Bridging Verbal Geometry Problems and Formal Proofs: A GeoGebra-Supported Element–Relation Detection Framework
DOI:
https://doi.org/10.58524/oler.v6i1.1225Keywords:
dynamic geometry software, Element detection, GeoGebra, Image visualization, Relation detectionAbstract
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.
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