Abstract
Geometry is one of the areas which learners seem to struggle with in South African schools. In order to improve learners’ scores in the final grade of high school (grade 12), there is a need to improve their understanding of geometry. According to the South African Mathematics curriculum document, geometry is a compulsory component of mathematics for everyone studying mathematics in the further education and training (FET) phase. Consequently, this study investigated how university students (pre-service primary school teachers) engaged with a component of a geometry course, designed for the purpose of teaching in the intermediate phase (Grade 4-6) in South Africa. A good understanding of geometry concepts in primary school learners prepares them well for high school geometry. The study sought to answer the main question: How does student teachers’ knowledge of geometrical shapes develop according to the levels of understanding geometric shapes as described by van Hiele (1959) in Usiskin (1982), in their third year geometry course for teaching in the primary school?
In a mixed method research design, 44 third year student teachers were taught concepts in geometrical shapes over a series of lectures. To determine their (conceptual) change of quadrilaterals, from one level to the next of the van Hiele model, recordings of lectures and student teachers’ assignments, tests and examination scripts were analysed. The quantitative analysis which was conducted was intended only to reflect on the patterns of attainment evident from this particular class. Together with the qualitative data, the extent to which there were shifts evident in the students’ understanding within the van Hiele levels was explored.
The research findings showed that student teachers struggled to understand the concepts of the interrelationship between quadrilaterals because they lacked knowledge of a ‘lower level’, which is about the properties of quadrilaterals, and which they needed to build on. There was a general decline in student scores in the test as compared to the assignment indicating evidence of collaboration in assignments, which was not possible in a test. The students’ scores however improved from the test to the examination, which could be attributed to students’ thorough preparation of geometric concepts. The study identified the areas in which students struggled and concluded that this may be because their existing geometric knowledge was not at the appropriate van Hiele level for them to be (proximally) ready to be in a ‘zone’ which...
M.Ed. (Education)