An integrated cognitive-affective spatial system for geometry

Background Mathematical reasoning involves perceptual, motoric, and affective processes alongside cognitive processes. While research on embodied geometric reasoning has examined the influences of gestures and spatial abilities, the role of affective processes remains under-researched. Aims This study investigated how an affective process, spatial anxiety, alongside spatial ability, functions as a component of an integrated cognitive-affective spatial system that predicts geometric reasoning and gesture production during geometry proof tasks. Sample Participants were 94 undergraduate students from a large Midwestern US university. Methods Participants completed spatial ability and anxiety measures, then provided verbal justifications for evaluating the truth of eight geometry conjectures. Video data was coded for quality of mathematical insight and proof, and for gesture production. Mixed-effects logistic regression models analyzed relationships between spatial systems and three outcomes: mathematical insight (correct gist), mathematically valid transformational proof (a form of deductive proof), and representational gesture occurrence (dynamic and nondynamic). Results Spatial ability positively predicted insight, proof, and dynamic gestures. Spatial anxiety significantly moderated the relationship between spatial ability and both insight and proof. At high spatial anxiety levels, the benefits of spatial ability for proof were substantially diminished. Participants with lower spatial ability and higher spatial anxiety were more likely to produce nondynamic representational gestures, suggesting cognitive offloading to embodied processes. Conclusions Spatial anxiety acts as a moderator between spatial ability and geometric reasoning, impacting mathematical insights, proof construction, and gesture production. Findings highlight the importance of considering affective processes alongside verbal and nonverbal cognitive processes in models of embodied mathematical cognition.