontology. According to him such study gave rise to the study of nature. He stated that scientific study is the separation of mind and body, heavily based on experimentation. He synthesized all those ideas into one discipline. He said that reality is objective, and thus it is bounded by absolutist view. His study gave rise to ‘study nature through experimentation’. After him, mathematics became more objectivists. Till date people keep on believing in absolutism and they have been influenced by Rene Descartes philosophy.
Menifestation (expression) of new renaissance by Ethnomathematics
After 1970 D’ Ambrosio started working in Ethnomathematics. He received several criticisms owing to the introduction of new idea and thus he could convince the people through conferences and writing articles, and thus the notion of Ethnomathematics gained popularity. After 1970, it became the forum for the people into discussion, so it was termed as renaissance by Ethnomathematics.
Introduction of Indo-Arabic System in Europe in 999 by Pope Silvester II and Leonardo Fibonacci in 1202. People traveled far and wide in Arabic places and brought some Mathematical ideas from Indo-Arabic system. They did thorough study of such system and thus later introduced in Europe, dominating the originality of ideas.
Arithmetic of Arab Helped in Merchant Trade
Arab Helped in Merchant Trade. The borrowed ideas from Indio- Arab helped European to pursue their trade and contextualized in trade. It became easier for them to do calculation and promoted their business without hindrances.
Relation between mathematical ideas and Economic Model
Frei Vicente de Salvador had recognized the parallel between mathematical ideas and economic models when he commented on the arithmetic of the indigenous Brazilians. Salvador mentioned that there was heavy dependence on Mathematics by Economic Model.
Counting with Fingers and Toes in South America (Brazil). The historians explained that Brazilians counted with their fingers and, if necessary with toes. With the development of civilization this mode of calculation made them to lag behind. But today they need the ideas of higher order of calculations which would ease them to carry out their commercial activities without hindrances.
Today’s Education, Youth and Culture
Today’s education system is the reflection of what people wanted to practice earlier. With deep rooted cultural practices their expectations were high, and thus their reasoning became stronger. In short, Today Mathematics is no doubt the cultural practices of the indigenous people around the world. Western world had dominated this ideas were they mentioned no originality of this artifacts.

The Cognitive Dimension
Mathematical ideas, in particular, comparing,classifying,quantifying, measuring, explaining, generalizing, inferring, and to an extent, evaluating, are forms of thinking present in the entire human species. These have been attributed by mind or of consciousness. Studies of the mind or of consciousness, common among neurologists, including neurosurgeons, have attracted the growing attention of mathematicians and theoretical physicists. To understand humans, it is of paramount important to study those primates who have similar characteristics to humans. The emergence of thinking of a mathematical nature, privileging the quantitative, has been noted in primates.
Australopithecus, that appeared after human species underwent transformation, influenced by the climate, food habits, and various other factors, and developed techniques an abilities that allowed their survival in the new situations, gathered experiences from previous situations, adapting them to new circumstances, thus incorporating to the memory new ways of knowing and doing.
When human species encounter with the other, the phenomenon of communication takes place. Through communication the information received by one individual is enriched by the information received by another. The knowledge generated by the individual, which is a result of processing the totality of information available, is, also through communication, shared, at least, partially, with the other. Through the shared knowledge, the behavior of each individual is modified and consequently the compatibilized behaviors of the group are developed. The culture is the set of shared knowledge and compatibilized behaviors.
A first example of Ethnomathematics was practiced by Australopithecus to select instrument made of chiseled stone to clean animal carcasses. To select the stone, one must evaluate its dimensions and compare the best among the many. Evaluating and comparing dimensions is one of the most elementary manifestations of mathematical thinking.
The Challenges of Everyday Life
The most important relationship of human species with the environment was obtaining nutrition and protection from the elements. Once humans had mastered techniques of agriculture, raising livestock, and construction, humans were able to remain in the same location, to be born and die in the same place. They perceived the time needed for germination and gestation, the time that passed between planting and harvest. Recognizing and recording the menstrual cycle, associated with the phases of the moon, appear to have been among the first forms of ethnomathematics.
People practicing agriculture in and around Mediterranean sea knew the correct time for planting & harvesting send thus for the betterment and worst of crops depends on the well-being of deity. Geometry was learned from the Egyptians, for whom it was more than a mere measurement of land; it had everything to do with the system of taxation of productive areas.

The Epistemological Dimension
Knowing what? System of knowledge for what? Knowledge system made life possible and depended on the response of fundamental existential questions, such as: where did I come from? Where am I going? What is the past and past of my people? What will the future be, mine and that of my people?
The great controversy of the history of science is the relation between the empirical and the theoretical, which can be summarized in three direct questions:
1. How do we move from ad hoc observations and practice to experimentation and method?
2. How do we move from experimentation and method to reflection and abstraction?
3. How do we proceed toward inventions and theories?
These sequence serve as the basis for explaining the evolution of knowledge, i.e., for a theory of knowledge, or epistemology.
The Political Dimension
Due to colonization, the English spoken people became more powerful and started to dominate other culture and kept the inferior people under their control. With the adoption of Christian monotheism in the 14th century, Rome imposed not only its polities, science, technology and philosophy, but primarily, the new religion on a large part of Eurasia above the tropic of Cancer. When speaking about conquest, conqueror did not allow the conquest to manifest themselves. The fundamental strategy in the process of conquest adapted by a [dominant] individual, group, or culture, was to maintain the other [dominated] individual, group, or culture in an inferior position. One very efficient way to keep an individual, group, or culture inferior is to weaken their roots, removing the historical ties and historicity of the dominated. Removing the historicity implie4s removing the language, production, religion, authority, recognition, land and nature, and systems of explanation in general.
Undeliberately, navigators from Spain and Portugal in 15th & 16th centuries circumnavigated the globe. They were soon accompanied by other European nations, and by sea, traveled to the north, south, east and west, in every direction conquering peoples and carrying with them their explanations and ways of dealing with the environment, models and styles of production and power. Thus, the process of globalization of the planet had begun.
Students enrolled in the school were not allowed to their own way of learning. They were criticized and compelled them to follow and transformed them with the culture of dominant. Usually, an individual spent many years carrying cultural roots that come from their home, from the day they were born have been vanished due to domination. But this manifest itself in creating negative effect to exercise their culture and people’s creativity would have been lost. But D’brosio keeps on emphasizing to give recognition of all cultures in the evolution of knowledge and give due respect to one’s culture and embed all these as one, and thus make a synthesized knowledge. Thus, Ethnomathematics fits into this reflection about de-colonization and the search for real possibilities of access for the subordinated, the marginalized, and the outcast, or excluded. D’Ambrosio (20010 maintains “recognition and respecting an individual’s roots do not signify rejecting the roots of the other, but rather in a process of synthesis, re-enforcing their own roots. This is according to my thinking, the most important aspect of Ethnomathematics.

The Educational Dimension
D’Ambrosio said Ethnomathematics does not signify the rejection of academic mathematics and bringing other cultural mathematics in practices, but rather perfecting those, incorporating the values of humanity, synthesized into an ethics of respect, solidarity, and cooperation. Part from quantitative reasoning(evolved from Algebra& Arithmetic), qualitative reasoning gained momentum at he beginning of 17th century and developed in the second half of the 20th century, such as statistics, probability, programming, modeling, fuzzies, and fractals. Ethnomathematics privileges qualitative reasoning. Ethnomathematics fits perfectly into a multicultural and holistic conception of education. Multiculturalism is analogous to intercultural encounters which generates conflict that can only be resolved based on ethics that result from the individual knowing himself/herself and knowing his/her culture, and respecting the culture of the other. Through the notion of multiculturism, peace will prevail in the society, and thus people live in harmony. No doubt, multiculturalism is impregnated with technology and people can live in the moving world of science and technology updated.
The dynamic acquisition of mathematics integrated with the knowledge and the practices of the future depends on offering students enriching experiences. It is upto the teacher of the future to idealize, organize, and facilitate these experiences. Thus, according to D’Ambrosio, the future generations teacher of mathematics should be well equipped with the knowledge of multi-multiculturalism and give due respect, consequently incorporate in his/her pedagogy. D’ Ambrosio (2001) maintains that

“The pedagogical proposal of Ethnomathematics is to bring mathematics to life, dealing with real situations in time [now] and space [here]; and, through critism, to question the here and now. Upon doing so, we plunge into cultural roots and practice cultural dynamics. We are effectively recognizing the importance, in education; of the various cultures and traditions in the formation of a new civilization that is transcultural and transdisciplinary” (p 34).


In Closing
Far and wide Ethnomathematics has taken its momentum to bridge the gap between the main stream mathematics and cultural mathematics. In short Ethnomathematics is a bricolage of secularism. Introduction of Ethnomathematics in the main stream mathematics would enable the learners to know the roots of main stream mathematics. Moreover, it talks about the contextualization of mathematics in society. More importance is given for the local artifacts through which people would understand the conceptual parts of mathematics which would enable the learners to cope with the procedural mathematics. Thus, Ethnomathematics is a post-modern concept of curriculum which emphasizes on the emancipatory curriculum.

Reference
D’Ambrosio, U. (2001). Ethnomathematics: Link between Traditional and Modernity. Rotterdam: Sense Publication.
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