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What Are Mathematical Cultures?

  • Brendan Larvor
Conference paper
Part of the Trends in the History of Science book series (TRENDSHISTORYSCIENCE)

Abstract

In this paper, I will argue for two claims. First, there is no commonly agreed, unproblematic conception of culture for students of mathematical practices to use. Rather, there are many imperfect candidates. One reason for this diversity is there is a tension between the material and ideal aspects of culture that different conceptions manage in different ways. Second, normativity is unavoidable, even in those studies that attempt to use resolutely descriptive, value-neutral conceptions of culture. This is because our interest as researchers into mathematical practices is in the study of successful mathematical practices (or, in the case of mathematical education, practices that ought to be successful).

I first distinguish normative conceptions of culture from descriptive or scientific conceptions. Having suggested that this distinction is in general unstable, I then consider the special case of mathematics. I take a cursory overview of the field of study of mathematical cultures, and suggest that it is less well developed than the number of books and conferences with the word ‘culture’ in their titles might suggest. Finally, I turn to two theorists of culture whose models have gained some traction in mathematics education: Gert Hofstede and Alan Bishop. Analysis of these two models corroborates (in so far as two instances can) the general claims of this paper that there is no escaping normativity in this field, and that there is no unproblematic conception of culture available for students of mathematical practices to use.

Keywords

Mathematics Education Mathematical Practice Mathematics Education Research Cultural Approach Epistemic Practice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Adam, J. (Ed.). (1902). The Republic of Plato. Edited, with critical notes, commentary, and appendices (2 Vols.). Cambridge: Cambridge University Press. Google Scholar
  2. Alexander, A. (2010). Duel at dawn. Cambridge, MA: Harvard University Press.zbMATHGoogle Scholar
  3. Alrø, H., Ravn, O., & Valero, P. (Eds.). (2010). Critical mathematics education: past, present and future. Rotterdam: Sense Publishers.zbMATHGoogle Scholar
  4. Arnold, M. (1978). Culture and anarchy. Cambridge: Cambridge Univ. Press. Reprint of the second (1875) edition.Google Scholar
  5. Azzouni, J. (2006). How and why mathematics is unique as a social practice. In R. Hersh (Ed.), 18 unconventional essays on the nature of mathematics. New York, NY: Springer.Google Scholar
  6. Banks, J. A., & McGee Banks, C. A. (1989). Multicultural education. Needham Heights, MA: Allyn & Bacon.Google Scholar
  7. Bishop, A. (1991). Mathematical enculturation: a cultural perspective on mathematics education. Dordrecht: Kluwer.Google Scholar
  8. Ernest, P. (2000). Why teach mathematics? In J. White & S. Bramall (Eds.), Why learn maths? London: London University Institute of Education.Google Scholar
  9. François, K., & Stathopoulou, C. (2012). In-between critical mathematics education and ethnomathematics. a philosophical reflection and an empirical case of a Romany students’ group mathematics education. Journal for Critical Education Policy Studies, 10(1), 234–247.Google Scholar
  10. Greiffenhagen, C. (2014). The materiality of mathematics: presenting mathematics at the blackboard. The British Journal of Sociology, 65, 502–528.CrossRefGoogle Scholar
  11. Hacking, I. (2014). Why is there philosophy of mathematics at all? Cambridge: Cambridge Univ. Press.zbMATHCrossRefGoogle Scholar
  12. Hardy, G. H. (2004). A mathematician’s apology. Cambridge: Cambridge Univ. Press [Original edition 1940].zbMATHGoogle Scholar
  13. Hegel, G. W. F. (1821). Elements of the philosophy of right. (Original German title: Grundlinien der Philosophie des Rechts).Google Scholar
  14. Hersh, R. (2006). 18 unconventional essays on the nature of mathematics. New York: Springer.zbMATHCrossRefGoogle Scholar
  15. Hofstede, G. (1984). National cultures and corporate cultures. In L. A. Samovar & R. E. Porter (Eds.), Communication between cultures. Belmont, CA: Wadsworth.Google Scholar
  16. Hofstede, G. (1986). Cultural differences in teaching and learning. International Journal of Intercultural Relations, 10(3), 301–320.CrossRefGoogle Scholar
  17. Huckstep, P. (2000). Mathematics as a vehicle for mental training. In S. Bramall & J. White (Eds.), Why learn maths? (pp. 88–91). London: Institute of Education.Google Scholar
  18. Kant, I. (1787). Critique of pure reason. (Original German title: Kritik der reinen Vernunft) first published in 1781, second edition 1787. Riga: Johann Friedrich Hartknoch.Google Scholar
  19. Kantor, J.-M. (2011). Mathematics and mysticism, name worshipping, then and now. Theology and Science, 9, 1.MathSciNetCrossRefGoogle Scholar
  20. Kroeber, A. L., & Kluckhohn, C. (1952). Culture: a critical review of concepts and definitions. Cambridge, MA: Peabody Museum of American Archeology and Ethnology Harvard University. Papers 47.Google Scholar
  21. Larvor, B. (2010). Review of the philosophy of mathematical practice. In P. Mancosu (Ed.), Philosophia mathematica (Vol. 18, pp. 350–360). Oxford: Oxford University Press.Google Scholar
  22. Larvor, B. (2012). The mathematical cultures network project. Journal of Humanistic Mathematics, 2(2), 157–160.MathSciNetGoogle Scholar
  23. Lockhart, P. (2009). Mathematician’s lament. New York, NY: Bellevue Literary Press.zbMATHGoogle Scholar
  24. Mancosu, P. (Ed.). (2008). The philosophy of mathematical practice. Oxford: Oxford University Press.zbMATHGoogle Scholar
  25. Manders, K. (2008). The Euclidean diagram. In P. Mancosu (Ed.), The philosophy of mathematical practice (pp. 80–133). Oxford: Oxford University Press.CrossRefGoogle Scholar
  26. Netz, R. (1999). The shaping of deduction in Greek mathematics. Cambridge: Cambridge Univ. Press.zbMATHCrossRefGoogle Scholar
  27. Nietzsche, F. (1887). On the genealogy of morality: a polemic. (Original German title: Zur Genealogie der Moral: Eine Streitschrift). Leipzig: C.G. Naumann.Google Scholar
  28. Parsons, T. (1949). Essays in sociological theory. Glencoe, IL: Free Press.Google Scholar
  29. Peirce, C. S. (1897). The logic of relatives. The Monist, 7(2), 161–217.CrossRefGoogle Scholar
  30. Plato. The republic. Google Scholar
  31. Rav, Y. (1999). Why do we prove theorems? Philosophia Mathematica, 7(1), 5–41.MathSciNetzbMATHCrossRefGoogle Scholar
  32. Brian, R. (1993). Ad infinitum: the ghost in Turing’s machine. Stanford: Stanford University Press.zbMATHGoogle Scholar
  33. Rosental, C. (2008). Weaving self-evidence: a sociology of logic. Princeton, NJ: Princeton University Press. Trans. by Catherine Porter.zbMATHGoogle Scholar
  34. Schiller, F. (1794). Letters on the aesthetic education of man. (Original German title: Über die ästhetische Erziehung des Menschen).Google Scholar
  35. Skovsmose, O. (1994). Towards a philosophy of critical mathematics education. Dordrecht: Kluwer.zbMATHCrossRefGoogle Scholar
  36. Spengler, O. (1926). The decline of the west, Vol. 1: form and actuality. London: G. Allen. Trans. C. F. Atkinson.Google Scholar
  37. Useem, J., & Useem, R. (1963). Men in the middle of the third culture: the roles of American and non-western people in cross-cultural administration. Human Organizations, 22(3).Google Scholar
  38. Weber, M. (1930). The protestant ethic and the spirit of capitalism. (Original German title: Die protestantische Ethik und der Geist des Kapitalismus). London: Allen & Unwin [Translated by Talcott Parsons].Google Scholar
  39. White, J., & Bramall, S. (Eds.). (2000). Why learn maths? London: London University Institute of Education.Google Scholar
  40. White, L. A. (1959). The evolution of culture: the development of civilization to the fall of Rome. New York: McGraw Hill.Google Scholar
  41. Wilder, R. L. (1965). Introduction to the foundations of mathematics (2nd ed.). New York: John Wiley (First published 1952).zbMATHGoogle Scholar
  42. Wilder, R. L. (1981). Mathematics as a cultural system. Oxford: Pergamon.zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of HertfordshireHatfieldUK

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