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Hear What They Say And Watch What They Do: Predicting Valid Mathematical Proofs Using Speech And Gesture, Caro C. Williams-Pierce
Hear What They Say And Watch What They Do: Predicting Valid Mathematical Proofs Using Speech And Gesture, Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
In mathematics, practices of proof are notoriously difficult for learners to adopt. In prior work, we found that when providing verbal justifications, learners’ speech patterns predict whether their justifications are mathematically sound. However, current views on the embodied nature of cognition suggest that actions and speech may co-constitute reasoning processes. The current study investigated whether the gestures learners use while formulating proofs also predict proof validity. 120 undergraduates provided verbal justifications for two mathematical tasks. We analyzed speech patterns in participants’ justifications using text analysis software, and we coded participants’ gestures as dynamic or static. Results showed that dynamic gestures …
Being Mathematical Relations: Dynamic Gestures Support Mathematical Reasoning, Caro C. Williams-Pierce
Being Mathematical Relations: Dynamic Gestures Support Mathematical Reasoning, Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
In mathematics classrooms, body-based actions, including gestures, offer an important way for students to become mathematical ideas as they engage in mathematical practices. In particular, a type of gesture that we call a dynamic depictive gesture allows learners to model and represent fluid transformations of mathematical objects with their bodies. In this paper, we report on two empirical studies – one in which dynamic gestures were observed, and one where these gestures were directed. We conclude that dynamic gestures are a key element in successful justification and proof activities in mathematics.