“The Play’s the Thing”: Mathematization as Dramatization

Abstract

Mobilizing prevalent themes in the fields of mathematics education, literary criticism, and philosophy, this paper contextualizes ‘the mathematical’, ‘mathematical thinking’, and ‘mathematical pedagogy’ with respect to ancient Greek concept of mathesis, modern notions of mathematical agency, the Keatsian concept of negative capability, and the analogy of ‘staging’ a dramatic/mathematical ‘play’. Its central claim is that mathematization is dramatization—that learning mathematics (indeed, learning to learn, which is what the Greek mathesis actually means) is an activity of setting things up and (in this ‘set’ or ‘setting’) allowing things to play out (e-ducere). Beginning with Paul Ernest’s identification of the difference between absolutism and fallibilism in the philosophy of math education, and incorporating concepts from Pythagoras, Hippasus, Heraclitus (the ‘ancients’), Descartes, Kant, Keats (the ‘moderns’), as well as Freud, Heidegger, and Badiou (‘nos prochains’, to quote Klossowski ), we argue that ‘mathematical knowledge’ cannot be understood simply within the framework of logicism, formalism, or even simply as an epistemological articulation. Rather, we endeavour to show that the process of ‘learning mathematically’ allows us to gain insight into the foundations of ‘being’ itself (i.e. ontology). Learning to learn (mathesis) proceeds, as such, by way of staging and playing-out the half-known or unknown (the ill-seen and ill-said) in the hopes of uncovering the mystery (Greek myesis) at the heart of things.

Keywords:

• Negative capability,
• Ontology,
• Epistemology,
• Emergent intelligence,
• Mathematical agency,
• Mathesis universalis,
• Poetics,
• Theatre,
• Dramaturgy,
• Pedagogy