Students’ conceptualization of Pythagorean theorem (in RME): Examination with APOS
Nehir Keyik 1 * , Seyma Sengil Akar 2 , Elif Saygı 1
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1 Department of Mathematics and Science Education, Faculty of Education, Hacettepe University, Ankara, TÜRKİYE2 Department of Elementary Education, Faculty of Education, Kastamonu University, Kastamonu, TÜRKİYE* Corresponding Author

Abstract

This study investigates how eighth-grade students conceptualize the Pythagorean theorem through an instructional design grounded in realistic mathematics education (RME), analyzed using the APOS (action, process, object, schema) theoretical framework. Employing a design-based research methodology, a classroom activity was developed in which students used square tiles and right triangles to explore and ultimately discover the relationship now known as the Pythagorean theorem. The study was conducted with an entire eighth-grade classroom, and data-including group work observations and student interviews- were analyzed to trace students’ transitions across APOS stages. Three focal student cases were examined in depth to illustrate diverse developmental trajectories. The results indicate that while all students began with physical manipulation and informal reasoning, two students progressed to object-level understanding. The findings provide insights into how RME-based tasks can foster conceptual development and highlight areas for refining instructional design to better scaffold students’ transitions across cognitive stages.

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

PEDAGOGICAL RES, Volume 11, Issue 1, January 2026, Article No: em0255

https://doi.org/10.29333/pr/18093

Publication date: 13 Mar 2026

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Article Downloads: 9

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