Analyzing Errors and Misconceptions of 11th Grade Learners in Solving Tangent-Chord Theorem Problems: A Case in Tshwane North District Secondary School

Abstract

This qualitative case study, grounded within the interpretive paradigm, analyzed the errors and misconceptions made by 11th-grade learners when tackling the tangent-chord theorem task in Euclidean geometry. Studying Euclidean geometry helps learners develop critical thinking skills, such as constructing arguments and applying logical reasoning. Analyzing facts and diagrams when addressing Euclidean geometry issues helps learners identify appropriate theorems. It focused on exploring, describing, and explaining errors and misconceptions based on Van Hiele's theory, which was used to understand the geometric reasoning levels of the learners. The study was conducted in a township public secondary school in the Tshwane North District of Gauteng, South Africa, involving 30 Grade 11 mathematics learners as participants. The finding reveals that most learners operated at or below Van Hiele levels 1 and 2, relying primarily on visual cues and memorized procedures rather than conceptual understanding. Errors and misconceptions arose due to the learners' incorrect angle labeling, flawed assumptions, poor diagram interpretation, and misuse of geometric terminology. Notably, 16,7% of learners showed no understanding of the concept. While 36,7% of learners made repeated statement errors, highlighting systematic challenges in visualization and reasoning. These misconceptions were found to be linked to instructional gaps, overgeneralization of geometric rules, and limited language precision. In response, the study suggests that teachers integrate dynamic visualization tools such as GeoGebra, embed open-ended conceptual tasks, promote collaborative peer learning, and contextualize geometry through real-world applications. These strategies aim to deepen learners' conceptual understanding, strengthen spatial reasoning, and support progression through the Van Hiele levels of geometric thinking.