The Role of Motion-Based Metaphors in Enhancing Mathematical Thought: a Perspective from Embodiment Theories of Cognition

Motion-based metaphors help explain a single, often a static, concept (e.g., number, mathematical function, limit of function, continuity of function) in terms of a human motion. In mathematics, many mathematical concepts, such as function and continuity, are described in terms of graphical representations. Although these graphical representations are static, they can be transformed into motion events and understood as motions by motion-based metaphors. This can be done by either using a hand gesture to depict the graphical representation of the target concept or by mentally simulating hand movements that depict the graphical representation. By employing these mechanisms, the motor system becomes engaged in the process of aiding the learner to understand static mathematical concepts (concepts that are defined in terms of non-moving mathematical objects), acting as a cognitive resource to ground and understand non-motion mathematical concepts. In this paper, we theorize that visual representations of mathematical concepts have varying degrees of what we term to be “motor strength” whereby, for example, curves of functions may be either strongly or weakly motoric depending on the degree to which they aid in the development of associated deep mathematical thinking.