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Stratigraphy as a method for studying the different modes of existence arising in the mathematical classroom

  • Petra Mikulan
  • Nathalie SinclairEmail author
Original Article

Abstract

The growing number of interpretive lenses used in mathematics education research are often seen in terms of either/or, such as the individual or the social, the discursive or the bodily, the classroom interactive or the neurological events, the humanist or the post-humanist. We propose stratigraphy as a research (meta-)method that is conjunctive rather than disjunctive, resisting the temptation to collapse these different interpretations into a single, convergent narrative. Using a classroom episode involving young children working on counting with digital technology, and drawing primarily on the work of Gilles Deleuze and Étienne Souriau, we describe the philosophical assumptions of stratigraphy and show what stratigraphy might look like for mathematics education research. We aim to contribute to on-going discussions about how to handle different theories that are used in mathematics education, as well as the question of how to frame their current and future relationships.

Keywords

Stratigraphy Instauration Souriau Deleuze Virtual Method Gesture TouchCounts Number 

Notes

Acknowledgements

We thank our reviewers for their very helpful comments and suggestions on previous versions of this paper and David Pimm for an especially helpful last round of re-structuring.

References

  1. Barad, K. (2007). Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning. Durham: Duke University Press.CrossRefGoogle Scholar
  2. Barthes, R. (1973). S/Z. Paris: Editions du Seuil.Google Scholar
  3. Colebrook, C. (2016). ‘A grandiose time of coexistence’: Stratigraphy of the anthropocene. Deleuze Studies, 10(4), 440–454.CrossRefGoogle Scholar
  4. Coles, A., Barwell, R., Cotton, T., Winter, J., & Brown, L. (2013). Teaching secondary mathematics as if the planet matters. London: Routledge.CrossRefGoogle Scholar
  5. de Freitas, E., & Sinclair, N. (2014). Mathematics and the body: Material entanglements in the classroom. New York: Cambridge University Press.CrossRefGoogle Scholar
  6. de Freitas, E., & Sinclair, N. (2018). The quantum mind: Alternative ways of reasoning with uncertainty. Canadian Journal of Science, Mathematics and Technology Education, 18, 271–283 (on-line first).CrossRefGoogle Scholar
  7. Deleuze, G. (1995). Difference and repetition. New York: Columbia University Press.Google Scholar
  8. Deleuze, G. (2006). The fold: Leibniz and the baroque. London: Continuum.Google Scholar
  9. Deleuze, G., & Guattari, F. (1994). What is philosophy? New York: Columbia University Press.Google Scholar
  10. Foucault, M. (1972). The archaeology of knowledge (1st edn.). New York: Irvington Publications.Google Scholar
  11. Foucault, M. (1995). Discipline and punish: The birth of the prison. REP edition. New York: Vintage.Google Scholar
  12. Jornet, A., & Roth, W.-M. (2018). Imagining design: Transitive and intransitive dimensions. Design Studies, 56, 28–53.CrossRefGoogle Scholar
  13. Lakoff, G., & Núñez, R. (2000). Where mathematics come from: How the embodied mind brings mathematics into being. New York, NY: Basic books.Google Scholar
  14. Latour, B. (2012). Enquête sur les modes d’existence: Une anthropologie des modernes. Paris: La Découverte.Google Scholar
  15. Menz, P. (2015). Unfolding of diagramming and gesturing between mathematics graduate student and supervisor during research meetings. Unpublished doctoral dissertation. Burnaby, BC: Simon Fraser University.Google Scholar
  16. Mikulan, P. (2017). Pedagogy without bodies. Unpublished doctoral dissertation. Burnaby, BC: Simon Fraser University.Google Scholar
  17. Mikulan, P. (2018). Étienne Souriau and educational literacy research as an instaurative event. In C. Kuby, K. Spector, J. Thiel & L. Vasudevan (Eds.), Posthumanism and literacy education (pp. 95–107). Abingdon: Routledge.CrossRefGoogle Scholar
  18. Mikulan, P., & Sinclair, N. (2017). Thinking mathematics pedagogy stratigraphically in the anthropocene. Philosophy of Mathematics Education Journal, 32. http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome32/.
  19. Netz, R., Noel, W., Wilson, N., & Tchernetska, N. (2011). The Archimedes palimpsest (Vols. 1–2). Cambridge: Cambridge University Press.Google Scholar
  20. Prediger, S., Arzarello, F., Bosch, M., & Lenfant, A. (2008). Comparing, combining, coordinating: Networking strategies for connecting theoretical approaches. ZDM—The International Journal on Mathematics Education, 40(2), 163–164.CrossRefGoogle Scholar
  21. Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connecting theoretical approaches: First steps towards a conceptual framework. ZDM—The International Journal on Mathematics Education, 40(2), 165–178.CrossRefGoogle Scholar
  22. Queneau, R. (1947). Exercises de style. Paris: Gallimard.Google Scholar
  23. Robinson, A. (1966). Non-standard analysis. Amsterdam: North-Holland Publishing.Google Scholar
  24. Rovelli, C. (2018). The order of time. London: Penguin.Google Scholar
  25. Ruffell, M., Mason, J., & Allen, B. (1998). Studying attitude to mathematics. Educational Studies in Mathematics, 35(1), 1–18.CrossRefGoogle Scholar
  26. Shaviro, S. (2009). Without criteria: Kant, Whitehead, Deleuze and Aesthetics. Cambridge: The MIT Press.Google Scholar
  27. Sinclair, N., & de Freitas, E. (2014). The haptic nature of gesture: Rethinking gesture with new multitouch digital technologies. Gesture, 14(3), 351–374.CrossRefGoogle Scholar
  28. Smythe, S., Hill, C., MacDonald, M., Dagenais, D., Sinclair, N., & Toohey, K. (2017). Disrupting boundaries in education and research. New York: Cambridge University Press.CrossRefGoogle Scholar
  29. Souriau, É (1939). L’instauration philosophique. Paris: Alcan.Google Scholar
  30. Souriau, É (1943/2015). The different modes of existence (E. Beranek & T. Howles, Trans.). Minneapolis: Minnesota University Press.Google Scholar
  31. Vinsonhaler, R. (2016). Teaching calculus with infinitesimals. Journal of Humanistic Mathematics, 6(1), 249–276.CrossRefGoogle Scholar
  32. Whitehead, A. (1929/1978). Process and Reality. New York: The Free Press.Google Scholar
  33. Žižek, S. (2012). Organs without bodies: On Deleuze and Consequences. London: Routledge.Google Scholar

Copyright information

© FIZ Karlsruhe 2019

Authors and Affiliations

  1. 1.Department of Educational Studies, Faculty of EducationThe University of British ColumbiaVancouver BCCanada
  2. 2.Simon Fraser UniversityBurnabyCanada

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