What Does Calculating Have to Do with Mathematics? Wittgenstein, Dewey, and Mathematics Education in Sweden

Chapter

Abstract

This paper concerns mathematics education in Sweden in relation to Ludwig Wittgenstein and John Dewey . Both Wittgenstein and Dewey were critical of an essentialistic, or dualistic, view of knowledge as a distinct (mental) phenomenon distinguishable from the (physical) result. This kind of view is commonly expressed in the research on mathematics education , where mathematical understanding is seen to take place in the mind or the brain, and the calculation that takes place on paper is a more or less contingent result of the mental process. I will exemplify how this view has influenced the classroom practice in Sweden and will argue that as well as being philosophically problematic in the framework of Wittgenstein and Dewey, it is counterproductive as regards the aims of mathematics education .

Keywords

Education Evaluation Mathematics Understanding Skill 

References

  1. Bergqvist, T., & Lithner, J. (2012). Mathematical reasoning in teachers’ presentations. The Journal of Mathematical Behavior, 31(2), 252–269.CrossRefGoogle Scholar
  2. Bråting, K., & Österman, T. (forthcoming in 2017). John Dewey and mathematics education in Sweden. In K. Bjarnadóttir, F. Furinghetti, M. Menghini, J. Prytz, & G. Schubring (Eds.), “Dig where you stand” 4. Proceedings of the Fourth International Conference on the History of Mathematics Education. Rome: Nuova Cultura.Google Scholar
  3. Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.Google Scholar
  4. Dewey, J. (1930). Quest for certainty: A study of the relation of knowledge and action. London: George Allen & Unwin Ltd.Google Scholar
  5. Dewey, J. (1966). Democracy and education. New York: The Free Press.Google Scholar
  6. Dewey, J. (1972). Reconstruction in philosophy. Boston: Beacon Press.Google Scholar
  7. Goldfarb, W. (2012). Rule-following revisited. In Jonathan Ellis & Daniel Gueavara (Eds.), Wittgenstein and the philosophy of mind. Oxford: Oxford University Press.Google Scholar
  8. Liljekvist, Y. (2014). Lärande i matematik: Om resonemang och matematikuppgifters egenskaper (Dissertation, p. 16). Karlstad University Studies.Google Scholar
  9. Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276.CrossRefGoogle Scholar
  10. Pongsakdi, N., Laine, T., Veermans, K., Hannula-Sormunen, M., & Lehtinen, E. (2016). Improving word problem performance in elementary school students by enriching word problems used in mathematics teaching. Nordic Studies in Mathematics Education, 21(2), 23–44.Google Scholar
  11. PRIM-gruppen, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik. (2015). http://www.su.se/primgruppen/matematik/%C3%A5k-9/bed%C3%B6mning. Accessed June 23, 2016.
  12. Wittgenstein, L. (1958). Philosophical investigations. Oxford: Basil Blackwell (PI).Google Scholar
  13. Wittgenstein, L. (1965). Blue and brown books. New York: Harper & Row (BB).Google Scholar
  14. Wittgenstein, L. (1978). Remarks on the foundations of mathematics. Cambridge, MA: MIT Press (RFM).Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Uppsala UniversityUppsalaSweden

Personalised recommendations