Mathematics as the science of material assemblage: Enactivist, quantum theoretical, and educational perspectives

This dissertation explores implications of reconsidering the nature of mathematics from a conjoined enactivist/quantum theoretical perspective. The research is motivated by the view that reinterpreting the nature of mathematics through more inclusive materialisms has the potential to reinforce the fundamental relationship between mathematics and the material world, and to deepen our collective understanding of the ways in which our models of mathematics ultimately take on the meanings that they do. Four core themes underpin the overall research trajectory (i.e., new materialisms and issues of dualism, epistemological uncertainty, matters of agency, and complexity associated with emergent systems); however, only the initial two will be directly addressed within this particular document. Both yield insights into how specific facets of quantum theory and enactivism might supplement the more traditional discourse surrounding the nature of mathematics, and, in so doing, set conceptual groundwork for a broader mathematical (or rather material–mathematical) worldview. In light of these diverse themes, the program of research is necessarily interdisciplinary in scope, synthesizing literature from the interconnected domains of physics, mathematics, educational psychology, and philosophy more generally. Considering this literature alongside works from the established discourse of mathematics education, and reading it through a conjoined enactivist/quantum theoretical perspective, the dissertation elaborates points of disciplinary confluence, whilst expressing how such confluence might inform or reshape the sense of what mathematics is. By drawing upon the assemblage theory of Gilles Deleuze and Félix Guattari, Elizabeth de Freitas and Nathalie Sinclair's characterization of the body in/of mathematics, and the concept of quantum entanglement, the research also articulates a perspective regarding the mathematical structure of reality, and levies a view in which mathematics itself may be perceived as the science of material assemblage. A driving tenet of the research is the notion that a changed view of the material also changes one's view of the mathematical.