This study investigates to what extent educators’ pedagogical content knowledge affects learners’ achievement in quadratic functions. The components of pedagogical content knowledge (PCK) examined are: (i) mathematical content knowledge (MCK), (ii) knowledge of learners’ conceptions, and misconceptions, and (iii) knowledge of strategies. The participants were seventeen mathematics educators and ten learners from each educator’s class. The sample of educators was a convenient sample, while the sample of learners was selected by means of random sampling. A mixed method design was used to execute the study. Data about educators’ MCK, and knowledge of learners’ misconceptions were collected by means of a questionnaire. An interview was used to gather data about educators’ knowledge of strategies. Data on learners’ achievements and misconceptions was collected by means of a questionnaire. Descriptive statistics were used to describe the effect of each component of the educators’ PCK on learners’ achievements. The result indicates that the achievement of learners who are taught by educators who have strong PCK is higher than the achievement of learners who are taught by educators who have weak PCK. / Mathematical Sciences / M. Ed. (Mathematics Education)

This study investigates to what extent educators’ pedagogical content knowledge affects learners’ achievement in quadratic functions. The components of pedagogical content knowledge (PCK) examined are: (i) mathematical content knowledge (MCK), (ii) knowledge of learners’ conceptions, and misconceptions, and (iii) knowledge of strategies. The participants were seventeen mathematics educators and ten learners from each educator’s class. The sample of educators was a convenient sample, while the sample of learners was selected by means of random sampling. A mixed method design was used to execute the study. Data about educators’ MCK, and knowledge of learners’ misconceptions were collected by means of a questionnaire. An interview was used to gather data about educators’ knowledge of strategies. Data on learners’ achievements and misconceptions was collected by means of a questionnaire. Descriptive statistics were used to describe the effect of each component of the educators’ PCK on learners’ achievements. The result indicates that the achievement of learners who are taught by educators who have strong PCK is higher than the achievement of learners who are taught by educators who have weak PCK. / Mathematical Sciences / M. Ed. (Mathematics Education)

The exploratory study sought to elicit and document mathematics teachers‟ views on how they enacted the process of transition between contexts and mathematics. The study pursued to understand teachers‟ beliefs and knowledge of mathematics. A mixed methods sequential explanatory research design was employed where a quantitative phase was followed by the connecting phase and concluded through a qualitative phase involving three case studies. A purposive sample of 165 practicing teachers who had registered for a professional advancement developmental course at a university participated in the study by voluntarily completing a survey questionnaire. From this sample, three cases of individual teachers were pursued. The first two cases involved conducting in-depth interviews with the teacher who had rated sentences in the questionnaire differently while the last case involved the recording of an interview of one individual using field notes. The questionnaire sought teachers‟ biographical details (section A), their views on contexts and mathematics (section B) and their rating of sentences in a passage with regard to the mathematics embedded in the sentences (section C). Semi-structured interviews were conducted in the qualitative phase to elicit in-depth views of the teachers‟ regarding the research problem. All the instruments were tested for validity and reliability. Quantitative data gathered was analysed using frequencies, percentages, cross tabulations, bar charts and pie charts as well as the calculation of Pearson chi-square tests (Cohen, Manion & Morrison, 2011). Descriptive and inferential statistics were used to collate teachers‟ views from which themes were drawn and related to make inferences. It was found that teachers‟ positive views about contexts and mathematics did not translate into them recognising mathematics in some mathematics potent contexts as captured in their ratings in section C of the questionnaire. Statistically significant associations were recorded to support this. The study also conceptualised a mathematical participation model (MP-model) as a tool to describe and analyse participation that involves the use of real world data in the teaching and learning of mathematics. The MP-model involves four components, viz. the community of practice (CoP), real world data, mathematics and a model in which members of the CoP tap into the real world data and mathematics to model their participation. The study recommends the MP-model as tool for description and enactment of full mathematical participation. / Mathematical Sciences / D.Litt.et. Phil. (Mathematics Education)