AN EXPLORATION OF HIGH SCHOOL LEARNERS’ UNDERSTANDING OF GEOMETRIC CONCEPTS

Abstract

There is much concern in South Africa about the poor performance of learners in mathematics, particularly in geometry. The aim of this research was to explore the understanding of basic geometry concepts by grade 10 and grade 11 learners in terms of the van Hiele’s levels of geometry thinking. The participants of the research were 147 learners from three high schools in a rural area in the south of KwaZulu Natal, South Africa. The results showed that the learners had difficulties with problems involving definitions of geometric terms, interrelations of properties and shapes, class inclusion and changing semiotic representations. It was also found that most of the learners were operating at the visual and the analysis levels of the van Hiele levels of geometric thinking. It is recommended that teachers should provide learners with tasks that require movements between semiotic representations, and to also focus attention on improving learners’ skills in proving aspects of mathematical relations. Keywords: geometry, high school, van Hiele theory, class inclusion, mathematical proof, necessary and sufficient conditions.