The Korea Society Of Educational Studies In Mathematics
[ Original Article ]
Journal of Educational Research in Mathematics - Vol. 31, No. 2, pp.131-152
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 31 May 2021
Received 25 Mar 2021 Revised 30 Apr 2021 Accepted 30 Apr 2021

A Case Study on Learning Proofs of the Pythagorean Theorem through Diagramming: Based on the Châteletean Perspective

Jeong-Won Noh1 ; Kyeong-Hwa Lee2, ; Sung-Jae Moon3
1Graduate Student, Seoul National University, South Korea
2Professor, Seoul National University, South Korea
3Lecturer, Gyeongin National University of Education, South Korea

Correspondence to: Kyeong-Hwa Lee, Email:

Copyright © The Korea Society of Educational Studies in Mathematics
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study aims to reveal how diagramming in the everyday mathematics classroom supports students’ mathematical learning, based on the Châteletean perspective. To this end, we analyzed the diagramming of two 9th grade students who participated in the task of proving the Pythagorean theorem through diagrams in a geometry lesson. In particular, we focused on the epistemic distance as well as the material directness between the students and the diagrams. As a result, the students discovered mathematical ideas while they engaged in direct or indirect diagramming; they actualized virtual mathematical objects and relationships that were not visible in the given diagrams. During diagramming, the epistemic distance between the students and the diagrams was also dynamically changing. The findings suggest that diagramming in mathematics classrooms is not just a static representational activity, but an indeterminate and mobile engagement, which materially interacts with diagrams at varying degrees of epistemic distance.


diagram, diagramming, Châteletean perspective, inclusive materialism, materiality, indeterminacy, epistemic distance


No potential conflict of interest relevant to this article wasr eported.


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