Abstract
Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue that the concept of event—rather than object—better captures the vitality of mathematics, and offers new ways of thinking about mathematics education. In this paper I draw on two different but related theories of event articulated in the philosophies of Alain Badiou and Gilles Deleuze to argue that the central activity of ‘problem solving’ in mathematics education should be recast in terms of a problematic of events.
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Notes
He offers a counter-reading of Plato that reclaims the idea and the realm of ideas as a site of eternity and multiplicity (Badiou 2011).
Fomin, D., Genkin, S., Itenberg, I. Mathematical circles: Russian experience.
In Logic of worlds (2009), Badiou briefly discusses Deleuze’s theory of the event, as articulated in the book The logic of sense (Deleuze 1990), summarizing what he considers to be Deleuze’s “axioms” of a theory of the event, and then contrasts these with his own axioms. Many scholars (Bowden 2011; Smith 2005; Williams 2009) have identified the ways in which Badiou entirely misrepresents Deleuze’s concept of the event.
The solutions are immanent to mathematics, but the problems transcend mathematics. Both Deleuze and Badiou use this approach to go backwards, through the solutions found in mathematics, to the problems of interest to philosophy.
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de Freitas, E. The Mathematical Event: Mapping the Axiomatic and the Problematic in School Mathematics. Stud Philos Educ 32, 581–599 (2013). https://doi.org/10.1007/s11217-012-9340-5
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DOI: https://doi.org/10.1007/s11217-012-9340-5