An exploration of FET mathematics learners' understanding of geometry.
This research study explored the FET learners’ understanding of geometry. The aim of this research study was to explore how grade 10 and grade 11 learners perform on tasks based on basic geometric concepts. The research also aims to make deductions about the van Hieles’ levels of geometry thinking of the learners. The research study will also provide recommendations on how some of the arising issues could be addressed. The study is framed within the theoretical framework of social constructivism and is located within the qualitative research paradigm. This study was carried out in three high schools in rural KwaZulu-Natal, South Africa. The study used qualitative data analysis methods to analyse data generated through task based worksheets and semi-structured interviews for individuals. A total of 147 learners completed the task based worksheet, of which 74 learners were doing grade 10 and 73 were doing grade 11. Eighteen learners were invited to participate in the interviews after the analysis of the task based worksheets. The research revealed a lack of understanding of many geometric concepts by the learners. Learners had difficulties with problems involving definitions of geometry terms, interrelationships of properties and shapes, class inclusion and proof type questions. Learners also showed lack of procedural and conceptual understanding. The study also revealed that the majority of the learners involved in the study were operating at the visual level and analysis level of the van Hiele levels of geometry thinking with a few learners able to reason at the informal deduction level. The research recommends that educators should explain and use relevant geometry vocabulary in their everyday teaching of geometry to try and address the issue of the language barrier, allow learners to work with a diversity of registers of semiotic representations of geometric concepts instead of sticking to the traditional geometric figures only, expose learners to shapes involving common properties (class inclusion) and allow them to come up with their own conclusions, use manipulatives, real life objects and cite real life examples when teaching geometry to make it more relevant to everyday life, use teaching methods that encourage conceptual understanding instead of rote learning and provide learning experiences that improve learners’ proof skills.