This study explores the phenomenon of mathematics anxiety with respect to a group of matric students at a secondary school in KwaZulu-Natal. The contextual factors associated with mathematics anxiety were examined from the perspective of ten mathematics students and three teachers of mathematics. In this study, qualitative research methodology was used. The data was gathered through semi-structured interviews and questionnaires. Various factors, such as the belief in mathematical myths and negative experiences during the early school years, interact to contribute to the phenomenon of mathematics anxiety. The study revealed the need to dispel mathematical myths, to create supportive learning environments for students, and to provide support for mathematics teachers in the form of on-going professional development. / Thesis (M.Ed.)-University of Natal, Durban, 2000.

<p>The aim of this study was to investigate the hypothetical view that the use of familiar social institutions in the formulation of mathematical problems by mathematics pre-service teachers will enable them to find solutions to problems by taking meaning, context and realities of a problem into consideration. The approach to investigate this hypothetical view was to describe the mathematical behaviour of pre-service teachers in an application and modelling context. This study, therefore, described the strategies used to arrive at solutions for problems from real life situations that are familiar to the participants.</p>

This dissertation begins by reviewing the difficulties experienced in teaching mathematics to pupiis, weak in mathematics, in the Senior Secondary phase of Cape Education Department schools. The possible use of computer-aided instruction (CAl) in improving the examination performance of such pupils is considered. A suitable CAl software program, viz. the SERGO system, is identified and its operation is described in detail. The researcher investigates, both from a quantitative and a qualitative aspect, the change in mathematics examination performance of a number of weak in mathematics pupils, as a result of receiving an extended period of extra tuition on the SERGO system. It needs to be noted that these pupils are passing candidates in other subjects, and have above average intelligence. They are not slow learners. The researcher identifies three categories of pupils who are weak in mathematics. Different programmes of remediation are recommended for each category. The possible use of the SERGO system as a stand-alone instrument of remediation , for pupils working in pairs, and the possible use by H.G. pupils in combined H.G./S.G. classes are also investigated.

Like many South African high school mathematics teachers I have followed the development of computers with interest and I have tried wherever possible to gain some experience on them. Thus when microcomputers became more readily available the mathematics department at our school, Graeme College in Grahamstown, motivated for the school to acquire this powerful new tool. The eventual outcome was that the Old Boys' Association donated to the school 3 BBC B microcomputers with monitors, a disc drive, a printer and two tape recorders. These have now been in the school for three years. The acquisition prompted this research project which takes the following form:- 1) An investigation into some of the uses of microcomputers in schools and, in particular, in the mathematics classroom. 2) A statement on the present position adopted by the Cape Education Department on the use of computers in schools. 3) A study of what the experience has been in other countries, particularly in Britain and the United States of America. 4) A description of an investigation which was undertaken at our school using the method of Action Research and Triangulation. Its aim was to investigate the feasibility of using a microcomputer to aid in the teaching of mathematics and the reaction of the pupils to this innovation. Three different approaches were implemented. a) The algorithmic approach: In this investigation a class of standard eight pupils were required, with the help of the teacher, to write, enter and test a short computer program which would solve any pair of simultaneous linear equations of the form, ax + by = c. Their reaction to this form of instruction was noted by myself and a non-participant observer. The pupils themselves were also asked to express their reactions, both verbally and by filling in a prepared questionnaire. Examples of worksheets, exam questions and analysed questionnaires are given in the appendix. Short programs which examine various other mathematical concepts are also listed and discussed. b) The audio-visual approach: In this case use was made of a graphs software package in which the computer would draw either a straight line, circle, parabola or hyperbola when the appropriate variables were entered. This package also includes a graph game facility where participants are required to find the equation of the graph which will pass through three given points. Points are awarded if the correct type of graph is chosen and the variables are entered within a certain time interval. The pupils involved in this investigation were standard eight higher grade mathematics pupils and their reaction to this form of instruction was again noted using the methods described in (a) above. c) Computer Aided Instruction: Here I was most fortunate to be able to make use of the Rhodes University PLATO Centre. This allowed me to take a class of eighteen standard eight higher grade mathematics pupils to the Centre. Here during four sessions, each of just over an hour, the pupils interacted with the software on the computer terminal. The software used was a set of five lessons written by Barbara Lederman of the Community College Maths Group, of the University of Illinois in 1976. The lessons give instruction and require the pupils to transform, plot and draw the graphs of linear equations of the form, ax + by + c = 0, x = c and y = b. They are also taught and required to find the equations of given straight lines. Their reactions to this form of instruction are discussed after each session. 5) In conclusion some thoughts are given on how computers can best be utilised in the school situation, with particular reference to the teaching of mathematics.

Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2007. / Twelve years into a democracy, South Africa still faces many developmental challenges. Since 2002 Universities of Technology in South Africa have introduced Foundational Programmes/provisions in their Science and Engineering programmes as a key mechanism for increasing throughput and enhancing quality. The Department of Education has been funding these foundational provisions since 2005. This case study evaluates an aspect of a foundational provision in Mechanical Engineering, from the beginning of 2002 to the end of 2005, at a University of Technology, with a view to contributing to its improvement. The Cape Peninsula University of Technology (CPUT), the locus for this case study, is the only one of its kind in a region that serves in excess of 4.5 million people. Further, underpreparedness in Mathematics for tertiary level study is a national and international phenomenon. There is thus a social interest in the evaluation of a Mathematics course that is part of a strategy towards addressing the shortage in Engineering graduates. This Evaluation of integration of the Foundation Mathematics course into Foundation Science, within the Department of Mechanical Engineering at CPUT, falls within the ambit of this social need. An integrated approach to curriculum conception, design and implementation is a widely accepted strategy in South Africa and internationally; this approach formed the basis of the model used for the Foundation programme that formed part of this Evaluation. A review of the literature of the underpinnings of the model provided a theoretical framework for this evaluation study. In essence this involved the use of academic literacy theory together with learning approach theory to provide a lens for this case study. The research methodology used was largely qualitative, with both qualitative and quantitative methods used for purposes of triangulation. The evaluation was conducted of four key aspects of integration of foundation mathematics into foundation science, namely conception, design, implementation and impact. This provided the framework for the main argument of this thesis, namely that conceptual and design flaws in the integration modelled to student learning of Mechanics concepts (in Foundation Science) not being effectively supported. The final section of the study outlines recommendations for improvement of the foundation mathematics course. It also identifies areas for future research. / National Research Foundation (NRF)

D.Ed. (Didactics) / The purpose of this research project was to ascertain whether the Mathematics curriculum for apprentices comply with scientifically defensible criteria. Important conclusions regarding characteristics of Mathematics, tuition and learning guides, and the aims of Mathematics, were reached ...

This research study investigated the ways in which a mathematics module, informed by an enactivist philosophy, enabled pre-service teachers to unpack the reality of their teaching practice in terms of proficient teaching. Given the generally poor mathematics results in South Africa it is not enough for teachers to be merely proficient in Mathematics. They also need to be in a position to explain important mathematical concepts to children in a manner that will encourage and develop an understanding of the basic mathematical concepts. It was my intention with this study to determine whether a mathematics education module, that embraced the underlying themes of enactivism as part of its teaching pedagogy, could have the potential to develop and increase the skills of pre-service teachers’ teaching for proficiency in Mathematics. The mathematics module was underpinned by five themes of enactivism namely: autonomy, embodiment, emergence, sense-making and experience and was designed to supplement the pre-service teachers’ basic skills in Mathematics in the Intermediate Phase. This mathematics module was offered to fourth year pre-service teachers completing a B.Ed. in the Foundation Phase at a private institute specialising in the training of teachers. The theoretical framework was informed by enactivism and how the themes of enactivism could be used as a vehicle to develop teaching proficiency. The study was qualitative in nature and situated within an interpretivist paradigm. The specific perspectives of interpretivism that were used were hermeneutics, phenomenology and reflexivity. The research design was a case study that contained elements of action research and encompassed three phases of data collection. The first phase focused on the pre-service teachers’ approach to teaching Mathematics and what this brought forth in terms of the reality of their teaching practice and the problems they encountered. The second phase undertook to determine what growth and development of teaching proficiency in Mathematics had emerged over the research period. The final phase was undertaken after the pre-service teachers had graduated and were employed as full time teachers in the Intermediate Phase. The analytical framework and lens through which the data was analysed was that of Kilpatrick, Swafford and Findell’s (2001) strands of mathematical proficiency. The argument that I present is that the themes of enactivism did contribute to the growth of the pre-service teachers’ teaching for mathematical proficiency. The themes of embodiment and experience were major contributions in revealing that this was a reality for the pre-service teachers from a practical perspective and was what they would be able to take away with them. However the theme of emergence stood out as the principle that generated the most awareness and growth and which, in turn, affected the participants’ autonomy.

M.Ed. (Subject Didactics) / The ideal in education is that the curriculum provided (by the teacher) and the curriculum received (by the pupil), as originally drafted by the designers, should agree. However, there are indications that this ideal is often not achieved in the teaching of Mathematics, the reason being, inter alia, the backlog in the subject arising from inadequate knowledge as a result of misconceptions in regard to certain basic concepts. Misconceptions among pupils indicate that the shaping of understanding and mastering the concepts have been inadequate. It should be kept in mind that frame of reference and world view are peculiar to each pupil and will be utilized by him for interpreting and processing new concepts. It is therefore essential that the world view of the pupil should be investigated as being the factor which is probably basic to the problem of misconception. The point of departure is therefore that pupils have divergent world views, which invariably affect their understanding of Mathematics. Throughout the ages misconceptions were inextricably part of natural science in general and Mathematics in particular. During modern times, since the 1960s, Boyd has paved the way for reflection regarding misconceptions in natural scientific teaching by using the term "unfounded beliefs", and the attention was actively drawn to the problems surrounding misconceptions. Terms now mostly used as synonyms for misconceptions are conceptual framework, alternative frameworks, and alternative conceptions...

Average students -- 6th, 7th, 8th grades (middle schools) -- Manipulatives and authentic materials -- Administrative responsibilities.

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