Mathematical Thinking in Movement

In this dissertation the role and importance of movement in mathematical thinking and learning in the context of a longitudinal study is investigated. The idea of mathematical thinking in movement as one that brings forth the attempt of capturing the manifold potentiality of thinking with main attention to the bond of movement and the virtual dimension of mathematical concepts is presented. The concepts of movement (Sheets-Johnstone) and virtuality (DeLanda, Deleuze and Châtelet) inform this vision, and a theoretical discussion of how they sustain each other beyond tangling with each other is offered. Therefore, mathematical thinking in movement captures a duality of grasp within the same expression: mathematical thinking in movement (that is, thinking in movement in the doing of mathematics) and mathematical thinking in movement (that is, the process of thinking mathematically as emerging from movement). The dissertation addresses the overarching aim of characterising mathematical thinking in movement in the context of graphing motion with WiiGraph, an interactive graphing motion application that leverages two controllers and allows for graphing motion by capturing the positions over time of two users when they hold the controllers and move in front of a sensor.