Reconceptualising The Geometry Gap: Theoretical Insights From Van Hiele And Constructivist Perspectives On Triangle Theorem Instruction In South Africa

Abstract

Geometry forms a fundamental component of secondary school mathematics because it supports the development of spatial reasoning, logical thinking, and deductive proof skills. However, persistent learner difficulties in understanding geometric concepts, particularly triangle theorems, remain a significant concern in many education systems. This conceptual paper examines the factors contributing to the geometry gap in South African schools, with a particular focus on the teaching and learning of triangles and their associated theorems. The paper adopts a conceptual research approach that synthesises recent literature and theoretical perspectives in mathematics education, including the van Hiele theory of geometric thinking, constructivist learning theory and socio-cultural perspectives on learning. Through an integrative analysis of recent scholarship, the paper identifies structural, pedagogical and cognitive factors that collectively influence learners’ geometry learning outcomes. The study further proposes a conceptual framework explaining how these dimensions interact to produce persistent gaps in learners’ geometric reasoning and problem-solving abilities. The interconnected nature of these challenges offers theoretically grounded insights that may inform curriculum development, teacher professional development and instructional innovation aimed at improving geometry education. The findings contribute to ongoing debates on mathematics education equity and provide a foundation for future empirical research on strategies for strengthening geometry instruction in South African schools.