From Agency to Narrative: Tools in Mathematical Learning

This dissertation explores ideas from new materialism as a theoretical lens for understanding the role of tools within mathematical practice. I propose that new materialism, particularly within a post-humanist perspective, offers the opportunity to articulate a non-dualist approach to mathematics—with a focus on the entanglement of tools, humans and concepts. Theoretically reshaping the traditional approach of seeing learning as occurring solely within the individual, the focus of mathematical learning in this dissertation is neither on the student nor on the tool, but on the coupled entity “student–tool”. The theoretical perspective developed in this dissertation draws mainly on scholars from outside the field of mathematics education, including the anthropologist Tim Ingold and the feminist science studies scholar Karen Barad. Both articulate forms of post-humanist materialism that attend to the interplay between tools and cognition. In addition to these scholars, I draw on the inclusive materialism of de Freitas and Sinclair, who in their recent book Mathematics and the Body extend Barad’s ideas to mathematics, and who argue that material engagement with a tool in a mathematical activity is mathematics. This dissertation is structured around three papers, in addition to two introductory chapters, two interludes and a concluding chapter. The introductory chapters begin by inquiring into the notion of agency (especially in the work of Pickering and Latour), and evolve into an examination of the work of Barad and Ingold. The first paper presents mathematical practice as a continued process, meaning that the ‘partners’ of student–tool and of mathematics are not static but processes of ‘becoming’. The second paper applies the idea of mathematics-as-becoming to the concept of the circle. Paper three uses a variety of post-humanist, materialist constructs to analyse data taken from a high school geometry classroom. In it, I employ a very recent methodological approach called diffractive analysis, novel to mathematics education.In the concluding chapter, I explore potential and productive overlaps between the different post-humanist, materialist theories and indicate how the new theoretical ideas that this dissertation engages with might pose and address certain questions in mathematics education research.