The Korea Society Of Educational Studies In Mathematics

Current Issue

Journal of Educational Research in Mathematics - Vol. 30

[ Special ]
Journal of Educational Research in Mathematics - Vol. 30, No. SP1, pp.199-211
Abbreviation: JERM
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 31 Aug 2020

Supporting Students’ Argumentation Structure Construction using Indeterminacy of Diagram
Kyeong-Hwa Lee* ; Jeong-Won Noh**, ; Sung-Jae Moon**
*Professor, Seoul National University, South Korea
**Graduate Student, Seoul National University, South Korea

Correspondence to : Email:,,

Please cite this article as: Lee, K., Noh, J., & Moon, S. Supporting students’ argumentation structure construction using indeterminacy of diagram.


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.

Keywords: Argumentation structure, Indeterminacy of diagram, Virtual network diagram, Semiotic mediation, Semiotic potential

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