Research on the Roles of Gesture in the Process of Constructing Geometric Proofs

Abstract

　　The purpose of this study is to reveal the roles of gestures that promote the interpretation of diagrams and language. We perceived of association between gesturing and proof construction by examining the process of constructing geometric proof from the semiotic viewpoint of gesturing. We analyzed the interviews of the four pairs of ninth graders who solved and discussed the four problems of proof including the understanding of generality of proof. We suggest that gestures have three roles.

　　First, gestures promote the interpretation of a diagram and language during the process of constructing a proof.

　　Second, gestures allow for the understanding of the generality of proving. By showing meaning of language as action, they can relate the different parts of each diagram together, and can interpret relationships between the diagram and language. Also, by showing one form of deduction in one diagram on another diagram, students can interpret correct deduction.

　　Last, there is a possibility to promote an inter-intra double semiotic process of interpretation through simultaneous use of gestures and language for diagrams. Gesture can be an important vehicle to convey one’s own massages to others.