Basic mathematical competency seems to be lacking for engineering students starting their studies in this field. Students generally find the cognitive transition from secondary to tertiary mathematics challenging which in turn negatively influences their academic achievement in mathematics. The cognitive challenge is the transition from the application of mathematics to familiar questions to applying mathematical principles to varying practical application and problem solving. Mathematics provides the foundation for the cognitive toolset required for the development of skills required for analysing engineering systems and processes. It is therefore important to assess mathematical and cognitive competency and ability at the time of admission to a tertiary institution in order to identify and address gaps. This research demonstrates that first-year engineering students need to have a specific level of mathematical competency and cognitive ability to use mathematics within the context of engineering studies. This research attempts to connect the mathematic competency of first year engineering students to their academic results for subjects in the first year curriculum that rely heavily on mathematical competency. To satisfy the research question, the study firstly looks at relevant literature to identify the mathematical competency levels as well as the operational specification. Secondly, development theories and taxonomies were analysed to gain insight into the development processes associated with learning, cognitive development and the gap between cognitive competencies in transition from secondary to tertiary education. Further, cognitive competencies were identified that are essential for successful completion of first year engineering modules. Through synthesis of the different theories and taxonomies a framework was identified. This framework was used to analyse secondary data in order to measure mathematical and cognitive levels. Thirdly, the theoretical investigation was followed by a three-phase empirical study. A mixed quantative-qualitative (QUAN-qual) approached was followed. Phase 1 uses the assessment framework to measure first year students‟ mathematical competency at the inception of their studies as well as at the completion of their first semester. The mathematical competency at inception was measured with their Grade 12 mathematics marks and with relevant analysis of their initial bridging assessments, on a question by question basis. In addition, their first semester exams questions were analysed using the same approach as above. Phase 2 comprises the measurement of the relationship between the mathematical competency of first year enigineering students at admission and their achievement levels in selected first year subjects that required mathematical competency. Phase 3 includes the guidelines derived from the gaps and shortcomings identified. These gaps were identified in order to inform appropriate study support to first year students and to assists academic personnel with setting appropriate and dependable admission standards. The analysis of mathematical competency creates quality data that gives a clearer picture than a simple comparison of admission scores and first semester marks. The empirical study contributes to a better understanding of the problems associated with the transition from secondary to tertiary learning environments. From the study it was derived that study inception information of the students correlated only with their academic results on questions that tested mathematical and programming application. The inception information was not a predictor of mathematical achievement and results for both the lowest and highest mathematical competency levels. Futher study in this field is required to create frameworks for the measurements of both low and high levels of mathematical competency. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

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

Basic mathematical competency seems to be lacking for engineering students starting their studies in this field. Students generally find the cognitive transition from secondary to tertiary mathematics challenging which in turn negatively influences their academic achievement in mathematics. The cognitive challenge is the transition from the application of mathematics to familiar questions to applying mathematical principles to varying practical application and problem solving. Mathematics provides the foundation for the cognitive toolset required for the development of skills required for analysing engineering systems and processes. It is therefore important to assess mathematical and cognitive competency and ability at the time of admission to a tertiary institution in order to identify and address gaps. This research demonstrates that first-year engineering students need to have a specific level of mathematical competency and cognitive ability to use mathematics within the context of engineering studies. This research attempts to connect the mathematic competency of first year engineering students to their academic results for subjects in the first year curriculum that rely heavily on mathematical competency. To satisfy the research question, the study firstly looks at relevant literature to identify the mathematical competency levels as well as the operational specification. Secondly, development theories and taxonomies were analysed to gain insight into the development processes associated with learning, cognitive development and the gap between cognitive competencies in transition from secondary to tertiary education. Further, cognitive competencies were identified that are essential for successful completion of first year engineering modules. Through synthesis of the different theories and taxonomies a framework was identified. This framework was used to analyse secondary data in order to measure mathematical and cognitive levels. Thirdly, the theoretical investigation was followed by a three-phase empirical study. A mixed quantative-qualitative (QUAN-qual) approached was followed. Phase 1 uses the assessment framework to measure first year students‟ mathematical competency at the inception of their studies as well as at the completion of their first semester. The mathematical competency at inception was measured with their Grade 12 mathematics marks and with relevant analysis of their initial bridging assessments, on a question by question basis. In addition, their first semester exams questions were analysed using the same approach as above. Phase 2 comprises the measurement of the relationship between the mathematical competency of first year enigineering students at admission and their achievement levels in selected first year subjects that required mathematical competency. Phase 3 includes the guidelines derived from the gaps and shortcomings identified. These gaps were identified in order to inform appropriate study support to first year students and to assists academic personnel with setting appropriate and dependable admission standards. The analysis of mathematical competency creates quality data that gives a clearer picture than a simple comparison of admission scores and first semester marks. The empirical study contributes to a better understanding of the problems associated with the transition from secondary to tertiary learning environments. From the study it was derived that study inception information of the students correlated only with their academic results on questions that tested mathematical and programming application. The inception information was not a predictor of mathematical achievement and results for both the lowest and highest mathematical competency levels. Futher study in this field is required to create frameworks for the measurements of both low and high levels of mathematical competency. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

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