The purpose of this study was to investigate, with or without prompts, students’ small group discussions of their solutions to mathematical problems and to determine the extent to which the students demonstrate mathematical power. Mathematical power was defined in terms of student assessment standards (SAS) and their integration. SAS, each of which has associated with it categories of mathematical activities, comprise communication, problem solving, mathematical concepts, mathematical procedures, and mathematical disposition. Other insights perceived to be important from the discussions were also documented. Grade 9 students of the regular school program were used for the study. There were 18 students in the class but only one group of students comprising 2 females and 2 males was the focus of the study. They responded to mathematical problems individually for 20 minutes and then used 40 minutes to discuss, in groups, their solutions to the problems. Also, they responded to questionnaire items. The group discussions were video recorded and analyzed. Data were collected on 7 different occasions using 7 different problems over a period of 3 months. - Results of the study indicate that students demonstrated mathematical power to the extent that at least one category of the mathematical activities associated with each SAS was reflected by the small group discussions of students’ solutions to mathematical problems. Other results indicate that combining students written scripts with students’ talk provides a better insight into the things about which students are talking. Also, monitoring students and providing them with prompts while they work in groups is useful in helping them accomplish tasks in which they are engaged. Finally, when students work in groups, they can shift their viewpoints consensually or conceptually to align their viewpoints with majority viewpoints.

This study investigated the teaching of mathematics in the Intermediate phase, in Itsoseng circuit. The study adopted a survey as its research design. Data was drawn from a sample size of 14 mathematics educators from 5 primary schools, which were selected from 9 Itsoseng primary schools. , Questionnaires, interviews and observation were used to elicit data on classroom practices during the teaching and learning of mathematics. Lesson observation was used to triangulate the information collected through questionnaire and interviews. The investigation indicated that Itsoseng primary mathematics educators are still using traditional methods used in the apartheid education system to teach mathematics. The conclusion drawn from the study is that there is a need for professional development of educators to broaden their knowledge on the teaching strategies that col:'ld be used to teach mathematics in the Outcomes Based Education (OBE) context.

This study investigated the teaching of mathematics in the Intermediate phase, in ltsoseng circuit. The study adopted a survey as its research design. Data was drawn from a sample size of 14 mathematics educators from 5 primary schools, which were selected from 9 ltsoseng primary schools. ' Questionnaires, interviews and observation were used to elicit data on classroom practices during the teaching and learning of mathematics. Lesson observation was used to triangulate the information collected through questionnaire and interviews. The investigation indicated that ltsoseng primary mathematics educators are still using traditional methods used in the apartheid education system to teach mathematics. The conclusion drawn from the study is that there is a need for professional development of educators to broaden their knowledge on the teaching strategies that could be used to teach mathematics in the Outcomes Based Education (OBE) context. / (M.Ed.) North West University, Mafikeng Campus, 2006

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The topic of this half-thesis was conceived after the author had noted with interest, that an alarmingly high number of pupils in the Mdantsane Central District of the Ciskei were registering for Higher Grade (HG) mathematics for their final (Standard 10) year. What mattered most was that the failure rate was abnormally high. As a teacher of the subject for 14 years as at the end of 1988, the author had seen very weak pupils passing through his hands who had nevertheless insisted on registering for the examination in HG mathematics. A look through the Human Sciences Research Council (HSRC) Report of 1971 which recommended the syllabus differentiation, revealed that the intention of the relevant HSRC Committee was to offer a subject at a level in accordance with a pupil's interest, aptitude and ability. In a survey undertaken by the author, samples of teachers, pupils and parents indeed confirmed the existence of a very high number of HG candidates, as suspected. The survey also revealed an aversion to the standard grade (SG) course by some pupils, teachers and even principals. A desire for university education was shown to be in the minds of most pupil respondents. Well sourced registration statistics clearly showed that the Department of Education and Training (DET) in the Republic of South Africa and the Department of Education in the Ciskei had by far the greatest proportion of pupils on the HG in mathematics in comparison with the other race groups.Standard 10 (Std 10) results for two years taken separately confirmed the author's suspicion that aptitude and/or ability were not taken into consideration by most pupils, in the choice of grade. The results were not good at all. In most cases the uninformed pupil was acting alone in taking the important decision, perhaps with only peer group pressure to contend with. Three independent opinions suggested that there was probably a general feeling that Black education was already inferior, even without the syllabus differentiation hence the reluctance to register for the SG option. Furthermore, the investigation indicated that there was no adequate provision for technical education for Blacks in either the RSA or Ciskei which would provide the alternative to a university career for a pupiL Amongst other things, a mild form of pupil screening and a well structured careers guidance programme are suggested in the concluding chapters

The purpose of this study was to identify preferred learning styles and strategies of secondary school students and to examine the prevailing problems that restrict them to use their own preferences. The study was intended to highlight a number of issues that need to be revealed and addressed in the learning of mathematics. The types of preferred learning styles and strategies students need to employ in learning mathematics, the assistance students require from their teachers, the conduciveness of the design of mathematics curriculum and the challenges they might face to use their own preferred learning styles and strategies in the learning of mathematics were addressed as basic research questions. The study dealt with various elements that were related to environmental, emotional, sociological, physiological and psychological categories of learning in the identification of the types of learning styles and strategies. This study is believed to contribute a lot in addressing the problems of learning styles and strategies, provide feedback to the concerned government bodies to help them improve the teaching learning processes in secondary schools. It is also to reduce the bias or prejudice on mathematics by assisting students to use their own preferred learning styles and strategies, and contribute to further investigations to make the learning of mathematics more enjoyable, participatory and lifelong career. This study was conducted in four secondary schools in West Shoa Zone. A qualitative method that was descriptive in nature was employed in the study while the instruments of the study were questionnaires and an interview. The sample comprised of 249 (128 male and 121 female) secondary school students and 30 (25 male and 5 female) secondary school mathematics teachers selected randomly. The result has shown that students were not learning mathematics on the basis of their preferred learning styles and strategies and the teachers were practicing autocratic teaching styles. Most of the students did not prefer learning mathematics through plasma television; they required brief outlines and concrete presentations, and indicated that there is not enough time to check and recheck the answers they found for the problems. These imply that the organization of secondary school mathematics curriculum requires reform to accommodate the preferred learning styles and strategies of students. / Further Teacher Education / M. Ed. (Mathematics Education)

D.Ed. (Curriculum Studies) / This study investigated the impact of mathematics interventions on learner participation and performance in mathematics within Gauteng 47 high schools in the Johannesburg area over a five year period. Motivating the study was the perpetual implementation of mathematics interventions against the backdrop of persistent mediocrity in learner matriculation achievement in this subject. The essence of the research problem was the scarcity of knowledge relating to the effectiveness and impact of mathematics interventions. The strategy of inquiry employed was an explanatory research design which entailed a sequential collection and analysis of quantitative and qualitative data. Quantitative findings revealed that only 10% of learners who participated in interventions were enabled to enroll in mathematics essential to pursue mathematics related professions at tertiary level. Thus, the intention to redress the prevalent limited access to professional careers requiring a strong basis in mathematics has not been dented. Regarding learner performance in mathematics, Friedman tests for nonparametric hypothesis testing revealed that there was no significant evidence that the interventions had an impact on learner performance over the five year observation period. Qualitative data analysis explained the quantitative findings and further uncovered the positive impact of mathematics interventions. Furthermore, strengths and weaknesses of the mathematics interventions were identified as opposed to the quantitative findings which seemed to negate the existence of the impact of mathematics interventions. Through the findings of this study, factors that may be limiting the effectiveness of mathematics interventions were uncovered. These were interwoven into a base knowledge that can influence positive practices and future research related to optimizing the impact of mathematics interventions in high schools.

M.Ed. / Our world is becoming more mathematical. We are constantly surrounded by mathematical situations and are regularly required to make mathematical decisions. These decisions require number sense, estimation skills, ability to analyse data intelligently, knowledge of two and three-dimensional geometry and many other abilities not often taught in school. Halpern (1992:1) states: "...as a nation we not only need competent scientists and engineers, we also need a citizenry that is literate in mathematics issues." Reyes and Stannic (1998:26) support this view as they state: "Knowledge of mathematics is essential for all members of our society. To participate in our democratic processes and to be unrestricted in career choice and advancement, people must be able to apply mathematical ideas." Learners leaving school need to be able to use available technology and to reason mathematically, be confident of their abilities, be able to communicate mathematically and be problem solvers. The introduction of technology into the lives of many people has called upon their background of mathematics to cope with mathematical problems and manipulating technological instruments. The relationship between mathematics and technology is emphasised by Dowling and Noss (1990:24) when they say: "New technology is a powerful tool which opens up new areas of mathematics and changes the way in which society makes use of mathematics in the factory, office and home". The Cockcroft Committee (1982), in their report on an inquiry into the teaching of Mathematics in schools, sees the main task of mathematics teachers as: "Enabling each learner to develop within his own capabilities the mathematical understanding and skills required for adult life, for employment and further study". The most important contribution for the purpose of this study, was the emphasis placed on cognitive aims to equip learners with numerical understanding and skills. Other contributions were to develop logical thinking and to expand their ability to look for patterns and explain them and to develop an awareness of the link between mathematics and everyday situations. This report (1982) motivated the researcher to review how teachers are teaching. This means that there will be an investigation into how children learn mathematics and not just what should be taught. Naidoo, Smit and Van Heerden (1995:7) also emphasise this by stating that "...the advance in technology at this time changed educational thinking more, making it even more important to further investigate how children actually learn." Yildirim (1994:28) argues that "... improving student's thinking ability is accepted as an important goal of education, and schools are considered places where thinking skills can be promoted. However, ways in which this should be done is a matter of controversy among educators." He further postulates that the best way to improve student thinking involves deep and thoughtful subject matter instruction in which students are encouraged to think reflectively rather than to merely cite the facts. The central characteristics of mathematical thinking are the determination of relationship and their application. It includes the ability to analyse a given situation or experience; to distinguish between applicable data and those which are not applicable; to classify and arrange these data; to abstract relationships from them, and finally to symbolize them for future use and application in new situations. Therefore it is important and essential for students to be taught how to approach the problems. This is one way of encouraging inquisitive and creative mathematics. Well-developed thinking skills are useful in almost every life situation, therefore there is a need to design instructional programmes that focus on the acquisition and uses thinking skills that are needed to find and solve mathematical problems.

The general goal of the present study was to assess mathematics achievement at the end of Grade 12 in the Dominican Republic, with particular attention to school and regional differences, as well as gender differences. Also, gains in achievement were examined by comparing the achievement of students in Grade 12 to that of students finishing Grade 11. In addition, the performance of Grade 12 students was compared to that of Grade 8 students as assessed in the Teaching and Learning of Mathematics in the Dominican Republic (TLMDR) study and to that of students from other countries in the Second International Mathematics Study (SIMS). The sample included 1271 students in Grade 12 and 1413 in Grade 11, distributed over 49 schools. Three types of schools were sampled, public schools, and two kinds of private schools. They were urban schools located in the twelve largest cities of the country. These cities were grouped into three regions of similar size. The mathematics test consisted of 70 multiple-choice items distributed over two test forms. Students' scores were analyzed to assess how much mathematics students in Grade 12 know. Grade 11 data were used as a surrogate for pre-test scores to estimate gains in achievement. School means were used in an analysis of variance designed to examine the effect of school type and region on mathematics achievement. Males' and females' scores were used to analyze gender differences in achievement at the item level, and within each of the school types and regions in the sample. Grade 12 students' responses to 14 items were compared to those of Grade 8 students. Finally, Grade 12 students' responses to 10 items were compared to those of students from other countries in SIMS. Among the findings of this study were: 1. Students in Grade 12 scored poorly on the mathematics test. Grade 11 and Grade 12 students obtained similar achievement levels which indicated that the achievement gains between the two grades were very small. 2. School type and region were found to significantly affect mathematics achievement, but no interaction effect was found. 3. The comparison of school type means showed that only one type of private school significantly outperformed public schools. This type of school also outperformed the other type of private school. 4. The comparison of region means did not produce the predicted outcome. The pairwise comparisons showed that none of the regions was significantly different from the other, despite the fact that the region factor was significant. 5. The analysis of gender differences in mathematics achievement showed that males performed significantly better than females. At the item level, males outperformed females on only 19 items. Most of these items dealt with geometry, or were at the application level. 6. Gender differences favoring males were found to be independent of school type and region. 7. Comparison between Dominican Grade 12 and Grade 8 students revealed that mathematics achievement improved between the grades for most items. 8. Dominican performance was very poor on the SIMS items and it was far behind that of other countries. / Education, Faculty of / Graduate

The purpose of this study was to investigate, with or without prompts, students’ small group discussions of their solutions to mathematical problems and to determine the extent to which the students demonstrate mathematical power. Mathematical power was defined in terms of student assessment standards (SAS) and their integration. SAS, each of which has associated with it categories of mathematical activities, comprise communication, problem solving, mathematical concepts, mathematical procedures, and mathematical disposition. Other insights perceived to be important from the discussions were also documented. Grade 9 students of the regular school program were used for the study. There were 18 students in the class but only one group of students comprising 2 females and 2 males was the focus of the study. They responded to mathematical problems individually for 20 minutes and then used 40 minutes to discuss, in groups, their solutions to the problems. Also, they responded to questionnaire items. The group discussions were video recorded and analyzed. Data were collected on 7 different occasions using 7 different problems over a period of 3 months. - Results of the study indicate that students demonstrated mathematical power to the extent that at least one category of the mathematical activities associated with each SAS was reflected by the small group discussions of students’ solutions to mathematical problems. Other results indicate that combining students written scripts with students’ talk provides a better insight into the things about which students are talking. Also, monitoring students and providing them with prompts while they work in groups is useful in helping them accomplish tasks in which they are engaged. Finally, when students work in groups, they can shift their viewpoints consensually or conceptually to align their viewpoints with majority viewpoints. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate