Online Learning in Educational Research
Vol. 6 No. 1 (2026): Online Learning in Educational Research

Bridging Verbal Geometry Problems and Formal Proofs: A GeoGebra-Supported Element–Relation Detection Framework

I Putu Wisna Ariawan (Universitas Pendidikan Ganesha, Indonesia)
I Made Ardana (Universitas Pendidikan Ganesha, Indonesia)
I Made Sugiarta (Universitas Pendidikan Ganesha, Indonesia)
Sariyasa Sariyasa (Universitas Pendidikan Ganesha, Indonesia)
Raphita Yanisari Silalahi (Universitas Pendidikan Ganesha, Indonesia)
Agus Adiarta (Universitas Pendidikan Ganesha, Indonesia)
Dewa Gede Hendra Divayana (Universitas Pendidikan Ganesha, Indonesia)



Article Info

Publish Date
30 Mar 2026

Abstract

Geometry proof problems presented without diagrams require students to transform verbal information into accurate visual representations before constructing formal deductive arguments. However, instructional approaches that explicitly support this transition remain limited. This study investigated the effectiveness of a GeoGebra-supported Element–Relation Detection (ERD) framework in strengthening undergraduate students’ plane geometry proof performance. A quasi-experimental design was conducted with first-year mathematics education students assigned to four instructional conditions combining the ERD framework, conventional Polya-based instruction, and the presence or absence of GeoGebra support. Students’ proof performance was evaluated through validated tasks measuring diagram construction, conjecture generation, proof organization, and argument validity. The findings indicate that learning environments supported by GeoGebra consistently produced stronger proof performance than conventional instruction without dynamic visualization. The ERD framework further assisted students in identifying essential geometric elements and relationships before constructing formal proofs, resulting in more coherent reasoning and fewer errors during the proof process. These findings suggest that the primary contribution of GeoGebra lies in facilitating accurate mathematical representations, while the ERD framework provides a structured pedagogical approach for bridging verbal geometric information and formal deductive reasoning. This study offers a practical instructional framework for improving geometry proof learning in technology-enhanced mathematics education.

Copyrights © 2026






Journal Info

Abbrev

oler

Publisher

Subject

Education

Description

Online Learning in Educational Research (OLER Journal) is a medium of communication for researchers, academicians, and practitioners that provides a means for sustained discussion of relevant issues that fall within the focus and scopes of the journal which examined empirically. Journal Online ...