Western mathematics, as part of western European culture that perpetuate imperialist goals, is seen as a secret weapon which maintains the imposition and domination of western cultural values on indigenous cultures around the world. Bishop used the term “secret weapon” to reveal how, even today, the belief that mathematics is a culturally neutral knowledge persists in contemporary schools.
This perception stems from the fact that universal validity of mathematical truths, which are abstractions from the real world, seemingly makes the knowledge as though it is neutral and context-free. To say, for instance, that a kilo of wild bananas harvested in Guinea Bissau equates to 2.20462 pounds is valid everywhere. However, it should be noted why kilo and pounds are used for standard measurement of mass and why the conversion from kilo to pound always equates to 2.20462.
The answer to these questions, according to Bishop, essentially points to an authority that determines the standardization of measurement and other mathematical ideas which, like any other ideas, are a product of cultural history and human construction. Mathematics, as Bishop argues, is a cultural product present not only in contemporary schools that uses standard Western mathematics but also in indigenous communities all over the world.
As shown in anthropological literature, alternative mathematical systems exist through the study of ethno-mathematics, defined as “a localized and specific set of mathematical ideas which may not aim to be as general or as systematized as ‘mainstream’ mathematics”. Through ethno-mathematics, we find out that different counting systems in the world exist; for instance, in Papua New Guinea, 600 various cycles of numbers and body-part counting system are documented (Lean, 1991). Also, even the conception of space differs from one culture to another; for instance, Menninger (1969) observed that in contrast to Euclidean geometry which relies on the object-oriented ideas of points, lines, planes, and solids, the Navajos perceive space as something that cannot be divided or objectified. Moreover, in contrast with western hierarchical classification matrix, people of Papua New Guinea adopt a linear form of classification resulting to a different logic and ways of relating to phenomena.
In the Philippines, a study on ethno-mathematics conducted by UP College of Baguio (1991) reveals the existence of algebra in the weaving patterns, gong music, and kinship system of the Kankana-ey in Mountain Province. These studies on ethno-mathematics provide us with better understanding of mathematics as a pan-cultural phenomenon. However, western mathematics, as part of western European culture, has succeeded in internationalizing and standardizing math for indigenous communities around the world for more than three hundred years.
With this, Bishop points to three major mediating agents in the cultural invasion of western mathematics in colonized countries: 1.) trade and commerce, 2.) administration and government, and 3.) education. The commercial field serves as the area where western currencies, measures, and units are employed and imposed on trade and business transactions. In the government, western numerical procedures are used for computation on tracking numbers of people and commodities. Most importantly, it is through education that western mathematical ideas and western culture are propagated. As Bishop views it, western mathematics is “abstract, irrelevant, and elitist” for indigenous students who are educated “away from their culture and away from their society”.
The adaptation of western mathematics by indigenous cultures has had and continues to have powerful implications in the indigenous culture when it comes to education, national development and continuation of cultural imperialism. The clusters of values associated by this system of knowledge have had tremendous impact their logic and ways of thinking. First, western mathematics embrace rationalism as its spirit which invigorates and drive human minds. Second, the value of objectism found in western mathematics forces indigenous cultures to decontextualize the way discrete objects are perceived and abstracted. Lastly, western mathematics emphasizes man’s power and control over his physical and social environment in contrast to other indigenous thinking.
Indeed, western mathematics has remained a powerful and useful tool for almost every country in the world. The mathematico-technological culture has rapidly grown and its implications are now being understood. As Bishop suggests, our responses to the domination of western mathematics should be that: 1.) we create interest in ethno-mathematics, 2.) produce greater awareness of one’s culture, and 3.) re-examine the history of western mathematics. In this way, even as the world has generally accepted western mathematics in its system, recognizing and understanding its implications on indigenous cultures is important for critical debate in education and resistance to cultural hegemony and imperialism.
Bishop, Alan J. 'Western Mathematics: The Secret Weapon of Cultural Imperialism'. Race and Class 32(2), 1990
UP College of Baguio. The Algebra of the Weaving Patterns, Music, and Kinship System of the Kankana-ey of Mountain Province, 1996.