National and international studies show that the standard of mathematics teaching and learning in South Africa is very low compared to other countries. These statistics are worrying because mathematics is one of the ‘gatekeeper’ subjects that determine learners’ access to higher learning and a better future. My study, aimed at exploring two Foundation Phase teachers’ selection and use of examples and representations when teaching number, forms part of a longitudinal study currently underway within the Wits Maths Connect Primary (WMC-P) Project. One of the broad aims of the WMC-P Project is to improve primary teachers’ mathematics content knowledge and also to see this translated into improved pedagogy on the ground. This qualitative study was carried out within the WMC-P Project’s 20-Day in-service training course and one of the ten government schools participating in the broader study. My study aimed to build on research that has been carried out on teachers’ use of examples and representations with a focus on the South African terrain. The dataset comprised of two Foundation Phase teacher’s pre-tests, course-work tasks, field notes, and transcripts of observed lessons. Data was analysed using an analytical framework based on current literature related to examples and representations within mathematics teaching. Findings from my study show possible associations between a higher content knowledge score and the extent of a teacher’s example space and more coherent connections between different representational forms. More studies around this topic are needed because research shows that teachers’ examples and representations in mathematics teaching are important for good teaching and conceptual understanding.

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Science, 2002.

Research Project in Education for: Masters in Education / This study analyzed the pedagogical practices of three Grade 10 Mathematical Literacy (ML) educators. The rationale behind the study was to add information and insight into the very new and under researched Further Education and Training secondary school subject of ML. Botha (2011) discussed how one of the main concerns with ML integration into the South African national curriculum was that the educators being asked to teach ML were moved into it from other subjects without any real education or training, and so when teaching, relied on previously learned pedagogical practices from other subjects. It is the contention of this study that this is a real issue in terms of the teaching of ML in classrooms and in terms of damaging its perceived academic status. In order to offer insight into how ML is its own distinct subject and not simply a lesser version of Mathematics, this study analyzed three lessons of each of the three educators through the lens of Pedagogical Link Making (PLM) (Scott, Mortimer, & Ametller, 2011). PLM was the conceptual framework that guided the observations and post observation interviews, and through analysis of the educators’ pedagogical practices as well as a thematic analysis of discussion points during the interviews, this study came to five major findings. The findings suggested that the ML educators were not properly educated in ML pedagogy and that the educators made the majority of pedagogical decisions in the classroom based on generating learner interest and motivation for work. It also found that the educators used many of the links outlined by PLM, but also admitted to holding a lower academic expectation of ML and ML learners. A call is made to increase research into the relatively new subject of ML along the lines of pedagogical practices in order to assist new ML educators to translate and transmit the goals and content of ML provided for by the Curriculum and Assessment Policy Statement (CAPS

M.Ed. / This study investigates junior primary teachers' conception of problem-centred Mathematics teaching with the view to describe and also explain their conception. The rationale for the investigation is derived from the move being made in South African Mathematics teaching from traditional teaching to constructivist and problem-centred teaching. Teachers have had to change from being authoritative and focused on the product to become facilitators of the learning process. This move implies that teachers have to put aside most of what they have been doing up till now to be able to adopt constructivist ways of thinking. Problem-centred teaching is in strong contrast to these traditional teaching methods. Such a shift in paradigm could prove to be traumatic for teachers and pupild. The report of the study commences with a theory framework in which constructivism is clearly explicated. The constructivist view of knowledge, with the relationship between public knowledge and personal knowledge and the forming of personal knowledge is discussed. The focus then shifts to learning through cognitive restructuring which is facilitated by assimilation and accommodation. In the constructivist view, learning is also facilitated by social interaction and reflection. Both the processes and the relationship between social interaction and reflection are discussed. Most importantly, learning is facilitated through constructivist teaching, but successful teaching depends on teachers'conception thereof. Conception is described as one of the most important components of teachers' personal teaching theory. Teachers use their personal teaching theory to reflect on teaching and learning. The literature review is concluded with a discussion on the nature of constructivist teaching and the role of the teacher in such a teaching model. The theory framework is complemented by a chapter on the design of the research, substantiating the choice of format and methods of data collection and analyses. The data is reported in the final chapter in which examples of raw data from transcriptions and sketches are presented. Finally, the consolidated data is interpreted. - The most significant finding of this study is that junior primary teachers in this group have a negative conception of problem-centred Mathematics teaching. It appears that the most important reason for their negative conception is that they were not adequately equipped for the contructivist approach towards Mathematics teaching. This study then proposes that for teachers to be able to teach from a constructivist paradigm they need relevant constructivist training, more support from the experts, but also more support from each other. They need to change their teaching conception to a constructivist conception of teaching.

Improving learner achievement and performance remains a global challenge for many governments, especially in developing countries. Countries spend a sizeable percentage of their national budgets on education with the hope to achieve desired learner outcomes. In South Africa, legislation has made provision for companies to contribute 1% of their net profit towards social development, including education. It is within this background, that the Epoch and Optima Trusts invested significant sums of money to improve the quality of maths results in secondary schools. The study investigates school level activities to ascertain whether and to what extent these may be implicated in improved teaching practices leading to improved performance. We interrogate the assumption commonly stated in the school effectiveness literature that teaching practices in schools are stimulated and facilitated by activities occurring at that school level. The literature is inclined to the view that whatever happens in classrooms is influenced by school level instructional leadership practices, professional development of teachers and the maintenance of internal accountability measures. We preferred to make use of case study research method in order to explore teacher practices in schools because the purpose is to understand behavioural detail and impact mechanisms. A matched pairs sampling technique was used to select four schools from a population of 78 public schools which were continually supported by the Trusts over a period of two years. One pair was classified as former Model C schools (one high performing and one low performing), while the other pair consisted of two former Department of Education and Training schools (one high performing and one low performing). This design reduces the socio-economic and cultural differences between the two schools in each pair. A framework was derived from the literature to guide the collection and analysis of data. The framework commences with the three categories of school level practices, disaggregated into eight specific activities. A set of indicators was then formulated to assess the degree to which each of the specific practices was present in schools. Collective responses of four interviewees at each school were rated and triangulated during this process. Given the nature and the size of the sample, we cannot generalise on the basis of four case studies. However, the value of this report is that we have developed:  a scheme for describing and analysing school-level practices that may facilitate and optimise teaching and learning, and  a set of hypotheses for accounting for improved school performance. In conclusion, we inferred that schools that institutionalised some practices and systems as identified were able to increase and maintain the number of quality passes in mathematics and as such, meeting the objectives of the donors. The factors which appear to hold the most potential for optimising performance in the two high SES former Model C schools are collegial practices on curriculum, pedagogy and assessment. In the two low SES former DET schools performance advantage seems to be enhanced by the systematic use of assessment data and by an increased sense of intrinsic motivation on the part of teachers.

The central position in this study is that the professional identities, and consequently the classroom practices, of mathematics teachers are continuously being shaped by their narratives of past and present experiences. The primary research question explores the narratives that shape the professional identities of seven mathematics teachers; and the secondary research question, how their narratives shape their professional identities. Furthermore, the potential implications of this study for the design and implementation of pre-service teacher education programmes and in-service teacher development initiatives are considered. This study is framed by Socioculturalism; a theoretical perspective of human thinking as social in origin and of learning as participation in social practices. Futhermore, in line with Situated Learning Theory, the key theoretical notions are: identity (or learning as becoming); community (or learning as belonging); practice (or learning as doing); and meaning (or learning as experience). Identity is construed here as a conceptual bridge between learning and its cultural settings; and also between the individual and the social. In this study, the identity-shaping narratives of seven mathematics teachers, all purposively sampled from schools in the Port Elizabeth and Grahamstown education districts of the Eastern Cape Province of South Africa, were accessed via a narrative inquiry; followed by a horizontal analysis to identify common patterns or recurring themes in the narratives of all seven participants; and, a vertical analysis of the narratives of four of the participants to determine how their narratives shape their professional identities. Recurring themes that emerged during the horizontal analysis include the influence of: family support; role models; changing work environments; continuous professional development; professional recognition; religion; and, micro-politics. The vertical analysis demonstrated how, through a process of interpreting the narratives and restorying them into a meaningful core narrative; it is possible to gain insights into how personal narratives shape a professional identity. This study highlights the importance of listening to the narratives of mathematics teachers; because their professional identities, and consequently their teaching practices, are continuously being shaped by their narratives. It is anticipated that this research will be of interest and benefit to researchers, policy-makers, and teachers; especially in the area of Mathematics Education, where both narrative inquiry as a research method and research into teachers’ professional identities are relatively new.

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)

M. Tech. Business Information Systems / Information technology (IT) rapidity, and the pervasive implementation of new technologies in the education system, has tremendously improved the way teaching and learning is conducted. Institutions are being reshaped by the rapid provision of education services anytime, anywhere regardless of the constraint of space and geographical boundaries. This has enhanced collaboration among educators as well as their learners by sharing and disseminating of knowledge. However, this sharing of knowledge is still limited as educators have not fully exploited IT to share knowledge. The major objective of this study was to develop a framework for utilizing IT to enhance knowledge sharing for mathematics and science teachers.

Department of Curriculum Studies and Education Management / MEDCS

Mathematics and science form an integral part people’s daily lives. South African people suddenly find themselves on a technological highway, where mathematical, scientific and creative thinking as well as problem solving skills take centre stage. However many people fear these, and believe that they are unable to tackle them. Mathematics and science educators therefore have need to have knowledge and understanding regarding 6 the foundation of the teaching of these subjects in the intermediate and senior phases at schools. This should enable them to contribute positively towards changing people’s perceptions about these subjects. Based on the above information I felt it imperative for me to investigate the impact of shortages of maths and science educators with special reference to the Buffalo City Area. Purpose of the study: 1 To determine whether schools are able to attract and retain qualified maths and science educators, 2 To identify the quantity of quality maths and science learners schools are able to produce for tertiary education, 3 To investigate the rate of turnover of maths and science educators, 4 To identify the number of maths and science learners who are willing to study maths and science at tertiary level and thereafter join the teaching fraternity.