An exploration of learning difficulties experienced by grade 12 learners in euclidean geometry : a case of Ngaka Modiri Molema district

Abstract

The purpose of this study was to investigate the learning difficulties experienced by Grade 12 learners in Euclidean geometry. Despite the efforts exerted in terms of time, material and human resources in the teaching and learning of Euclidean geometry, learners’ performance in Euclidean geometry remains unsatisfactory. As a result, this study sought to answer the research question: What are the learning difficulties that the Grade 12 learners experience in the learning of Euclidean geometry? Van Hiele levels of geometric thinking were a used as a framework to explore Grade 12 learners’ learning difficulties. The study adopted a sequential exploratory mixed method design. The participants in the study were mathematics educators, learners, head of departments (HOD) from a sample of six schools in Ngaka Modiri Molema district, North West Province. As part of data collection procedure, Euclidean Geometry test developed in accordance with Van Hiele levels was administered to 60 Grade 12 learners who were randomly sampled from six schools which were purposively sampled. In addition, two HODs’, four educators and 12 learners completed questionnaires. Furthermore, semi-structured interviews were purposively conducted with 12 learners and four educators based on learners’ test results. Data analysis involved the identification of misconceptions and errors committed at each Van Hiele level and were interpreted as learners learning difficulties. The test analysis involved categorising learner performance in the test by frequency distributions of those who achieved and those who did not achieve 50% and above in the question(s) set at each Van Hiele level. In addition, questionnaires were analysed by determining the frequency distribution of respondents’ levels of agreement and disagreement to sets of predetermined questions at different Van Hiele levels. The findings of the study revealed that Grade 12 learners experience difficulties across Van Hiele levels of geometric thinking. These included amongst others learners’ difficulties in identifying and naming angles between parallel lines and a transversal (Visualisation level); using analytical skills and correct geometry terminology to describe components of a circle (Analysis level); completing proofs of circle theorems and problem solving involving short deductions and multistep geometric riders (Informal deductive level); presenting a series of deductive steps leading to the desired geometric solution (Formal deductive level). Based on these findings of the study, the recommendations were that educators should give learners the opportunity to discover geometry concepts through hands-on activities with geometric shapes to ground their understanding of geometry concepts. Furthermore, it was recommended that educators should use the Van Hiele model as a framework for teaching Euclidean geometry by introducing learners to geometry concepts in a hierarchical manner from first developing among learners’ visualisation skills up to formal deductive reasoning.