An exploration of General Education and Training (GET) teachers’ mathematical knowledge and its influence on the quality of instruction in the teaching of functions.

Abstract

This thesis documents a study of the General Education and Training teachers’ mathematical knowledge of functions and what this knowledge brings to the quality of instruction. The study made use of Variation Theory and Mathematical Knowledge for Teaching as theoretical frameworks. With regard to the methodology, data generation methods included, semi-structured interviews, pen and paper (written items), lesson observations, field notes and document analysis. The sample was chosen through purposive sampling. The participants were four mathematics teachers from four varying schooling contexts in KwaZulu-Natal. Data generation took place in 2016 and 2017 and a total of 28 lessons were observed. Data generated from pen and paper items corroborated the results of the interviews and the data generated from the classroom observations. This suggested that teacher knowledge does influence the quality of classroom instruction. The findings support the literature which shows that teachers’ subject matter knowledge hugely impacts on the quality of instruction. The study, however, concluded that a lack of subject matter knowledge does not stop teachers from delivering lessons of an acceptable level as required by the Curriculum and Assessment Policy Statement if they follow readily designed lesson plans and make use of prescribed curriculum materials including learner workbooks. It was concluded that when out of field teachers use these prescribed curriculum resources effectively, they are able to involve learners in worthwhile learning of mathematics similar to that made available to learners in classrooms where the teacher has a sound knowledge of the subject matter. It is equally important that textbooks and learner workbooks are checked thoroughly for errors before being printed out and distributed to schools as this can have an adverse effect on learning especially in subjects like mathematics. It is the conclusion of this study that when teachers focus on creating a space of learning which enhances in learners the capabilities to discern which knowledge is germane, the learner and the content are placed at the centre of the process of teaching and learning which improves the quality of instruction. Finally, the study proposes a new knowledge domain based on the model of reflective practice which aims to assist teachers with identifying individual knowledge areas of need for continued professional development.