INVESTIGATING PRESERVICE SECONDARY SCHOOL TEACHERS’ MATHEMATICAL KNOWLEDGE FOR TEACHING EQUATIONS. Thesis Submitted to the Department of Curriculum and Teaching Studies, School of Education, in fulfilment of the requirements for the degree of Doctor of Philosophy in Curriculum and Teaching Studies (Mathematics Education)

This qualitative case study investigated four preservice secondary school teachers’ mathematical knowledge for teaching equations and the influence their mathematical knowledge for teaching had on their teaching practices. Data were generated using two open ended paper and pencil tests, semi-structured interviews, video lesson recordings, and lesson plans. I analysed the data using thematic analysis. The findings show diversity in the preservice teachers’ Mathematical Knowledge for Teaching. The results also reveal the preservice teachers’ subject matter knowledge influenced their pedagogical content knowledge and that their limitations in knowledge of errors and misconceptions influenced their choices of methods of handling the misconceptions. The preservice teachers were also able to use different methods to solve mathematical problems when they were encouraged to do so. The findings indicate that the preservice teachers’ classroom practices were shaped by their mathematical knowledge for teaching and algebraic thinking skills. The results illustrate that the preservice teachers used their mathematical knowledge for teaching to plan instruction, to construct and give instructional explanations, to elicit and develop students’ mathematical thinking, and to articulate ideas from examples and students’ solution processes. The study also adds ‘articulating ideas in examples and students’ solution processes’ as one of the high-leverage teaching practices by Ball and colleagues. The preservice teachers’ limitations in the knowledge of the “why” of mathematical procedures influenced limitations in articulating their teaching practices.

DOI: 10.13140/RG.2.2.20729.21607