Errors and misconceptions in Euclidean geometry problem solving questions: The case of grade 12 learners

Abstract

Euclidean geometry provides an opportunity for learners to learn argumentation and develop inductive and deductive reasoning. Despite the significance of Euclidean geometry for developing these skills, learner performance in mathematics, particularly geometry, remains a concern in many countries. Thus, the current study examined the nature of learners’ errors in Euclidean geometry problem-solving, particularly regarding the theorem for angle at the centre and its applications. Van Heile’s theory of geometric thinking and teacher knowledge of error analysis were used as conceptual frameworks to make sense of the nature of learners’ errors and misconceptions. Using a participatory action research approach, the study was operationalised by five mathematics teachers from four secondary schools in Motheo district in the Free State Province of South Africa and three academics from two local universities. The study analysed 50 sampled midyear examination scripts of Grade 12 learners from four schools. The findings of this study revealed that most learner errors resulted from concepts on Van Heile’s operating Levels 0 and 1, while the questions mainly required Level 3 thinking. The study recommends that teachers determine their learners’ level of geometric thinking and integrate this knowledge in their lesson preparations and material development.