Grounded and embodied mathematical cognition: Promoting mathematical insight and proof using action and language

Nathan, Mitchell J.; Walkington, Candace

2017

Abstract

We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants' actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This occurs through a process of transduction that promotes valuable mathematical insights by eliciting dynamic depictive gestures that enact spatio-temporal properties of mathematical entities. Our focus here is on pre-college geometry proof production. GEMC suggests that action alone can foster insight but is insufficient for valid proof production if action is not coordinated with language systems for propositionalizing general properties of objects and space. GEMC guides the design of a video game-based learning environment intended to promote students' mathematical insights and informal proofs by eliciting dynamic gestures through in-game directed actions. GEMC generates several hypotheses that contribute to theories of embodied cognition and to the design of science, technology, engineering, and mathematics (STEM) education interventions. Pilot study results with a prototype video game tentatively support theory-based predictions regarding the role of dynamic gestures for fostering insight and proof-with-insight, and for the role of action coupled with language to promote proof-with-insight. But the pilot yields mixed results for deriving in-game interventions intended to elicit dynamic gesture production. Although our central purpose is an explication of GEMC theory and the role of action-cognition transduction, the theory-based video game design reveals the potential of GEMC to improve STEM education, and highlights the complex challenges of connecting embodiment research to education practices and learning environment design.

Keywords

mathematical insightproof productiongesture and languagevideo game-based learningSTEM educationembodied cognition

Concepts

Embodied cognitionCognitionAction (physics)GestureComputer scienceMathematical proofHuman–computer interactionCognitive sciencePsychologyArtificial intelligenceMathematicsNeuroscienceQuantum mechanicsPhysicsGeometry

Citation

Nathan, M, Walkington, C (2017). Grounded and Embodied Mathematical Cognition: Promoting Mathematical Insight and Proof Using Action and Language. Cognitive Research: Principles and Implications https://doi.org/10.1186/s41235-016-0040-5

Metadata

Source: Cognitive Research Principles and Implications
Domain: Social Sciences
Field: Social Sciences
Subfield: Education
Topic: Mathematics Education and Teaching Techniques
Open access: Open Access
Citation count: 118
Work ID: W2583159728