शनिवार, नवंबर 07, 2009

गुरुवार, जनवरी 03, 2008

KATHMANDU UNIVERSITY
SCHOOL OF EDUCATION
ETHNOMATHEMATICS
Gorakh Chand

REFLECTION ON MY UNDERSTANDING OF MATHEMATICS IN EVERYDAY LIFE:
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 them. 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.
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).
Ethnomathematics places wonderful value upon the empowerment (to give somebody power or authority) of learners to resolve problems using situational or real life perspectives. With interdisciplinary activities, students learn to see mathematics as linked to other areas by using research tools that analyze problems and develop mathematical models. However, the selection of content alone is not enough to guarantee their meeting of mathematical objectives. The way in which the classroom teacher (pedagogy) organizes subjects as equally important, since individual or personal responsibility, involvement and connection to the disciplines are important to the success of each new aspect of the mathematics learners find for themselves. This enables the formation of flexible, curious teachers and learners who readily engage in the basic research and critical exploration needed to collect the mathematical data and tools necessary for life in a globalize information-rich society.However, the majority of programs training teachers to teach mathematics currently do not make this an easy objective. Most of the mathematics that was transmitted to them is hardly critical in nature, but passive, that is, with the emphasis on the achievement and memorization of basic facts. The universality of mathematical knowledge is often not revealed. Too often, mathematics is transmitted in a crystallized (to become or make an idea or feeling become fixed or definite) form and learners rarely interact with the subject. Mathematics comes from using a dynamic process of communication, testing, and experimentation. It is really a series of interactive (communicating or collaborating) questions, and is alive and growing, not static or confined to mere arithmetic or algebra. This somewhat uncertain but dynamic science contrasts greatly with the traditional processes of becoming a student and lifelong learner later teacher and again life long learner.
It does not mean that the mathematics of the past is limited, but it was applicable in a context much more limited than of that today (D'Ambrosio, 1993).
Today, such important ideas such as fractals and chaos theory can be shown as prime examples of mathematics that are all but disregarded by the standard school curriculum. These two areas alone offer truly engaging experiences and powerful ideas for young people. Yet they seem to be all but ignored by the politics of high stakes testing, accountability and back to basics. The great part of the traditional school-university curricula is based on the mathematics found in the 16th to 19th centuries, and when something referring to 20th century mathematics presents itself, it is more than often consolidated into what it became in the 19th century.
Many new teachers enter the profession with limited or an obsolete knowledge of mathematics. Yet the world they train children to live in is a dynamic information-rich, interactive, diverse and globalize world. Like their teachers, students condition their minds to this static, obsolete and mechanized knowledge while in school. Much of the mathematics curriculum and instruction found in schools and textbooks contributes to the pacification of their learners. The mastering of obsolete mathematics is often considered important for those who seek to go on to advanced classes in mathematics. Mindless memorization has been deemed sufficient for those who have succeeded in this form of mathematics. More often than not, it has been these same students who have been identified as brilliant and intelligent. This then forms the basis for numerous complaints related to current math reform. Learning to think and reason creatively is difficult work, difficult to assess, and of a higher order than memorization.
An ethnomathematics perspective can give a child the responsibility to learn basic information. Learners can learn how to make connections from the past to the present. In ethnomathematical contexts, as in real life, skill and creativity are most important for success. If schools and communities allow the trust, freedom, space and encouragement for mathematical creativity in their teachers and students, they contribute to the formation of truly empowered and active citizens for the 21st century. The role of the teacher in an ethnomathematical learning process is not that of being the conductor of learning (sage on the stage), but of a facilitator or coach, for the student (a guide on the side) and teacher should not follow the cold reason.
Therefore, it is that educators must find ways to support and encourage teachers to integrate the outside interests and culture of their students and communities. Teachers must be encouraged to organize engaging and useful projects that pay attention to the outside reality of the school. It is the common sense of an ethnomathematical perspective that must be organized so that each learner fined his or her own slot (place, position), giving and extending to them the intellectual resources necessary. Each learner must allow them the opportunity to construct knowledge from their own reality. Thus, mathematics becomes something good and useful to them. It then is something essential to the learner, community, and society. For example, a 15-year-old student who entered school as a 7-year-old has lived about 131,000 hours. Depending on where they live, they have passed approximately 9,000 hours pertaining to school tasks. S/he has watched about 16,000 hours of TV and slept approximately 44,000 hours. It is doubtful that in the 122,000 hours the individual spent outside of school, they did not stop learning. Learning most certainly happens as part of play, in living, and coexists even as we sleep (dreaming). It is not confined to the six or so hours a day the child spends at school.
What I am attempting to describe here is the functioning of an ethnomathematical perspective. What is important to understand is that this perspective gives individuals a chance to learn mathematics in a natural and realistic context. By having students carryout projects, work with people that they may not know or have chosen to work with, to form teams of diverse and talented individuals, with each one contributing to the project students learn to use mathematics with realistic relevance. Learners must develop the capacity for living and coexisting in a dynamic and diverse society, by respecting the strengths and weaknesses of others, by becoming critical and self-sufficient individuals, and with a willingness to be agents of social transformation.
Using a pedagogical point of view that fully incorporates the history of mathematics, we can see that science evolves and is born from diverse cultural systems. We can construct relationships to what often are seen as distant, foreign or strange cultures that are not part of the learner’s universe. While taking care not to be artificial, it is important to become knowledgeable with the contributions made by the Mayans, Aztecs, Egyptians, Greeks, Babylonians and other peoples of antiquity. Western science is not the only form of thinking that developed answers to interesting problems, learning this is extremely important in connecting children to our human heritage. In addition, learning from the past can help us keep us from making similar mistakes in the present. This perspective tells us that we also need to introduce and study the unique mathematical perspectives and situations originating in our daily lives. Students must have a chance to practice, observe, reflect, and question things from a mathematical perspective. Children naturally construct their own knowledge base with active questions, by making use of such things as patterns, quantification, geometric forms, space, and time. Adults call it play, Piaget referred to it as children’s work.
Constructivist theory tells us that children learn to draw conclusions from the interactions they have with objects and with peers, when using concrete experiences in their own personal environment. This paradigm shows us how we can learn to develop methods in which children experience the mathematics found in their environment. This natural necessity to discover and explore new ideas and situations touches upon the core emotions of the child. It often manifests itself in the form of games and play. During the early stages of learning, children often feel that they alone are making discoveries. The children become engaged, as they become personally involved in the search for explanations and the ways they invent in coming to understanding their world. It is this process of knowledge creation, which consequently allows the learner to create mathematical models, leading to a dynamic process of understanding and the ability to decode their own reality. Children in all cultures enjoy a natural drive and ability to understand mathematics. This is evident in preschool and primary children worldwide. Over the length of their schooling, however, many come to feel that mathematics is not useful, interesting or enjoyable. Ways must be found to overcome this aversion and give children the tools by which they can explore alternatives for solving problems in an academic setting.
The life experiences that learners possess need to be taken into account. For example, consider a child who lives in capital city. This child might be better able to digest content of political issue much more easily rather than that of beyond capital city. In the case of the urban child, it would be wise to include the child’s experience of leaving their home for the school. Scheming experiences that take into account their daily trips to school - turning corners, crossing streets, mindful of traffic, public transportation and other urban realities.
The gaining of the daily necessities of life, the important people and places that are most certainly examples of other useful connections to mathematics for younger children. Asking children to observe, that is, to truly pay attention and to use the real experiences as they learn to observe and interact with the world around them is an important connection to mathematics and the scientific method. Yesterday I was teaching mathematics of grade 10 and I was teaching profit and loose .There was a student who is of business family and he understood with a very concept what I was teaching rather than the other student though he was poor in mathematics. The student learned to see mathematics in the very journey they make to school. He began to perceive what happened every time his business later on. He is trying to find more typical problem of profit and loose and related to his business
In this way must learn to search, to observe, to pay attention to mathematical problem. This will enable him to observe and find the mathematics around him, and incorporate his own unique cultural and social reality.
The inclusion of the real world gives conceptual tools to learners. It serves to establish a true sense of continuity between school and real-life. It assists both educators and learners to find ways that enable them to construct a sense of intellectual autonomy and freedom. This autonomy is most certainly not the exclusive goal of traditional mathematics. These methodological concerns in mathematics education must become those of the teacher. They are in reply to the questions and concerns between student and teacher.
References
1. D’Ambrosio, Ubi. “Reflections on Ethnomathematics.” International
Study Group on Ethnomathematics Newsletter 3 (1) (September 1987).
2. “Literacy, Matheracy, and Technoracy: A Trivium for Today.” Mathematical Thinking and Learning 1 (2) (1991): 131–53.
3. Forrester, Viviane. The Economic Horror. London: Blackwell Publishing, 1999.
4. Hiebert, James, ed. Conceptual and Procedural Knowledge:
The Case of Mathematics. Hillsdale, N.J.: Lawrence Erlbaum Associates, 1986.
6. Kamii, Constance, and Barbara Ann Lewis. “Achievement Tests
in Primary Mathematics: Perpetuating Lower-Order Thinking.”
6. Arithmetic Teacher 38 (May 1991): 4–9.
7. Reyes, Laurie Hart, and George M. A. Stanic. “Race, Sex,
8. Socioeconomic Status, and Mathematics.” Journal for
Research in Mathematics Education 19 (January 1988):26–43.
9. Michael S. Pilant, Microsoft Reference Library 2005. 1993-2004 Microsoft Corporation.
10 Luitel, B.C & Taylor, T. C (2003) (in press) Envisioning transition towards transformative mathematics education: A Nepali educator’s auto ethnographic perspective. Sense publication, Norway (p. 1-12).




Ethnomathematics

Ethnomathematics
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Kathmandu University

Kathmandu University

About Myself

Kathmadnu, Far Western, Nepal
Gorakh Chand Working for KU, in Ethnomathematics of Far western Region of Nepal, Academic Co-ordinator of Om Siddhartha Publication.