From Errors to Insights: Exploring the Geometric Misconceptions of Secondary Students with Specific Learning Disabilities

Abstract

Despite its importance, research on geometry learning among students with specific learning disabilities remains limited. This study interviewed three students with specific learning disabilities to examine their errors in learning the Pythagorean theorem and to analyze their geometric thinking levels based on the van Hiele model. Errors were categorized as conceptual, procedural, representational, computational, and nonsystematic. Conceptual errors, involving misunderstandings of key terminology, and representational errors, reflecting difficulties in translating verbal descriptions into diagrams, were mainly linked to Level 1 (visualization). Procedural errors, particularly missing steps such as extracting square roots, were associated with Level 2 (analysis). Computational errors involved incorrect calculations, whereas nonsystematic errors included guessing solutions and misreading questions. Despite these challenges, students demonstrated flexible reasoning. The findings identify specific breakdowns in geometric thinking and suggest implications for targeted instructional support.