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Mathematics Education Research Journal

, Volume 27, Issue 3, pp 359–384 | Cite as

Mathematics is always invisible, Professor Dowling

  • John Cable
Original Article
First Online:

Abstract

This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a ‘gift’ to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between ‘expression’ and ‘content’) instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between ‘public’ and ‘esoteric’ mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the ‘myth of participation’, which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling’s ‘essentially linguistic’ conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

Keywords

Social bias Dichotomy Unwieldy complement Realistic mathematics Linguistics Concepts Formalism Language games 
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Notes

Acknowledgments

I am most grateful for comments and assistance received from various colleagues, especially Margaret Brown and Jeremy Hodgen. I also owe much to Peter Gates and other anonymous reviewers of earlier drafts of the article.

References

  1. Brown, A., & Dowling, P. (1998). Doing research/reading research: a mode of interrogation for education. Master Classes in Education Series. London: Falmer.Google Scholar
  2. Cable, J. (2014). How-many-ness and rank order—towards the deconstruction of ‘natural number’. In S. Pope (Ed), Proceedings of the 8th British Congress of Mathematics Education: 33-40. www.bsrlm.org.uk
  3. Cooper, B., & Dunne, M. (2000). Assessing children’s mathematical knowledge: social class, sex and problem-solving. Buckingham: Open University Press.Google Scholar
  4. de Saussure, F., Bally, C., Sechehaye, A., Riedlinger, A., & Harris, R. (1983). Course in general linguistics. London: Duckworth.Google Scholar
  5. Detlefsen, M. (2005). Formalism. In S. Shapiro (Ed.), The Oxford Handbook of Philosophy of Mathematics and Logic, Chap 8. Oxford: OUP.Google Scholar
  6. Dowling, P. (1998). London. Washington D.C.: Falmer Press. The sociology of mathematics education: mathematical myths, pedagogic texts.Google Scholar
  7. Dowling, P. (2009). Sociology as method. Rotterdam: Sense.Google Scholar
  8. Dowling, P. (2013). Social activity method (SAM): a fractal language for mathematics. Mathematics Education Research Journal, 25, 317–340.CrossRefGoogle Scholar
  9. Duval, R. (2006). A cognitive analysis of problems of comprehension in the learning of mathematics. Educational Studies in Mathematics, 61, 103–131.CrossRefGoogle Scholar
  10. Einstein, A. (2005). Ideas and Opinions. London: Souvenir Press.Google Scholar
  11. Ferreiros, J. (1999). Labyrinth of thought: a history of set theory and its role in modern mathematics. Science networks. Basel: Birkhauser.CrossRefGoogle Scholar
  12. Frege, G. (1999). Begriffsshrift [1879]. In J. Van Heijenoort (Ed), From Frege to Godel. San Jose: to Excel Press.Google Scholar
  13. Frege, G., & Gabriel, G. (1984). Collected papers on mathematics, logic, and philosophy. Oxford: Blackwell.Google Scholar
  14. Hilbert, D. (1971). Foundations of geometry (2nd ed.). La Salle, Ill: Open Court.Google Scholar
  15. Irwin, T., & Fine, G. (Eds.). (1995). Aristotle selections. Indianapolis: Hacket.Google Scholar
  16. Lewis, C. I., & Langford, C. H. (1956). History of Symbolic Logic. In J. R. Newman (Ed.), The world of Mathematics (pp. 1833–1850). Redmond: Tempus Books.Google Scholar
  17. McDermott, T. (1993). Thomas Aquinas: selected philosophical writings. World’s classics. [Selections.]. Oxford: Oxford University Press.Google Scholar
  18. Morgan, C., Tsatsaroni, A., & Lerman, S. (2002). Teachers’ positions and practices in discourses of assessment. British Journal of Sociology of Education, 23(3), 445–461.CrossRefGoogle Scholar
  19. Newman, J. (1956). The world of Mathematics, vol. one. London: Allen and Unwin.Google Scholar
  20. Ormell, C. (1972). Mathematics, applicable versus pure-and-applied. International Journal of Mathematics Education in Science and Technology, 3(2), 125–131.CrossRefGoogle Scholar
  21. Ormell, C. (2013). Mathematics, a third way. The Mathematical Gazette, 97(538), 101–106.Google Scholar
  22. Pring, R. (1975). Bernstein’s classification and framing of knowledge. Scottish Educational Studies, 7, 67–74.Google Scholar
  23. Vygotsky, L. S., Lurii, A. R., Golod, V. I., & Knox, J. E. (1993). Studies on the history of behavior: ape, primitive and child. Hillsdale, Hove: Lawrence Erlbaum.Google Scholar
  24. Wittgenstein, L., Pears, D., & McGuinness, B. (1974). Tractatus logico-philosophicus. London: Routledge & Kegan Paul.Google Scholar
  25. Wittgenstein, L., Anscombe, G. E. M., Hacker, P. M. S., & Schulte, J. (2009). Philosophical investigations (4th ed.). Chichester: Wiley-Blackwell.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2015

Authors and Affiliations

  1. 1.King’s College LondonLondonUK
  2. 2.Squirrels Oak Tree Corner, Chichester CloseWitley, GodalmingUK

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