Originally published in the International Study Group on Ethnomathematics (ISGEm) Newsletter, Volume 5, Number 2, May 1990. Located at: http://web.nmsu.edu/~pscott/isgem52.htm. Article reproduced 2003 with permission of the ISGEm Newsletter editor for use in the Ethnomathematics Digital Library (www.ethnomath.org) developed by Pacific Resources for Education and Learning (www.prel.org).

Ethnomathematics,
Complementarity and Bhutan
Jerome Turner
St' Francis Xavier University

The following is a transcnpt of a presentation made at the Annual Meeting of the NCTM in Salt Lake City, April 20, 1990.

Ladies and gentleman, via a slide presentation, I would like to present a summary of the ethnomathematical research that I conducted in the country of Bhutan from 1986 - 1988.

At its grassroots level, this ethnomathematics research dealt with the teaching of elementary mathematics through the games, songs and play activities of Bhutanese children. At its theoretical level, I conclude that this form of pedagogy is an actualization of the principle of complementarity and further conclude that complementarity can be used as a theoretical foundation for the concept of ethnomathematics.

This research has made an original contribution to lcnowledge by extending and applying the Principle of Complementarity to human behavior. By definition, the Principle of Complementarity states that two descriptions or sets of concepts, though mutually exclusive, are nonetheless both necessary for a complete description of the situation. The physicist and Nobel Laureate, Niels Bohr, firmly believed that the Principle of Complementarity had wide application outside the realm of physics and declared that one day complementarity would be taught in schools and become part of public education.

The most recent research on hemispheric specialization of the human brain has extended the validity of the concept of complementarity as a theoretical explanation of human behavior. Together they reveal that there are two complementary modes of knowing: the intuitive and the rational.

This slide portrays a summary of the predominant functions of the hemispheres of the human brain. The predominant functions of the right hemisphere are complementary to the predominant functions of the left hemisphere. The non-verbal is complementary to the verbal, the holistic is complementary to the analytic, the viso-spatial is complementary to the rational, and so
on.

The second major contribution to knowledge of this research derives from the study of ethnomathematics. The Brazilian mathematics educator Ubiratan D'Ambrosio has been credited with coining the term ethnomathematics, and in this research it related to how counting, ordering, sorting, measuring and weighing were inherent within the games, songs and play activities of Bhutanese children.

There are two major reasons why the Far East, Buddhist nation of Bhutan was an ideal setting for this investigation. First, Niels Bohr has stated: "for a parallel to the lessons of atomic theory we must in fact turn to the kind of epistemological problems that a thinker like Buddha has confronted."

As the Bhutanese religious historian Rigzin Dorji has revealed, Buddhism permeates the everyday life of Bhutan's people. From the religious songs sung during the construction of a house, to the spiritual songs of celebration performed in honor of his majesty's birthday, to a Buddhist prayer recited by primary school children prior to the beginning of a school day, from the national sport of archery, to the painting of murals, Buddhist philosophy and beliefs significantly influence each day in the life of a Bhutanese citizen.

The second reason why Bhutan was an ideal setting for this investigation centers upon the concept of ethnomathematics. This concept was originally created in the context of developing countries who are struggling for a more meaningful way to help their children learn mathematics. Ninety-five percent of the Bhutanese people are agrarian and are involved in subsistence farming. The per capita income of this Third World national is $116.00 U.S. dollars per year and it is classified by the United Nations as one of the 31 least developed countries of the world. Consequently, Bhutan was an ideal setting to investigate ethnomathematics and to establish a theoretical framework for this concept.

During the school year of 1987, at the Teachers' Training Centre and Demonstration School, Paro, Bhutan, a case study was conducted involving two lower primary classes and their teachers. Also participating in this study were teacher trainees and the investigator as participant observer. This case study focused on a pedagogical process involving the complementary relationship between the world of play, and mathematics within the world of school, of Bhutanese children.

The analysis of data presented the analytical term: propositional theme. In the context of this investigation, it was defined as a recurring behavioral pattern which denoted a fundamental truth that was shown through demonstration to be an actualization of complementarity. Three such propositional themes were derived from the data; they were:

Propositional Theme I - Complementarity: The Voices of Bhutanese Children.

Propositional Theme II - Complementarity: The Games of Bhutanese Children.

Propositional Theme III - Complementarity: The Play Activities of Bhutanese Children.

This research concluded that the teaching of elementary school mathematics through the games, songs, and play activities of Bhutanese children could be considered to be actualization of complementarity; and that complementarity could be regarded as a theoretical foundation for ethnomathematics.

Lastly, implications of this research are drawn for the education of the whole child; that is, to educate children in a holistic manner we must give equal emphasis to art, dance, drama, music, and physical education along with the 3Rs. Further, complementarity can become a theoretical structure for ethnomathematics.

Bhutanese people are involved in the ethnomathematical practices of counting, ordering, sorting, measuring, and weighing during their weekly market day, indicating that these ethnomathematical practices are a part of many cultural activities of the Bhutanese.

Another implication of this research is that Bhutan's NAPW Project can be effective, and can create a positive attitude in the learner towards acquiring knowledge.

In conclusion, this research implies that children can learn the necessary numeracy and literacy skills through their songs, games and play activities that will help them to adininister UNICEF's GOBI project.