The new outcomes based education (OBE) in the form of the Revised National Curriculum Statements (RNCS, 2002) advocates for the use of contexts in the teaching and learning of mathematics. The motivation for this advocacy is the expectation of the promotion of understanding of the subject. Such expectations however cannot be achievable without consideration of factors such as what contexts are appropriate for use in the teaching and learning of mathematics, how the contexts have to be used in order to promote understanding and more importantly how are teachers involved in this process. The study explores the ways in which a Grade 7 teacher selects contexts in the learning support materials or in any other source for use in order to promote understanding of the concept of variable among learners. It draws on socio-cultural theories and is underpinned by the notion that understanding of a concept presupposes and is presupposed by the formation of the concept. The research method employed was a case study and data was mainly collected through interviews as well as materials that were availed by the teacher. The following three key issues emerged from the study and were taken up for discussion: a) what does it take to make the transition from context to mathematics in terms of the promotion of the understanding of the concept of variable? b) to what extent were the materials selected by the teacher adequate to deal with issues of transition from context to mathematics in terms of the promotion of the understanding of the concept of variable? and c) what possibilities were available for the teacher to use context in order to promote understanding of the concept of variable? This study further explores the extent to which the notions of mathematisation and transition from context to mathematics may be used as the means by which the selection and use of contexts in the learning and teaching of the concept of variable may facilitate the promotion of understanding of the concept variable.

This investigative study was undertaken against the background of the recent calls for back to basics by the Schooling 2025 initiative, as well as to address the 2000 and 2009 Review Committees’ reports on the training and development of teachers and on the variable quality of learning support materials. The act of systemic transformation has led to two curriculum revisions taking place within the South African education sector and has inevitably culminated in the identification of shortcomings in teacher development and learning materials. This study has positioned itself to address these shortcomings at pre-service level through the preparation of Mathematics student teachers as prospective Mathematics teachers. In addressing the issue of inadequate training, the focus of the study was not only on cognition, but also on how affect could influence the learning of Mathematics so as to ensure a more encompassing approach in understanding how student teachers learn and do Mathematics. Integrated research on affect and cognition could lead to optimal performance in the teaching and learning of Mathematics and researchers in mathematics education need to acknowledge the role and impact of the affective domain and integrate it into studies of cognition. If learners are going to become competent learners of Mathematics, their affective responses to Mathematics are going to be much more intense than if they are merely expected to achieve satisfactory levels of performance in low-order mathematical skills. In the studies on mathematics cognition, the focus of mathematical competencies is on abilities and capabilities while, in the affective domain, competencies in mathematics are more than the abilities to perform observable tasks. Rather, the focus of the affective competencies lies in the direction, the degree and the levels of intensities of affect constructs (or their variables) that will define mathematical competencies within the affective domain. Evidentiary (qualitative) data from this study supported the contention that affect does influence the learning of mathematics since there were distinct patterns in the overall expressions of participants towards this aspect of the research. The acknowledgment of the concerns of student teachers during field practicum could possibly help in ameliorating these concerns through the identification of what student teachers were mostly concerned about when teaching Mathematics and how, by addressing these concerns, could help improve their teaching skills and abilities. Based on the quantitative evidence, the three subscales of self, task and impact used in the Student Concerns Questionnaire (SCQ) were modified on the basis of factor analysis to a two-factor model (concerns about self-benefit and concerns about learner-benefit). Some of the statistical results were integrated with the narrative data to provide substantive support for the expressions of student teachers. No classical trends, as noted in the concerns theory, could be detected in this study. It was statistically inferred that a majority of Mathematics student teachers who participated in this study were moderately concerned about most of the concerns statements noted in each of the items on the SCQ. In addressing the variable quality of the learning material the study focused on the development and the use of social context learning packages. The utilisation of these learning packages (in an intervention strategy) was aimed at strengthening social context knowledge and education, and explored its role in the translation (if any) of student teacher concerns within a hierarchical spectrum. The evidence on how student teachers perceived the use of these learning packages was recorded during the interviews. Analyses of the verbal data revealed that the participating student teachers agreed with the use of social context learning packages as part of their Mathematics lessons. In sum, the need to prepare effective Mathematics teachers and raise the academic calibre of prospective Mathematics teachers was fundamental to the overall design of this study. It is trusted that curriculum planners and designers will consider the recommendations of this study to address the so-called inadequacies within the education system of South Africa. / Thesis (PhD (Mathematics Education))--North-West University, Potchefstroom Campus, 2013

This investigative study was undertaken against the background of the recent calls for back to basics by the Schooling 2025 initiative, as well as to address the 2000 and 2009 Review Committees’ reports on the training and development of teachers and on the variable quality of learning support materials. The act of systemic transformation has led to two curriculum revisions taking place within the South African education sector and has inevitably culminated in the identification of shortcomings in teacher development and learning materials. This study has positioned itself to address these shortcomings at pre-service level through the preparation of Mathematics student teachers as prospective Mathematics teachers. In addressing the issue of inadequate training, the focus of the study was not only on cognition, but also on how affect could influence the learning of Mathematics so as to ensure a more encompassing approach in understanding how student teachers learn and do Mathematics. Integrated research on affect and cognition could lead to optimal performance in the teaching and learning of Mathematics and researchers in mathematics education need to acknowledge the role and impact of the affective domain and integrate it into studies of cognition. If learners are going to become competent learners of Mathematics, their affective responses to Mathematics are going to be much more intense than if they are merely expected to achieve satisfactory levels of performance in low-order mathematical skills. In the studies on mathematics cognition, the focus of mathematical competencies is on abilities and capabilities while, in the affective domain, competencies in mathematics are more than the abilities to perform observable tasks. Rather, the focus of the affective competencies lies in the direction, the degree and the levels of intensities of affect constructs (or their variables) that will define mathematical competencies within the affective domain. Evidentiary (qualitative) data from this study supported the contention that affect does influence the learning of mathematics since there were distinct patterns in the overall expressions of participants towards this aspect of the research. The acknowledgment of the concerns of student teachers during field practicum could possibly help in ameliorating these concerns through the identification of what student teachers were mostly concerned about when teaching Mathematics and how, by addressing these concerns, could help improve their teaching skills and abilities. Based on the quantitative evidence, the three subscales of self, task and impact used in the Student Concerns Questionnaire (SCQ) were modified on the basis of factor analysis to a two-factor model (concerns about self-benefit and concerns about learner-benefit). Some of the statistical results were integrated with the narrative data to provide substantive support for the expressions of student teachers. No classical trends, as noted in the concerns theory, could be detected in this study. It was statistically inferred that a majority of Mathematics student teachers who participated in this study were moderately concerned about most of the concerns statements noted in each of the items on the SCQ. In addressing the variable quality of the learning material the study focused on the development and the use of social context learning packages. The utilisation of these learning packages (in an intervention strategy) was aimed at strengthening social context knowledge and education, and explored its role in the translation (if any) of student teacher concerns within a hierarchical spectrum. The evidence on how student teachers perceived the use of these learning packages was recorded during the interviews. Analyses of the verbal data revealed that the participating student teachers agreed with the use of social context learning packages as part of their Mathematics lessons. In sum, the need to prepare effective Mathematics teachers and raise the academic calibre of prospective Mathematics teachers was fundamental to the overall design of this study. It is trusted that curriculum planners and designers will consider the recommendations of this study to address the so-called inadequacies within the education system of South Africa. / Thesis (PhD (Mathematics Education))--North-West University, Potchefstroom Campus, 2013