The Constitution (1996) of the Republic of South Africa forms the basis for social transformation in our new society. The Constitution (Act 108 of 1996) and the amendments that followed provided a basis for curriculum transformation and development in South Africa. The Department of Education introduced the present curriculum known as the National Curriculum Statement, which is modern and internationally benchmarked, in grade 10 in 2006. It required the learners to do seven subjects in grades 10 to 12 of which mathematics or mathematical literacy was prescribed as compulsory subjects. To attain social transformation, the South African Government attached a great deal of importance to the learning and teaching of mathematics and sciences in the South African schools. This study was undertaken in an effort to improve the understanding of geometry and, consequently, the performance and achievement of senior secondary school learners in geometry. The study was inspired by the van Hiele theory. The study made use of the different levels of the van Hiele theory for the development of an instructional framework for geometry in senior secondary schools. The research was conducted in a previously disadvantaged area in South Africa. Given the setting of this study and the wider application of it, the use of ‘hands-on’ and practical approach to use manipulatives and worksheets to improve the geometric understanding was tried and tested in this study. The assumption was that such experiences would make the learning of geometry more relevant and enjoyable for learners from limited financial and underprivileged circumstances. A quasi-experimental design was chosen. A total of 359 learners from five purposively selected schools in Mthatha district in the Eastern Cape Province participated in this study. Qualitative data through interviews were gathered. The data were analysed using IBM SPSS Version 19 and Microsoft Excel. Findings indicated that there was a notable improvement in the performance of learners who were taught by the application of the van Hiele theory. The results revealed that most of the learners were not ready for the application of deductive principles of geometry in terms of formal proof in senior secondary school geometry. Based on the results, some recommendations are made to enhance the teaching and learning of geometry in senior secondary schools.

The aim of this study was to investigate the relationship between teachers' instructional practices in terms of specific areas of focus pertaining to the teaching and learning of geometry described in literature and, their learners' levels of geometry thinking as elaborated in the Van Hiele theory. A review of literature on the development of geometry understanding was conducted to frame what is meant by 'teachers' instructional practices' as they pertain to the teaching and learning of geometry in this study. These instructional practices are understood to include the appropriate allocation of time for the facilitation of geometry concept development, the use of concrete apparatus, the use of relevant and level appropriate language as well as the use of level appropriate geometry activities. The structure of the curriculum in terms of its content and opportunity for conceptual progression was also considered. Literature reveals continuing discourse regarding the levels of thinking described in the Van Hiele theory, and even though there is no consensus regarding the nature of the levels and that assessing learners' levels of thinking remains difficult and inconclusive, it is generally accepted that the Van Hiele test is a reliable measure in assessing learners' levels of geometry thinking. An exploratory case study design was chosen for this study. The phenomenon being explored is the teaching and learning of geometry in the Foundation and Intermediate Phases of a particular private school. In order to do this, the teachers' timetables and Work Schedules were analysed to determine how much time was allocated to the instruction of Mathematics in general and for the instruction of geometry in particular. These documents also yielded data regarding the type of geometry experiences included in the implemented curriculum. The learners' level of geometry understanding according to the Van Hiele theory was assessed using an instrument designed by Usiskin (1982). This assessment was facilitated by the researcher in the learners' home class and happened in June after six months of instruction in a particular grade level. Data regarding the teachers' perception of geometry and the best method to facilitate the learning of geometry was gathered through a teacher's questionnaire. The teachers were requested to facilitate geometry lessons, which were digitally recorded by the researcher. Each grade level (0-5) was regarded as a sub-unit and analysed as the case for that grade level. The data was then assimilated to present the case of geometry teaching and learning in the Foundation and Intermediate Phases in the school. The findings report that when juxtaposed alongside research, geometry instructional practices in this school, compare favourably with regards to the teachers' professed and observed practice of using concrete aids and tasks that engage the learners actively in developing geometry insight. There is also evidence that these instructional practices support progression through the levels however the shortfall of time allocated to facilitating this progression and the lack of conclusive data regarding the language used and the types of experiences may justify further research into whether this progression is satisfactory. Copyright / Dissertation (MEd)--University of Pretoria, 2011. / Science, Mathematics and Technology Education / unrestricted