Considerations of Embodiment in Geometry: Discovering New Ways of Moving, Perceiving, and Reasoning Across Micro, Meso, and Macro spaces

Embodied learning, rooted in the embodied cognition paradigm, posits that knowledge emerges from the interaction of perception, action, and cognition in a dynamic interplay with the environment (e.g., Pouw et al., 2014). This perspective challenges the dichotomy of mind and body, asserting that cognition is inherently sensorimotor and situated. The growing variety of approaches to embodied learning (Abrahamson et al., 2020; Radford et al., 2017; Sinclair & de Freitas, 2019) is gaining increasing significance in mathematics education. Embodied learning in geometry education, which emphasises physical manipulation, sensory experiences, and collaborative exploration to develop a conceptual understanding of spatial relationships and geometric properties, was identified as a major trend in the ICME-13 survey team report (Sinclair et al., 2016). In terms of Western scholarship, this perspective is philosophically grounded in Locke’s empiricism, particularly his discussion of the Molyneux problem (Figure 1, Locke, 1689/1998), which questions whether a person born blind, upon gaining sight, could visually recognise objects previously known through touch. Locke argued that cross-modal recognition must be learned through experience. Recent cognitive studies support this view, showing that neural plasticity and sensorimotor engagement are essential for integrating tactile and visual modalities (Held & Ostrovsky, 2011; Noë, 2004). The Molyneux problem, inherently geometric, underscores the importance of embodied interaction in transitioning from perceiving to reasoning about spatial forms—a process central to geometry education (Nathan et al., 2021).