Comparing technology-enhanced and conventional Van Hiele Phased Instruction in advancing learners through Van Hiele levels in transformation geometry

Abstract

Developing learners’ geometric reasoning remains a persistent challenge in secondary mathematics education, particularly in transformation geometry, where many learners struggle to progress through the hierarchical Van Hiele levels of geometric thinking. Although technology-enhanced instruction has been associated with improved mathematics learning, limited evidence exists on how integrating GeoGebra within the phases of Van Hiele instruction influences learners’ progression through these levels. This study compared Technology-Enhanced Van Hiele Phased Instruction (TVHPI) with Conventional Van Hiele Phased Instruction (CVHPI) in promoting learners’ progression through the Van Hiele levels in transformation geometry. Guided by Van Hiele theory and constructivist learning principles, a quasi-experimental design involving 483 Ugandan secondary school learners (TVHPI = 238; CVHPI = 245) was employed. Learners’ progression was assessed using the Van Hiele Geometry Achievement Test and analysed using Wilcoxon signed-rank tests, ordinal logistic regression, and Difference-in-Differences analysis. Both instructional approaches significantly improved learners’ geometric reasoning; however, learners receiving TVHPI demonstrated greater progression through the Van Hiele levels than those receiving CVHPI. The findings suggest that integrating GeoGebra within the phases of Van Hiele instruction is associated with higher levels of geometric reasoning and provides empirical support for technology-enhanced, competency-based geometry instruction that promotes deeper conceptual understanding.