Exploring pre-service teachers' knowledge of proof in geometry.

Abstract

Over the past years geometry has posed a challenge to most learners in South African schools. The Government, in particular the Department of Basic Education (DBE), have tried and are still trying to implement new innovations and strategies for teaching mathematics more effectively. South Africa has experienced many changes in mathematics curriculum with an aim of placing the country on an equal footing with countries globally. This study was conducted while there was the implementation of the new Curriculum and Assessment Policy Statement (CAPS), which reinstated the geometry section within the curriculum. Geometry was relegated to an optional paper in mathematics in 2006, 2007 and 2008 in Grades 10, 11 and 12 respectively. This study is framed within the theoretical framework lens of social constructivism and situated learning, and is located within the qualitative research paradigm. It takes the form of survey research in one of the universities in KwaZulu-Natal, South Africa. This university is referred to as the University of Hope (UOH) in this study to protect its identity. The main aim of this study was to explore the pre-service teachers' (PSTs) knowledge of proof in geometry. The study used qualitative analysis of data generated through a survey questionnaire, task-based worksheets and semi-structured interviews for both the focus group and individual interviews. In total 180 PSTs completed task-based worksheets. Within this group of 180 students, 47 were 4th year students, 93 were 3rd year and 40 were 2nd year students. After the analysis of a task-based worksheet, a total of 20 participants from the 3rd and 4th year were invited to participate in focus group interviews. The findings of the study exhibit that the PSTs have very little knowledge of proof in geometry. The study revealed that this lack of the knowledge stems from the knowledge proof in geometry the PSTs are exposed to at school level.