This study explores the feelings, perceptions and experiences of Mathematics educators as they use classroom management to improve Mathematics education in the sampled four secondary schools in the Gauteng province. The main research question was to understand the place and role of effective classroom management in the improvement of mathematics education. In answering this question, the researcher collected data through purposively and conveniently selected four schools in Gauteng province. The researcher engaged the Mathematics head of department and Mathematics educators of participating schools to conduct face-to-face semi-structured interviews with heads of departments, and focus group discussions with Mathematics educators. Data was also collected through limited observation of different administrative aspects in Mathematics classrooms. Data collected was thematically analysed. The data analysis resulted in four main themes emerging. Overall, it was identified that Mathematics educators are expected to perform multiple tasks which necessitate good classroom management skills thereby enhancing an improvement in the performance of learners. From the data obtained, analysed and discussed, the study established that good Mathematics teaching cannot be separated from effectively managing classes, and that effective classroom management is a necessity in Gauteng province. Several elements which enhance effective classroom management were found to be, possession of relevant and adequate resources in the form of material and physical or material, educator professional skills and characteristics, parental and school management support as well as positive learner participation. it was seen that educators were facing several challenges which interfere with their efforts to restore and maintain an organised teaching–learning environment. / Educational Management and Leadership / Ph. D. (Educational Management)

This mixed methods research design, which was modelled on the constructivist view of schooling, sets out to investigate the effect of developing mathematical problem solving skills of grade 8 learners on their performance and achievement in mathematics. To develop the mathematical problem solving skills of the experimental group, a problem-centred teaching and learning environment was created in which problem posing and solving were the key didactic mathematical activity. The effect of the intervention programme on the experimental group was compared with the control group by assessing learners’ problem solving processes, mathematical problem solving skills, reasoning and cognitive processes, performance and achievement in mathematics. Data were obtained through questionnaires, a mathematical problem solving skills inventory, direct participant observation and questioning, semi-structured interviews, learner journals, mathematical tasks, written work, pre- and post- multiple-choice and word-problem tests. Data analysis was largely done through descriptive analysis and the findings assisted the researcher to make recommendations and suggest areas that could require possible further research. / Mathematics Education / M. Ed. (Mathematical Education)

The aim of this study was to investigate the effect of context-based problem solving instruction (CBPSI) on the problem solving performance of Grade 10 learners, who performed poorly in mathematics. A cognitive load theory (CLT) was used to frame the study. In addition, CLT was used to: 1) facilitate the interpretation and explanation of participants‟ problem solving performance; and, 2) influence the design of CBPSI to hone participants‟ problem solving skills. The study was conducted in the Gauteng province of South Africa and involved a two-week intervention program in each of the nine participating high schools. Participants consisted of 783 learners and four Grade 10 mathematics teachers. A non-equivalent control group design was employed, consisting of a pre- and post- measure. In addition, classroom observations and semi-structured interviews were conducted with teachers and learners. Teachers employed conventional problem solving instructions in four control schools while the researcher implemented CBPSI in five experimental schools. Instruction in experimental schools entailed several worked-out context-based problem solving examples given to participants in worksheets. The main aspects of CBPSI embraced elements of the effects of self-explanation and split-attention, as advocated by CLT. Due to the design of CBPSI participants in experimental schools became familiar with the basic context-based problem solving tasks that were presented to them through the worked-out example samples. In turn, the associated cognitive load of problem solving tasks was gradually reduced. The principal instrument for data collection was a standardized Functional Mathematics Achievement Test. The pre-test determined participants‟ initial problem solving status before intervention. A post-test was given at the end of intervention to benchmark change in the functionality of CBPSI over a two-week period. Using one-way analysis of covariance (ANCOVA), Analysis of Variance (ANOVA), and other statistical techniques the study found that participants in experimental schools performed significantly better than participants in control schools on certain aspects of problem solving performance. In addition, semi-structured interviews and classroom observations revealed that participants rated CBPSI highly. On the whole, the study showed that CBPSI is an effective instructional tool to enhance the problem solving performance of Grade 10 mathematics learners. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education)

This mixed methods research design, which was modelled on the constructivist view of schooling, sets out to investigate the effect of developing mathematical problem solving skills of grade 8 learners on their performance and achievement in mathematics. To develop the mathematical problem solving skills of the experimental group, a problem-centred teaching and learning environment was created in which problem posing and solving were the key didactic mathematical activity. The effect of the intervention programme on the experimental group was compared with the control group by assessing learners’ problem solving processes, mathematical problem solving skills, reasoning and cognitive processes, performance and achievement in mathematics. Data were obtained through questionnaires, a mathematical problem solving skills inventory, direct participant observation and questioning, semi-structured interviews, learner journals, mathematical tasks, written work, pre- and post- multiple-choice and word-problem tests. Data analysis was largely done through descriptive analysis and the findings assisted the researcher to make recommendations and suggest areas that could require possible further research. / Mathematics Education / M. Ed. (Mathematical Education)

The aim of this study was to investigate the effect of context-based problem solving instruction (CBPSI) on the problem solving performance of Grade 10 learners, who performed poorly in mathematics. A cognitive load theory (CLT) was used to frame the study. In addition, CLT was used to: 1) facilitate the interpretation and explanation of participants‟ problem solving performance; and, 2) influence the design of CBPSI to hone participants‟ problem solving skills. The study was conducted in the Gauteng province of South Africa and involved a two-week intervention program in each of the nine participating high schools. Participants consisted of 783 learners and four Grade 10 mathematics teachers. A non-equivalent control group design was employed, consisting of a pre- and post- measure. In addition, classroom observations and semi-structured interviews were conducted with teachers and learners. Teachers employed conventional problem solving instructions in four control schools while the researcher implemented CBPSI in five experimental schools. Instruction in experimental schools entailed several worked-out context-based problem solving examples given to participants in worksheets. The main aspects of CBPSI embraced elements of the effects of self-explanation and split-attention, as advocated by CLT. Due to the design of CBPSI participants in experimental schools became familiar with the basic context-based problem solving tasks that were presented to them through the worked-out example samples. In turn, the associated cognitive load of problem solving tasks was gradually reduced. The principal instrument for data collection was a standardized Functional Mathematics Achievement Test. The pre-test determined participants‟ initial problem solving status before intervention. A post-test was given at the end of intervention to benchmark change in the functionality of CBPSI over a two-week period. Using one-way analysis of covariance (ANCOVA), Analysis of Variance (ANOVA), and other statistical techniques the study found that participants in experimental schools performed significantly better than participants in control schools on certain aspects of problem solving performance. In addition, semi-structured interviews and classroom observations revealed that participants rated CBPSI highly. On the whole, the study showed that CBPSI is an effective instructional tool to enhance the problem solving performance of Grade 10 mathematics learners. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education)