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Developing GeoGebra 3D-assisted interactive e-worksheet for composite solids visualization

Aug 2026 · Bulletin of Applied Mathematics and Mathematics Education · 0 citations · 17 references

TL;DR

This study aims to develop, validate, and evaluate the practicality of an interactive electronic student worksheet using Lumi education integrated with GeoGebra 3D dynamic applets, and indicates that the e-worksheet achieved "strongly valid" and "practical" criteria.

Abstract

Spatial ability is crucial in geometry learning; however, students frequently experience misconceptions when visualizing intersecting 3D composite solids, a challenge conventional static materials fail to address. Therefore, this study aims to develop, validate, and evaluate the practicality of an interactive electronic student worksheetusing Lumi education integrated with GeoGebra 3D dynamic applets. Applying the ADDIE development model, the e-worksheet features independent 3D object manipulation, composite solid decomposition simulations, scaffolding trigger questions, an "anti-forget formula" reference panel, and adaptive interactive evaluations. Product validity was assessed by material and media experts, while practicality was evaluated through small-group and field tests involving 10th-grade students at SMA Negeri 1 Bambanglipuro, a public high school in Yogyakarta, using Likert-scale questionnaires analyzed via descriptive statistics. Results indicate that the e-worksheet achieved "strongly valid" and "practical" criteria. The interactive 3D manipulations effectively reduced cognitive load and resolved surface area misconceptions. This product significantly enriches innovative interactive learning references for geometry visualization. Based on these evaluations, future research is recommended to incorporate gamification elements, optimize practice question portions, and conduct comprehensive effectiveness testing on students' spatial skills.

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