Embodied truths: How dynamic gestures and speech contribute to mathematical proof practices.

• Dynamic gestures are associated with constructing valid mathematical proofs. • Repetitive speech is associated with constructing valid mathematical proofs. • Syntactic complexity is associated with constructing valid mathematical proofs. • Logical inference is associated with constructing valid mathematical proofs. • Dynamic gestures and logical inference uniquely predict valid proof construction. Grounded and embodied theories of cognition suggest that both language and the body play crucial roles in grounding higher-order thought. This paper investigates how particular forms of speech and gesture function together to support abstract thought in mathematical proof construction. We use computerized text analysis software to evaluate how speech patterns support valid proof construction for two different tasks, and we use gesture analysis to investigate how dynamic gestures —those gestures that depict and transform mathematical objects—further support proof practices above and beyond speech patterns. We also evaluate the degree to which speech and gesture convey distinct information about mathematical reasoning during proving. Dynamic gestures and speech indicating logical inference support valid proof construction, and both dynamic gestures and speech uniquely predict variance in valid proof construction. Thus, dynamic gestures and speech each make separate and important contributions to the formulation of mathematical arguments, and both modalities can convey elements of students' understanding to teachers and researchers. [ABSTRACT FROM AUTHOR]