Mathematical modelling is an area in mathematics education that has been much researched but conspicuously absent from the South African curriculum. The last few years have seen a move towards re-inclusion of mathematical modelling in the South African school curriculum. According to the National Curriculum Statement (2003a), “mathematical modelling provides learners with the means to analyse and describe their world mathematically, and so allows learners to deepen their understanding of Mathematics while adding to their mathematical tools for solving real-world problems”. The purpose of this study was to explore pre-service mathematics teachers’ conception of mathematical modelling and the different strategies that pre-service mathematics teachers use when solving real-world mathematics problems. This study further investigated pre-service mathematics teachers’ ability to facilitate the understanding of specific mathematical modelling problems. Twenty-one fourth year Further Education and Training students from the Faculty of Education, University of KwaZulu-Natal participated in this study. In order to obtain appropriate data to answer the research questions, the researcher designed three different research instruments. The open-ended questionnaire and the task-based questionnaire were administered to all the participants, whilst ten participants were chosen to be interviewed. The data that was collected was analysed qualitatively. The research findings emanating from this study suggested that pre-service mathematics teachers did not have a suitable working knowledge of mathematical modelling, but were nonetheless able to use their mathematical competencies to solve the three real-world problems that formed part of the task-based questionnaire. It was found that although the participants were aware of different strategies to solve these real-world mathematics problems, they choose to use the ones that they were most familiar with. It is hoped that this study would prompt more universities to include mathematical modelling courses in the curriculum for prospective mathematics teachers. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2008.

Since 2002, the South African Qualifications Authority (SAQA) has included mathematical literacy as a compulsory fundamental component for the Further Education and Training Certificate (FETC). This constituted a radical development in education and is intended to empower individuals so that they can function effectively in, and contribute to the democratization of the country. This exploratory study examined the mathematical literacy experiences of 12 Early Childhood Development (ECD) practitioners training toward the National Certificate in ECD at NQF L4. The study was conducted at a non-government, nonformal ECD training organization based in Durban. The practitioners were undertaking their training as part of a Learnership programme. A qualitative research methodology was employed. The data was gathered through focus group interviews, semi-structured interviews, and documentary analysis. The study revealed that the practitioners held a positive view of mathematical literacy training. In addition, it was found that such training should remain as part of the ECD qualification owing to the fact that it added value at both a personal and professional level. In interrogating the curriculum, practitioners recommended the inclusion of ECD examples, and engagement with how mathematical literacy is used in the different contexts. In terms of relevancy of content, practitioners recommended content areas that could be applied in their personal and professional lives. Mathematical literacy that related to national issues was seen as abstract, for example balance of payment in terms of the national budget. The study revealed that the background of the ECD practitioners need to be taken into account as some practitioners may not have studied mathematics before. This implies that providers will need to take into account the NQF Level 3 entry requirements and the expected embedded knowledge that practitioners are supposed to have prior to the registration of practitioners for the NQF L 4 certificate. In this regard, policy makers may also need to re-examine the issue of whether mathematical literacy is needed at the level of the qualification. Dialogue on these issues between SAQA and the different stakeholders may be necessary. Not surprisingly, the study revealed the need for suitably trained mathematical literacy facilitators given that this is a new programme. This study is by no means exhaustive, and is but a small sample of views that could be further explored in a more comprehensive study. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2005.

A qualitative case study of critical consideration for the SMT in developing inclusive schools is reported in this study. The study was conducted in one rural district in the south coast area in the province of KwaZulu-Natal. The aim of the study was to determine the SMT’s understanding of inclusive education and to establish what they consider as important in ensuring that their schools are inclusive. Lastly, it sought to identify the challenges that they faced in making their school inclusive. This was a single case study. The study targeted 5 SMT members who were involved in a focus group interview. Data analysis in the study influenced by systems theory. The two concepts defined are inclusive education and school management teams. Both the theoretical framework and the theory were used as lenses to understand the critical considerations for the SMTs in developing inclusive schools. The findings gathered from the study indicate that the SMT had very limited and often distorted understanding of the policy of inclusive education. It was also clear that they are not sure of what they consider critical for them as the SMT in the process of developing inclusive schools. At the same time they were able to indicate many challenges that they are faced with in their school. The findings suggest that this might be lack or inappropriate training on inclusive education as well as misunderstandings on inclusive strategies. The study concludes that the introduction of policy processes that requires implementation should ensure that all stakeholders involved are brought on board. It is important to get buy in from other educators to embrace diversity and understand the purpose. The process of paradigm shift is difficult to individuals especially when there are so many changes in the system, people tend to resist change. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2012.

Text in Afrikaans / Educational Studies / M.Ed.

The quality of education in most historically black schools is a source of concern for many people. The high failure rate in mathematics in particular, is believed to result in part, from the inadequacy of the teacher preparation programs at many of the colleges of education in the country. Esikhawini College of Education in KwaZulu-Natal is one of the colleges which is involved in the preparation of secondary school mathematics teachers. The appropriateness of the mathematics curriculum of this College was the subject of the study. In particular, the study aimed at the following: (i) To analyse aims and philosophies underlying the prescribed mathematics curriculum of the College. (ii) To establish the teacher educators' and student teachers' perceptions of the appropriateness of the curriculum in general. (iii) To establish the teacher educators' and student teachers' perceptions of the mathematics curriculum content and processes. (iv) To establish the quality of available materials used at the College for realisation of the curriculum goals. (v) To offer proposals and recommendations for the improvement of the education of prospective secondary mathematics teachers. Data about the perceptions of the appropriateness of the mathematics curriculum was gathered through a questionnaire which was administered to one hundred and one student teachers. The issues that arose from the questionnaire study were followed up by an interview study. The interview schedule was administered to a sample of fourteen student teachers and all six mathematics teacher educators in the College. In addition, a survey of mathematics materials available at the College library and in the mathematics department was carried out to collect further data. Some of the significant findings of the, study were : • Limitations in the College mathematics curriculum in as far as the curriculum content and processes were concerned. • Inadequacy of mathematics curriculum materials that were available and used at the College. • Low attainment in mathematics at matriculation level of most of the student teachers. • Widespread dissatisfaction with the curriculum, especially that of Mathematics Didactics. The implications of the findings for the College were considered. Amongst other suggestions is the suggestion that the College introduces a preliminary STD course in which prospective student teachers' mathematics background is enriched to enable them to cope with the demands of the College curriculum.

The purpose of this case study was to investigate the experience of six Foundation Phase teachers implementing the Singapore Mathematics Curriculum (SMC). The study makes use of Kilpatrick, Findell & Swafford‟s (2001) framework for teaching for mathematical proficiency as a conceptual lens to analyse teaching practice in the classroom. The study took place in two schools currently implementing the SMC in East London, in the Eastern Cape Province of South Africa. This qualitative study was framed within an interpretive paradigm. It relies on data collected in semistructured interviews, individual questionnaires, focus group interviews, journals and presentations. In general, the SMC was well received, and the participating teachers isolated the following as particularly positive features of their experience: - The teachers and students were enjoying the discovery of mathematics using a variety of manipulatives as stipulated when using the SMC; - The use of the model method, a specific feature of the SMC, to solve problems helped students visualise the problem; - The teachers‟ understanding of teaching for mathematical proficiency was enhanced; - The spiral curriculum informed teaching practice by allowing for building on to concepts already mastered, creating a logical flow of ideas and careful progression; - Whilst the SMC provides a more structured approach to the teaching and learning of mathematics, it provides constant opportunities for creativity and logical thinking; and - The change in attitude of both students and teachers has resulted in a greater confidence when non-routine, openended problem solving activities are engaged in. From a critical perspective the participants found the following problematic when implementing the SMC: - The teachers felt that there was insufficient drill and practice once the concept was understood. More practice and exercises were called for; - The whole class teaching approach with every student having a textbook and workbook pertaining to the lesson required a change to classroom management; and - To obtain a deeper understanding of number concepts was time consuming and re-teaching the weaker students called for additional time and adjustments to the timetable.

This dissertation examines the knowledge and knower practices in the Master’s in Educational Leadership and Management (ELM) coursework programmes at South African public universities. This study was prompted by my growing awareness of problems and tensions in the field of ELM generally, and at the level of programme design of the M Ed degree in particular. Many of these had been identified by a national audit of coursework M Eds in ELM (CHE, 2010), and this study sought to find a way of theorising these with a view to improving both course design and teaching. To this end I employed Maton’s Legitimation Code Theory (LCT) which enables critical engagement with knowledge and knowers in programmes, how they are positioned, and how this positioning may be problematic. Hence my first research question sought to discover and critique what counted as knowledge in these programmes and why, while the second asked how knowers were positioned, and why this had come to be the case. LCT has its roots in the work of Bernstein and Maton, whose preoccupation with curriculum was/is driven by a sense of social justice: if we can understand how and why the curriculum is organised and presented in a particular way, it becomes possible to re-imagine teaching and learning, making it accessible to a broader, more inclusive body of learners. The study also drew on critical realism as an underlabourer. This philosophy provided a nuanced understanding of ontology, encouraging and enabling me, as researcher, to unearth causal mechanisms driving the status quo. Only seven South African universities currently offer the coursework option of a Master’s degree in ELM, compared to thirteen when the audit was conducted in 2010. Six of the universities agreed to take part in the study. Data was gathered through content analysis of the six course outlines and interviews with individual co-ordinators or academics centrally involved in the programmes. Through the development of a translation device I was able to establishing that a knower code was dominant in the programmes. Using this point as my departure, I interrogated the knowledge practices and found that different types of knowledge were being privileged across the programmes, with some having a practical/professional leaning and others a more academic/theoretical orientation. The resultant tension does, I argue, restrict knowledge building and helps to account for the fact that the field is generally considered to be under-theorised. The fact all of these programme are registered with the same national qualifications authority, ostensibly following the same national guidelines for Master’s degrees is worrying. The study attempts to find underlying, historically significant reasons for this unevenness. An analysis of the programmes revealed a leaning towards supportive pedagogical approaches. While all programmes promote a cultivated gaze their purposes are not always the same. While a hegemonic practices potential for opening counts as knowledge, cultivated gaze can enable transformation, it can also encourage that can impede real change and empowerment. The study has the up much needed debate on what is meant by a Master’s in ELM, what and what kinds of knower are envisaged.

The research presented in this thesis is a case study located in the interpretive paradigm of qualitative research. The focus is on the use of van Hiele's theory to explore problems encountered in circle geometry by grade 11 learners and making some policy recommendations concerning the curriculum structure and teaching of the geometry at all grades. The interpretation is based to the learners' background in geometry i.e. their prior knowledge and experience of learning geometry. The study was carried out over a period of three years. The data collection process took a period of two months (April and May 2003) with a group of 21 grade 11 mathematics learners in a rural senior secondary school in the Eastern Cape. The researcher used document analysis, worksheets, participants' observation, van Hiele tests, a questionnaire and semi-structured interviews to collect data. The study showed that the structure of the South African geometry syllabus consists of a some what disorganized mixture of concepts. It is not sequential and hierarchical and it sequences concepts in a seemingly unrelated manner. The study revealed that the South African high school geometry curriculum is presented at a higher van Hiele level than what the learners can attain. The findings of the study showed that many of the grade 11 learners were under-prepared for the study of more sophisticated geometry concepts and proofs. Three categories of reasons could be ascribed to this: Firstly, there was insufficient preparation of learners during the primary and senior phases. Secondly the study indicated that there is overload of geometry at the high school level in the South African mathematics curriculum. Thirdly, the over-reliance on the traditional approach to teaching geometry, poor presentation of mathematical technical concepts and language problems, were identified as possible additional reasons for the poor learner understanding of geometry in general and circle geometry in particular. The study recommends that the structure of the South African geometry curriculum should be revisited and redesigned. Teachers should be empowered and developed to be more effective in teaching geometry through further studies in mathematics and in-service workshops. They should also be engaged in the process of implementing the van Hiele's theory in the teaching of geometry in their classrooms.

The 1820 Foundation INSET Farm School Project is described in order to set the context in which this illuminative evaluation of a Teacher Development course took place. The concepts of training, education and development are discussed and it is suggested that the term 'education' encompasses a training-development continuum. The design and implementation of the Teacher Development course, which attempts to promote both personal and professional development, are presented, and the facilitator discusses i) her attempt to encourage teacher control of the course and, ii) the factors which mitigate against teacher control. The decision to use the illuminative evaluation method is placed in the context of interpretive research methodologies, and the methods of data collection are discussed. A wide range of data sources is used, but primary importance is attached to i) a questionnaire administered to the five teachers involved and ii) a group interview and individual interviews with the teachers. Factors which emerge in the illumination of the data indicate that teacher control of development courses in farm schools in the Eastern Cape is problematic, that the teachers' preference is for professional development, and that development seems to take place through implementation of training strategies.

South African education is in the process of undergoing what has become known as a "paradigm shift", requiring a change from the familiar transmission method to outcomes-based education (OBE) founded on social constructivist theories oflearning and teaching. Teachers, (45% of whom are poorly qualified), "will play a pivotal role in the success or failure of this change. There is therefore an urgent need to re-educate in-service teachers in the philosophy, and related methodologies underpinning Curriculum 2005. To this end, in-service education courses need to be developed "which will encourage teachers to reconstruct their beliefs about teaching and learning. INSET programmes in the past were aimed at either "topping up" qualified teachers, or "adding on" for under qualified teachers - neither of which have proved successful. It is therefore unlikely that applying similar methodologies to support teachers in the shift to OBE will meet with success, nor will simply "training" teachers to use the new learning programmes. Government documents on Education Policy are calling for teachers to become reflexive practitioners, able to guide learners in their efforts to achieve the critical outcomes which are intended to develop a competent citizenry of lifelong learners. Therefore, teachers ought to be empowered as curriculum developers in their own right. This interpretative case study hoped to find out from teachers themselves what aspects of an activity-based environmental education course acted as change agents in assisting them to begin the shift to constructivist theories of teaching and learning. A variety of research tools were used, including questionnaires, interviews, journals, narratives and concept maps, all of which provided a rich source of data for interpretation. From what was gained from four participants in this research, tentative suggestions for incorporation into the next cycle of action research in future INSET programmes are made.