Bulletin of Applied Mathematics and Mathematics Education
Vol. 6 No. 1 (2026)

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

Dianis Ahmad Faizal (Universitas Ahmad Dahlan)
Afit Istiandaru (Universitas Ahmad Dahlan)



Article Info

Publish Date
24 Aug 2026

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.

Copyrights © 2026






Journal Info

Abbrev

BAMME

Publisher

Subject

Mathematics

Description

BAMME welcomes high-quality manuscripts resulted from a research project in the scope of applied mathematics and mathematics education, which includes, but is not limited to the following topics: Analysis and applied analysis, algebra and applied algebra, logic, geometry, differential equations, ...