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MATHEMATICS AS AN IM/PURE KNOWLEDGE SYSTEM: SYMBIOSIS, (W)HOLISM AND SYNERGY IN MATHEMATICS EDUCATION

  • Bal Chandra LuitelEmail author
Article

ABSTRACT

The problem of culturally decontextualised mathematics education faced by Nepali students, teachers and teacher educators has often been oriented by the view of the nature of mathematics as a body of pure knowledge, which gives rise to an exclusive emphasis on an ideology of singularity, epistemology of objectivism, language of universality and logic of certainty whilst developing curriculum, conceiving pedagogies and implementing assessment strategies in school mathematics education and mathematics teacher education programmes. With epistemic referents of dialectical logics and performative imagination, an alternative view of the nature of mathematics as an impure knowledge is discussed with its possible disempowering features, such as essentialism, hegemony and dualisms. Finally, an inclusive view of the nature of mathematics as im/pure knowledge system is articulated with the help of various forms of dialectics.

KEY WORDS

Advaita Vedanta empowerment inclusion inclusive mathematics education logics negative dialectics 

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References

  1. Adorno, T. W. (1973). Negative dialectics. NY: Seabury Press.Google Scholar
  2. Apple, M. (2004). Ideology and curriculum. NY: Routledge.Google Scholar
  3. Ashcroft, B., Griffiths, G. & Tiffin, H. (2000). Post-colonial studies: The key concepts. NY: Routledge.Google Scholar
  4. Baldwin, J. R. (2006). Redefining culture: Perspectives across the disciplines. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  5. D’Ambrosio, U. (2006). Ethnomathematics: Link between traditions and modernity Rotterdam. The Netherlands: Sense.Google Scholar
  6. Davis, L. S. (2010). Advaita Vedanta and Zen Buddhism: Deconstructive modes of spiritual inquiry. London; New York: Continuum.Google Scholar
  7. DeBoer, G. E. (1991). A history of ideas in ecience education: Implications for practice. New York: Teachers College Press.Google Scholar
  8. Douglas, H. (2004). The irreducible complexity of objectivity. Synthese, 138(3), 453–473.CrossRefGoogle Scholar
  9. Ernest, P. (Ed.). (1994). Mathematics, education, and philosophy: An international perspective. London; NY: Falmer Press.Google Scholar
  10. Fraser, S. P. & Bosanquet, A. M. (2006). The curriculum? That’s just a unit outline, isn’t it? Studies in Higher Education, 31(3), 269–284.CrossRefGoogle Scholar
  11. Gergen, K. J. (1995). Social construction and the educational process. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 17–39). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  12. German-English Dictionary (2008). http://dict.tu-chemnitz.de/. Accessed 4 Dec 2008.
  13. Gilsdorf, T. E. (2012). Introduction to cultural mathematics: With case studies in the Otomies and Incas. Hoboken, NJ: Wiley.CrossRefGoogle Scholar
  14. Glas, E. (2006). Mathematics as objective knowledge and as human practice. In R. Hersh (Ed.), 18 unconventional essays on the nature of mathematics (pp. 289–304). NY: Springer.CrossRefGoogle Scholar
  15. Gutstein, E. (2007). Multiple language use and mathematics: Politicizing the discussion. Educational Studies in Mathematics, 64(2), 243–246.CrossRefGoogle Scholar
  16. Habermas, J. (1989). The new conservatism: Cultural criticism and the historians’ debate. Cambridge, Mass.: MIT Press.Google Scholar
  17. Hersh, R. (1997). What is mathematics, really? NY: Oxford University Press.Google Scholar
  18. Hirst, J. S. (2005). Samkara’s Advaita Vedanta: A way of teaching. London: Taylor & Francis Group.Google Scholar
  19. Horsthemke, K. & Schafer, M. (2007). Does ‘African mathematics’ facilitate access to mathematics? Towards an ongoing critical analysis of ethnomathematics in a South African context. Pythagoras, 65, 2–9.Google Scholar
  20. Jablonka, E. & Gellert, U. (2007). Mathematisation–demathematisation. In U. Gellert & E. Jablonka (Eds.), Mathematisation and demathematisation: Social, philosophical and educational ramifications (pp. 1–18). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  21. Kathmandu University (2006). Developing culturally contextualised mathematics resource materials: Capturing local practices of Tamang and Gopali Communities: Fieldwork report to UNESCO Kathmandu. School of Education, Kathmandu University.Google Scholar
  22. Kline, M. (1982). Mathematics: The loss of certainty. NY: Oxford University Press.Google Scholar
  23. Laudan, L. (1996). Beyond positivism and relativism: Theory, method, and evidence. Boulder, CO: Westview Press.Google Scholar
  24. Lerman, S. (1990). Alternative perspectives of the nature of mathematics and their influence on the teaching of mathematics. British Educational Research Journal, 16(1), 53–61.CrossRefGoogle Scholar
  25. Loy, D. (1997). Nonduality: A study in comparative philosophy. Atlantic Highlands, NJ: Humanities Press.Google Scholar
  26. Luitel, B. C. (2009). Culture, worldview and transformative philosophy of mathematics education in Nepal: A cultural-philosophical inquiry. Unpublished Thesis, Curtin University, Perth.Google Scholar
  27. Luitel, B. C. & Taylor, P. C. (2007). The shanai, the pseudosphere and other imaginings: Envisioning culturally contextualised mathematics education. Cultural Studies of Science Education, 2(3), 621–638.CrossRefGoogle Scholar
  28. Luitel, B. C. & Taylor, P. C. (2010). ‘What is ours and what is not ours?’ Inclusive imaginings of contextualised mathematics teacher education. In D. J. Tippins, M. P. Mueller, M. van Eijck & J. Adams (Eds.), Cultural studies and environmentalism: The confluence of eco-justice, place based (science) education, and indigenous knowledge systems (pp. 385–408). Dordrecht, The Netherlands: Springer.Google Scholar
  29. Nuñez, R. (2006). Do real numbers really move?: Language, thought, and gesture: The embodied cognitive foundations of mathematics. In R. Hersh (Ed.), 18 unconventional essays on the nature of mathematics (pp. 160–181). NY: Springer.CrossRefGoogle Scholar
  30. Panda, N. (1991). Maya in physics (1st ed.). New Delhi: Motilal Banarsidass Publishers.Google Scholar
  31. Pelias, R. J. (2008). Performative inquiry: Embodiment and its challenges. In J. G. Knowles & A. L. Cole (Eds.), Handbook of arts in qualitative research (pp. 185–194). Thousand Oaks, CA: Sage.Google Scholar
  32. Powell, A. B. & Frankenstein, M. (Eds.). (1997). Ethnomathematics: Challenging Eurocentrism in mathematics education. New York: State University of New York.Google Scholar
  33. Raju, P. T. (1954). The principle of four-cornered negation in Indian philosophy. Review of Metaphysics, 7, 694–713.Google Scholar
  34. Ramanan, K. V. (1975). Nagarjuna’s philosophy (2002 reprint). Delhi, Varanasi, Patna: Motilal Banarsidass.Google Scholar
  35. Rescher, N. (2006). Philosophical dialectics: An essay on metaphilosophy. Albany: State University of New York Press.Google Scholar
  36. Restivo, S. & Bauchspies, W. (2006). The will to mathematics: Minds, morals, and numbers. Foundations of Science, 11(1), 197–215.CrossRefGoogle Scholar
  37. Taylor, P. C., Taylor, E. & Luitel, B. C. (2012). Multi-Paradigmatic transformative research as/for teacher education: An integral perspective. In K. Tobin, B. Fraser & C. McRobbie (Eds.), Second international handbook of science education (pp. 373–388). Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
  38. Vithal, R. & Skovsmose, O. (1997). The end of innocence: A critique of ‘Ethnomathematics’. Educational Studies in Mathematics, 34(2), 131–157.CrossRefGoogle Scholar
  39. Wilber, K. (2000). Sex, ecology, spirituality: The spirit of evolution (2nd ed.). Boston, MA: Shambhala.Google Scholar
  40. Wong, W.-C. (2006). Understanding dialectical thinking from a cultural-historical perspective. Philosophical Psychology, 19(2), 239–260.CrossRefGoogle Scholar
  41. Wood, E. & Sankaracharya (1974). The glorious presence: The Vendanta philosophy including Shankara’a ode to the south-facing form. Wheaton, IL: Theosophical Publications.Google Scholar

Copyright information

© National Science Council, Taiwan 2012

Authors and Affiliations

  1. 1.Kathmandu UniversityDhulikhelNepal

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