Dynamic Visualization and Conceptual Understanding of Circle Theorems Through Teacher-Mediated GeoGebra Use: An Action Research in a Grade 10 Classroom in Nepal

Abstract

Developing conceptual understanding in geometry remains challenging when circle theorems are learned primarily through memorization, static diagrams, and procedural exercises. Dynamic geometry environments may provide opportunities for students to explore geometric relationships, but how such exploration contributes to mathematical reasoning requires closer qualitative examination. This study explored how Grade 10 students developed conceptual understanding of circle theorems during GeoGebra-supported learning activities in a secondary mathematics classroom in Pokhara, Nepal. A qualitative action-research design was conducted over 15 instructional days with 32 students, with six focal participants selected for detailed analysis. The intervention comprised three cycles of planning, action, observation, and reflection. GeoGebra applets were projected using a single teacher-operated laptop, with limited shared student manipulation during selected group activities. Data were generated through classroom observations, student worksheets and reflective responses, semi-structured interviews, and a reflective journal, and were analyzed thematically. Three interconnected themes emerged: developing conceptual understanding through dynamic visualization; moving from dynamic observation to mathematical reasoning and justification; and peer interaction and teacher scaffolding in mathematical reasoning. Students increasingly recognized invariants, explored conjectures, and connected visual observations with mathematical explanations, although some initially relied on visual appearance or repeated measurements without sufficient justification. The findings position GeoGebra as a teacher-mediated resource rather than an independent cause of conceptual learning. Its educational value depended on purposeful task design, teacher questioning, peer interaction, and opportunities to connect dynamic exploration with mathematical reasoning, particularly in resource-constrained classrooms.