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

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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

  1. See Barad (2007) for more on how quantum mechanics and field theory set the stage for a new kind of social science, and de Freitas and Sinclair (2018) for a particular example of this in relation to mathematical reasoning.

  2. Latour (2012) revises these five modes and adds many more.

  3. Indeed, some have argued that teaching calculus with infinitesimals might be a more intuitive approach (Vinsonhaler, 2016).

  4. In this paper we want to avoid the grand schemes of linear and progressive historicity. Our project is aligned closer to Foucault’s accounts of historicity as archeology (1972) and genealogy (1995).

  5. 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.

  6. 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.

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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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Correspondence to Nathalie Sinclair.

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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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