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.
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Notes
Latour (2012) revises these five modes and adds many more.
Indeed, some have argued that teaching calculus with infinitesimals might be a more intuitive approach (Vinsonhaler, 2016).
As Colebrook writes, “rather than humans reading the earth, recognising a history of capital and industry, and then dividing humanity according to those guilty of destruction of the earth as a living system opposed to the meek who shall inherit the earth, one might think of other planetary scales where organic life has no prima facie value” (p. 443). While this concern for the Anthropocene might seem far from mathematics education research, Coles et al. (2013) have charted out some important, potential connections—see also Mikulan and Sinclair (2017) for an approach rooted in the work of Colebrook.
This is similar to what Raymond Queneau (1947) did in his Exercises de Style where he wrote a story of a narrator getting on a bus in 99 different styles.
References
Barad, K. (2007). Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning. Durham: Duke University Press.
Barthes, R. (1973). S/Z. Paris: Editions du Seuil.
Colebrook, C. (2016). ‘A grandiose time of coexistence’: Stratigraphy of the anthropocene. Deleuze Studies, 10(4), 440–454.
Coles, A., Barwell, R., Cotton, T., Winter, J., & Brown, L. (2013). Teaching secondary mathematics as if the planet matters. London: Routledge.
de Freitas, E., & Sinclair, N. (2014). Mathematics and the body: Material entanglements in the classroom. New York: Cambridge University Press.
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).
Deleuze, G. (1995). Difference and repetition. New York: Columbia University Press.
Deleuze, G. (2006). The fold: Leibniz and the baroque. London: Continuum.
Deleuze, G., & Guattari, F. (1994). What is philosophy? New York: Columbia University Press.
Foucault, M. (1972). The archaeology of knowledge (1st edn.). New York: Irvington Publications.
Foucault, M. (1995). Discipline and punish: The birth of the prison. REP edition. New York: Vintage.
Jornet, A., & Roth, W.-M. (2018). Imagining design: Transitive and intransitive dimensions. Design Studies, 56, 28–53.
Lakoff, G., & Núñez, R. (2000). Where mathematics come from: How the embodied mind brings mathematics into being. New York, NY: Basic books.
Latour, B. (2012). Enquête sur les modes d’existence: Une anthropologie des modernes. Paris: La Découverte.
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.
Mikulan, P. (2017). Pedagogy without bodies. Unpublished doctoral dissertation. Burnaby, BC: Simon Fraser University.
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.
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/.
Netz, R., Noel, W., Wilson, N., & Tchernetska, N. (2011). The Archimedes palimpsest (Vols. 1–2). Cambridge: Cambridge University Press.
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.
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.
Queneau, R. (1947). Exercises de style. Paris: Gallimard.
Robinson, A. (1966). Non-standard analysis. Amsterdam: North-Holland Publishing.
Rovelli, C. (2018). The order of time. London: Penguin.
Ruffell, M., Mason, J., & Allen, B. (1998). Studying attitude to mathematics. Educational Studies in Mathematics, 35(1), 1–18.
Shaviro, S. (2009). Without criteria: Kant, Whitehead, Deleuze and Aesthetics. Cambridge: The MIT Press.
Sinclair, N., & de Freitas, E. (2014). The haptic nature of gesture: Rethinking gesture with new multitouch digital technologies. Gesture, 14(3), 351–374.
Smythe, S., Hill, C., MacDonald, M., Dagenais, D., Sinclair, N., & Toohey, K. (2017). Disrupting boundaries in education and research. New York: Cambridge University Press.
Souriau, É (1939). L’instauration philosophique. Paris: Alcan.
Souriau, É (1943/2015). The different modes of existence (E. Beranek & T. Howles, Trans.). Minneapolis: Minnesota University Press.
Vinsonhaler, R. (2016). Teaching calculus with infinitesimals. Journal of Humanistic Mathematics, 6(1), 249–276.
Whitehead, A. (1929/1978). Process and Reality. New York: The Free Press.
Žižek, S. (2012). Organs without bodies: On Deleuze and Consequences. London: Routledge.
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.
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Mikulan, P., Sinclair, N. Stratigraphy as a method for studying the different modes of existence arising in the mathematical classroom. ZDM Mathematics Education 51, 239–249 (2019). https://doi.org/10.1007/s11858-018-01018-4
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DOI: https://doi.org/10.1007/s11858-018-01018-4