Research Information System
Pedagogical Research, vol.11, no.1, 2026 (Scopus)
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.