Analysis of CSCL for Mathematical Proof Based on the Log Data of Learners’ Verbal and Nonverbal Communications

Abstract

In this study, we investigate the process by which university students produced mathematical proofs in a CSCL environment. Students discussed how to prove the addition theorem for trigonometric function while manipulating mathematical content generated by a dynamic geometry system. The log data of their utterances and manipulations was stored and visualized. Besides the annotated text data of their communication and videotaped images of their activity, we analyzed the fine-grained log data. Analyzing how students produce proofs is difficult because we must recognize the critical moment of the proof by observing their activities while they are still engaged in the proof work. Furthermore, their insufficient background in mathematics prevents them from fully explaining their thinking processes. The result of this study indicates that the comparison of qualitative data of learners’ communication and those multimodal log data can help us unfold their convergent conceptual change.