Effects of Variation Theory-Assisted Guided Inquiry-Based Instruction on Students' Conceptual Understanding and Task Value in Solid Geometry

Abstract Background: Solid geometry is a challenging topic for Ethiopian secondary students, often taught through traditional, teacher-centered methods that hinder conceptual understanding and motivation. Guided Inquiry-Based Instruction (GIBI) has shown promise, but its integration with Variation Theory (VGIBI) remains under-researched in this context. Methods: A quasi-experimental pre-test/post-test design was used with 102 tenth-grade students in Debre Tabor City, Amhara Region, Ethiopia. Participants were assigned to three groups: EG1 (VGIBI), EG2 (GIBI alone), and CG (traditional teaching methods). Data were collected using a conceptual understanding test and a task value questionnaire. MANOVA and ANCOVA were applied to analyze differences in task value dimensions and conceptual understanding, controlling for pre-test scores. Results: VGIBI significantly improved intrinsic value (p < .001) and attainment value (p = .001) compared to GIBI and traditional teaching methods, with no significant effect on utility value. Students in the VGIBI group also achieved significantly higher conceptual understanding post-test scores (p < .001), with the instructional method explaining 23.6% of the variance. Effect sizes were large for conceptual understanding improvement in the VGIBI group (d = 1.26). The findings suggest that VGIBI enhances both cognitive and motivational outcomes by making geometric concepts more discernible and engaging through structured variation. The lack of change in utility value indicates that perceived relevance may require longer-term or contextually explicit interventions. Conclusion: VGIBI is an effective pedagogical approach for improving students’ conceptual understanding and task value in solid geometry. It is recommended for adoption in Ethiopian mathematics classrooms and similar educational settings to support meaningful learning and motivation.