Tracing the use of pedagogical content knowledge in Grade 6 mathematics classrooms in KwaZulu-Natal.
The aim of this study was to explore the concept of pedagogical content knowledge, or PCK, and its use in the practice of teaching. Teacher knowledge is a significant factor in determining learner gains in all school subjects. However, little is known about the role of the different types of knowledge that teachers are supposed to possess in particular in a developing world context. PCK was introduced by Lee Shulman in 1986 and has since been the subject of much research in teacher education. Pedagogical content knowledge is thought to be a highly specialised form of teacher knowledge that intertwines subject matter (content) knowledge and general pedagogic knowledge. In this study, I examined the levels of PCK of 39 mathematics teachers; I tried to determine how they used PCK in their teaching of mathematics; what determined their PCK; and to what extent PCK influenced the mathematical achievement of their learners. The methodology that I used was lesson observation of 42 video-recorded grade 6 mathematics lessons from various schools in the greater Umgungundlovu district of Pietermaritzburg in KwaZulu-Natal. These schools were selected through random stratified sampling to participate in a larger regional achievement study, designed to investigate the factors which influence learning in schools. I was part of a research team that analysed the videos of the mathematics lessons, with the intention of getting the ‘big picture’ of mathematics teaching and learning in South Africa. Using the data from my observations, I developed a PCK instrument and attempted to measure the teachers’ PCK. I then tried to link these PCK scores to other variables in my study, which included a teacher’s test and learner tests. I tested the consistency of my instrument and the teachers’ PCK scores appeared fairly consistent across lessons, but that more research is needed to interrogate that. My initial findings suggested that all teachers possess PCK in some form, though their observed PCK levels were limited. The opportunity to develop proficiency, the use of examples and some engagement with learners’ prior knowledge though mostly in the form of checking homework were the areas most prevalent. The focus was mostly on procedural aspects. Only a minority of the teachers used representations, showed more than one method, displayed longitudinal coherence or engaged in more substantial ways with learner thinking (misconceptions and errors). Crucially, it emerged that a sound teachers’ knowledge of mathematical content was necessary for a high PCK rating, but there was no significant relationship between teachers’ PCK and learner gains in mathematics. It is likely that there are other factors which have a greater impact on learners’ learning than effective teachers, factors such as the socio-economic backgrounds of the learners. Given the random sampling of the schools in the study, and various attempts to ensure consistency in my coding and analysis, I hoped that these results would be valid for the greater KwaZulu-Natal area. However, because I used mainly the video analysis of lessons, and only a part of the teachers’ test, to determine the teachers’ PCK, it is possible that I may not have been able to get the full picture of the teachers’ PCK as I would have if I had also interviewed them.