Western mathematics: the secret weapon of cultural imperialism

G.A. Lean , Counting Systems of Papua New Guinea (Papua New Guinea , 1986); C. Zaslavsky , Africa Counts ( Boston, 1973); M.P. Closs , Native American Mathematics (Austin, Texas, 1986).

K. Menninger , Number Words and Number Symbols: a cultural history of numbers ( Cambridge, Mass, 1969).

R. Pinxten , I. van Dooren and F. Harvey , The Anthropology of Space (University of Pennsylvania Press , 1983).

D.F. Lancy , Cross-cultural Studies in Cognition and Mathematics (New York, 1983); H. Philp , 'Mathematical education in developing countries' in A.G. Howson (ed.), Developments in Mathematical Education (Cambridge, 1973).

See, for example, U. d'Ambrosio 'Ethnomathematics and its place in the history and pedagogy of mathematics', For the Learning of Mathematics (1985), and P. Gerdes , 'How to recognise hidden geometrical thinking: a contribution to the development of anthropological mathematics', For the Learning of Mathematics ( 1986).

'Pan-cultural' is used to convey the sense that all cultures engage in mathematical activities.

In the late nineteenth century and early twentieth century, one can also recognise the increasing contribution of American and Australian influences, which nevertheless stem from the western European cultural tradition.

A fourth candidate would be 'technology'. Its influence is clear: see, for example, D.R. Headrick's The Tools of Empire (Oxford, 1981); but what is rather less clear is the mathematical relationship with technology. As science and mathematics developed in their power and control, they undoubtedly influenced technology, particularly later in the imperialist era.

See Zaslavsky, op. cit. and Menninger, op. cit.

J. Jones, Cognitive Studies with Students in Papua New Guinea (Papua New Guinea, 1974).

See Ascher, op. cit.

Even today, the abacus has survived the calculator invasion and is still in prolific use in the countries of Asia.

See P.W. Bridgman, 'Quo Vadis', Daedalus (No. 87, 1958), and L C S Dawe, 'The influence of a bilingual child's first language competence on reasoning in mathematics' (unpublished PhD thesis, University of Cambridge, 1982). As Awoniyi points out: 'A foreign language is more than a different set of words for the same ideas; it is a new and strange way of looking at things, an unfamiliar grouping of ideas', T.A. Awoniyi, 'Yoruba language and the schools system; a study m colonial language policy in Nigeria 1882 - 1952', The lnternational Journal of African Historical Studies (Vol. VIII, 1975).

In the main, of course, there was felt to be little need for anything beyond reading, in order to understand either the bible translated into a local language, or simple work instructions. In India, after the orientalist phase, English was the language used predominantly in the schools and the acquisition of English became the goal of education to the exclusion of anything else.

For example, Budo College, Uganda, the Alliance High School, Kenya, Elphinstone College, India. See M. Carnoy, Education as Cultural Imperialism (Longman, 1974) and R.J. Njoroge and G.A. Bennaars, Philosophy and Education in Africa (Nairobi, 1986).

G.R.V. Mmari , 'The United Republic of Tanzania: mathematics for social transformation' in F.J. Swetz (ed.) Socialist Mathematics Education (Southampton, PA 1978). He also says: 'Textbooks of the period in question indicate the use of foreign units of measure of length, weight, capacity, volume, and currency which support this theory of direct interaction between business practices and the cultural background of the then dominant existing business community'.

P. Damerow says 'The transfer of the European mathematics curriculum to developing countnes was closely associated with the establishment of schools for the elite by colonial administrations Under these circumstances it seemed natural to simply copy European patterns', 'Individual development and cultural evolution of arithmetical thinking' in S. Strauss (ed.), Ontogeny and Historical Development (Pennsylvania , 1986).

J.K.P. Watson Education in the Third World ( London, 1982).

Indeed, there was no great attempt m the 'home' countries themselves to make science and mathematics relevant either.

M. Kline , Mathematics in Western Culture (London, 1972).

J. Gay and M. Cole , The New Mathematics in an Old Culture (New York, 1967).

See C.A. Ronan , The Cambridge Illustrated History of the World's Science (Cambridge Press, 1983), and C.H. Waddington , Tools for Thought (St Albans , 1977), for a recent analysis.

R. Horton , 'African traditional thought and Western science' Africa, (Vol XXXVII, 1967), also in M.F.F. Young (ed.), Knowledge and Control (London, 1971 ).

W.L. Schaaf , Our Mathematical Heritage (New York, 1963).

Horton , op. cit

For a fuller examination of these ideas, see A.J. Bishop , Mathematical Enculturation: a cultural perspective on mathematics education ( Dordrecht, Holland, 1988).

The caveat may perhaps seem unnecessary, but to a mathematician the word 'universal' does cause certain problems. For further discussion of this general issue, see G.P. Murdoch , 'The common denominator of cultures' in R. Linton (ed.), The Science of Man in the World Crisis (New York, 1945).

In order for mathematical knowledge to develop, it is necessary for these activities to integrate and to interact. Without this integration, the set of activities could be argued to be pre-mathematical.

See d'Ambrosio op. cit. and M. Ascher and R. Ascher , 'Ethnomathematics', History of Science (Vol XXIV, 1986) for different perspectives. The Aschersargue specifically for ethnomathematics to be the province of 'non-literate peoples', while d'Ambrosio's view encompasses all mathematical ideas not exposed by 'mainstream' mathematics.

See Gerdes (1986) op. cit and P. Gerdes , 'On possible uses of traditional Angolan sand drawings in the mathematics classroom', Educational Studies in Mathematics (No 19, 1988).

See P. Harris Measurement in Tribal Aboriginal Communities (Northern Territory Department of Education, Australia, 1980), and Closs, op. cit.

See S.H. Nasr , Islamic Science. an illustrated study (Essex, UK, 1976) and I.R. Al-Faruqi and A.D. Naseef , Social and Natural Science: the Islamic perspective (London, 1981).

I. van Sertima , Blacks in Science (New Brunswick, 1986 ).

For example, B. Lumpkin , 'Afnca in the mainstream of mathematics history', in van Sertima, op. cit.

G.G. Joseph , 'Foundations of Eurocentrism in Mathematics', Race and Class (Vol. XXVIII, 1987).

See C.A. Ronan , The Shorter Science and Civilization in China , Vol. 2 (Cambridge, 1981).

See, for example, D.S. Kothan's keynote address in the Proceedings of the Asian Regional Seminar of the Commonwealth Association of Science and Mathematics Educators (London, 1978).

See A.J. Bishop, P. Damerow, P. Gerdes and C. Keitel, 'Mathematics, Education and Society' in A. Hirst and K. Hirst, Proceedings of the Sixth International Congress on Mathematical Education (University of Southampton, 1988); also, there is a special UNESCO publication of the whole day's papers and proceedings (C. Keitel, A.J. Bishop, P. Damerow and P. Gerdes Mathematics, Education and Society (Document Series 35, Paris, 1989)).