Abstract
David Lancy (1983) in his major cross-cultural study in Papua New Guinea gives us a helpful introduction to the analysis of the values of Mathematical culture. He developed a stage theory to account for the differences he found in his research and compared his stages with those of Piaget. He first of all came to the conclusion that, regarding cognitive development culturally, it is not individuals who achieve concrete operational or formal operational stages, but rather it is societies which make such transitions (p. 169).
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Notes
Sydenham (1979) says this: “Today’s society still requires numerous routine measurements to regulate its function… A great deal of modern instrumentation is used to control, rather than gain, new knowledge in the scientific sense” (p. 30).
Khader (1984) comments, along with others: “Technology, in itself, is neither good nor evil, it is the use that it is put to that makes it so” (p. 38).
Kothari (1978) takes up this theme: “Should the emphasis of science and mathematics teaching lie in bettering, in strengthening, links between Science, Technology and Productivity, which is relatively easy to do, or to link S.T.P. with Wisdom, which is far more necessary but terribly difficult?” (p. 17). Kothari characterises modern society as knowledge-based, and acknowledges its virtues but reminds us also of its faults. What he seeks is a society that is ‘Knowledge-and-wisdom-based’ and he personally looks to Ghandi as his image of wisdom.
Gordon (1978) in his paper ‘Conflict and Liberation: Personal Aspects of the Mathematical Experience’ suggests that the teacher should replace phrases such as “What if”, “suppose” and “let”, with “what if I”, “suppose I” and “if I let” or “if we let”. He says “It is we who create the world, school, and mathematics. But the person is never alluded to in mathematics textbooks, except for those famous individuals whose efforts have been singular” (p. 267).
Crowe (1975) presents us with ‘Ten “Laws” concerning patterns of change in the History of Mathematics’ provoked by Wilder’s (1968) collection of ten laws. Crowe’s First Law states “New mathematical concepts frequently come forth not at the bidding, but against the efforts, at times strenuous efforts, of the mathematicians who create them”. His Second Law is “Many new mathematical concepts, even though logically acceptable, meet forceful resistance after their appearance and achieve acceptance only after an extended period of time” (p. 162).
An interesting discussion of this point, in relation to mathematics, is undertaken by White (1947) in his article ‘The Locus of Mathematical Reality’.
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© 1991 Kluwer Academic Publishers
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Bishop, A.J. (1991). The Values of Mathematical Culture. In: Mathematical Enculturation. Mathematics Education Library, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2657-8_3
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