What We Say and How We Do: Action, Gesture, and Language in Proving.

Caroline Williams-Pierce, Elizabeth Pier, Candace Walkington, Rebecca Boncoddo, Virginia Clinton, Martha Alibali, and Mitchell Nathan


This study examines that students’ gestures and speeches without pencil and papers when proving in mathematics in undergraduate level. They argue that researchers can investigate students’ mathematical idea by exploring their gesture as a tool, and their gesture can be new way for the mathematical reasoning. According to their findings, gesture with verbal explanation can benefit for students’ mathematical reasoning and proving, especially for the gesture illustrating their difficult idea only by language. Additionally, guiding students to utilize their action prior to asking the proof may influence students’ consequent reasoning, so there is a crucial relationship between reasoning and body actions. 

Comment 

This paper invited me to think about another way to prove in mathematics, compare to the idea in several articles I read before which are about writing mathematical proofs. I agree with their idea that gesture can support students’ verbal explanations. I am wondering how the students in my Japanese school use actions when proving in mathematics. Also, are there any cultural differences between Canada and Japan (and other countries)? Actually, Moore’s work (1990, 1994) did not involve students’ gestures when they learn definitions or concepts in mathematics, and physical expression also could be one of informal explanations in mathematics.  

Additionally, my other question is how teachers can evaluate their physical actions. (Or should their action be accepted one of the student’s performances which teachers need to evaluate such as verbal expression or writing?) And, how teachers work with the students’ gesture and apply it to their teaching approach?