Supporting Students' Argumentation Structure Construction using Indeterminacy of Diagram - Kyeong-Hwa Lee; Jeong-Won Noh; Sung-Jae Moon (Korea Society of Educational Studies in Mathematics, 2020)
In this study, we analyze students' argumentation structures constructed using semiotic mediation activities involving a task with indeterminate diagrams. The main purpose of this article is to reveal how semiotic mediation activities engaged indeterminacy of diagram to support students' argumentation structure construction. To this end, we use Toulmin's model to illustrate how students construct and elaborate their conjectures and arguments about geometrical properties in the process of actualizing virtual relationships between the given diagrams. The findings indicate that the various ways in which the students explored the argumentation structures latent in the task emerged from the indeterminacy of the given diagrams and their potential meanings and relationships. In particular, both constructive argumentation and structurant argumentation were promoted in the process of logically connecting the diagrams. We also observed that the students used kinematic and spatial metaphors to describe the possibilities in the logical connections between diagrams while constructing argumentation structures. As a conclusion, we claim that diagrammatic indeterminacy can be considered semiotic potential or its source.