Students' Mathematical Thinking in Movement

Mathematics education research is increasingly focused on how students' movement interacts with their cognition. Although usually characterized as embodiment research, movement research often theorizes the body in diverse ways. Ingold (Making: Anthropology, archaeology, art and architecture, 2013) proposes that thinking and knowing emerge from the entwined, dynamic flows of human and non-human materials in a process called making and, following Sheets-Johnstone (The primacy of movement (Vol. 82), 2011), contends that humans think in movement. The study that this paper draws on employs Ingold's making to study students' movement during mathematical problem solving. In this paper I also recruit Laban's movement elements (Laban & Ullmann, 1966/2011) as a framework to describe and analyse how the body moves in space and time and to incorporate the often-forgotten dynamic qualities of movement. This paper investigates the movement of a small group of tertiary students as they engage with a mathematical prompt (a task in Abstract Algebra), using thick description, to answer the questions: (1) How do students think mathematically in movement? (2) How do Laban's elements help inform research into students' movement? Through the lens of Laban's movement elements, my analysis demonstrates that students think mathematically in movement. These findings suggest that mathematics educators may be overlooking valuable instances of students' mathematical thinking and knowing: the thinking and knowing in movement which may not be available through verbalizations or artefacts. Although thinking in movement does not fit a traditional conceptualization of undergraduate mathematics, which privileges written communication heavily reliant on notation, to understand students' mathematical cognition more comprehensively, mathematics educators need to reconsider and appreciate students' mathematical thinking in movement.