Exploring learning difficulties experienced by Grade 9 mathematics learners in understanding 3D shapes in Geometry

Abstract

This study aimed to explore learning difficulties experienced by Grade 9 Mathematics learners in understanding 3D shapes in Geometry. To achieve that aim, the study focused on achieving three objectives, namely to: identify learning difficulties experienced by the Grade 9 learners in learning 3D shapes; determine learning processes that enhance the students‟ cognitive understanding of 3D shapes in Grade 9 Mathematics; and suggest how the 3D shapes learning difficulties in Grade 9 can be minimised. Furthermore, this study was underpinned by van Hieles‟ (1984) Levels of Geometrical Thinking. The study adopted a longitudinal mixed-methods research design in which sixty grade 9 learners Lydenburg Circuit, Mpumalanga Province, in South Africa and five grade 9 Mathematics teachers from two schools in the Lydenburg Circuit, Mpumalanga Province, in South Africa participated. Qualitative data were collected through semi-structured interviews with the five grade 9 Mathematics teachers. Quantitative data consisted of learners‟ scores in the two tests which were administered before and after the intervention activities. The tests were structured according to van Hieles‟ (1984) Levels of Geometrical Thinking. The first was administered before the intervention activities while the other was administered after the intervention activities. The study revealed several difficulties that learners face in learning 3D shapes and can be classified as those that relate to the teacher, the learner and the learner‟s environment. In the findings, difficulties relating to the learner include leaners‟ poor foundations in arithmetic and learners‟ inherent challenges with 3D questions that required the abstraction of 3D shapes. Secondly, the teacher‟s lack of knowledge and inexperience in teaching 3D shapes and unclear instructions were some of the reasons for the difficulties that learners faced in learning 3D shapes. Furthermore, inadequate learner support outside the school and large class sizes which made it difficult to individualise learner support to specific learners‟ needs were some of the environmental factors which were revealed in this study. The study also found that learners failed to understand questions posed in a language other than the learner's home language. Language difficulties were also reflected in learners‟ inability to understand instructions that were given in learners‟ first additional language, English. The structure of questions was also identified as another difficulty, especially where questions are structured in such a way that follow-up questions lead to learners being penalised more than once for the error in earlier questions. Learners‟ lack of understanding in other Mathematics areas such as change of subject of the formula, algebra and simple arithmetic also led to learners failing questions on 3D shapes in which those skills and knowledge were required. Finally, abstraction was another difficulty common in many learners. Learners failed to work out 3D shapes questions where shapes were not given and learners were required to use their knowledge of the 3D shapes in question to work out answers to activities. The implications of this study include the need for teachers to comprehensively plan lessons on 3D shapes, taking into account learners‟ diversity and the general learning environment. For policy-makers, there is a need to facilitate a tripartite learner support system, which empowers the learner to take charge of his/her learning and development, encourage parents/guardians to provide conducive out-of-school learning environments and help schools to provide the necessary stimulus to learners‟ urge for development. These implications should be viewed in light of some of the limitations of this study, including the small sample size and potential for cultural biases in the study due to limitations relating to time and resources.