An Assessment of the Alignment of Transformation Geometry with Van Hiele Levels in Uganda’s Lower Secondary Mathematics Curriculum

Abstract

This study investigates the alignment of transformation geometry learning outcomes with the Van Hiele levels of geometric reasoning within Uganda’s secondary mathematics curriculum. Using the Van Hiele model as a framework, the study evaluates whether the curriculum effectively supports students’ cognitive development in geometry. An analysis of the learning outcomes associated with transformation geometry specifically reflection, rotation, and enlargement reveals a partial alignment with the Van Hiele levels of visualization, analysis, abstraction, and deduction. The findings indicate that while outcomes related to visualization and basic analysis are well-aligned, there are significant gaps in outcomes requiring higher-order reasoning, particularly at the abstraction and deduction levels. Specifically, the curriculum underemphasizes tasks that involve formal deductive reasoning and the application of complex geometric transformations. These gaps suggest that the curriculum may not fully support students' progression to higher levels of geometric understanding. The study concludes with recommendations for curriculum enhancement to better align learning outcomes with the cognitive demands of the Van Hiele model, thereby fostering deeper mathematical reasoning among secondary students in Uganda.