M.Ed. (Didactics) / Please refer to full text to view abstract

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Science, 2002. / In this thesis I consider how mathematics students in a traditional firstyear Calculus course at a South African university appropriate mathematical objects which are new to them but which are already part of the official mathematics discourse. Although several researchers have explained mathematical object appropriation in process-object terms (for example, Sfard, 1994; Dubinsky, 1991, 1997; Tall, 1991, 1995, 1999), my focus is largely on what happens prior to the object-process stage. In line with Vygotsky (1986), I posit that the appropriation of a new mathematical object by a student takes place in phases and that an examination of these phases gives a language of description for understanding this process. This theory, which I call “appropriation theory”, is an elaboration and application of Vygotsky’s (1986) theory of concept formation to the mathematical domain. I also use Vygotsky’s (1986) notion of the functional use of a word to postulate that the mechanism for moving through these phases, that is, for appropriating the mathematical object, is a functional use of the mathematical sign. Specifically, I argue that the student uses new mathematical signs both as objects with which to communicate (like words are used) and as objects on which to focus and to organise his mathematical ideas (again as words are used) even before he fully comprehends the meaning of these signs. Through this sign usage the mathematical concept evolves for that student so that it eventually has personal meaning (like the meaning of a new word does for a child); furthermore, because the usage is socially regulated, the concept evolves so that its usage is concomitant with its usage in the mathematical community. I further explicate appropriation theory by elaborating a link between the theoretical concept variables and their empirical indicators, illustrating these links with data obtained from seven clinical interviews. In these interviews, seven purposefully chosen students engage in a set of speciallydesigned tasks around the definition of an improper integral. I utilise the empirical indicators to analyse two of these interviews in great detail. These analyses further inform the development of appropriation theory and also demonstrate how the theory illuminates the process of mathematical object appropriation by a particular student.

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

This study was based on the Scientific and Technology Literacy Project study done between 1996 and 2001. It sought to determine whether Vee-diagramming could help enhance grade 10 township learners understanding of some aspects of electricity. It also sought to find out whether age and gender influenced the learners understanding of these concepts.

This thesis is a study of the problems of teaching poetry to English speaking pupils at South African senior schools. It is a study of what is generally agreed to be 'a peculiarly difficult department of teaching' Reeves 1958. Some would go as far as to suggest that the teaching of poetry is the most difficult aspect of any school subject : "No topic in the school curriculum has so many pitfalls as the teaching of poetry in the classroom: it is easier to go astray in attempting to promote aesthetic responses to a poem than in any other kind of lesson. 'Currey {19S8) p. 126.' If one may judge too by the number of complaints from a large body of teachers (see Chapter Four) about the difficulty of teaching poetry successfully the assessments given by Reeves and Currey appear to be well- founded. Additional weight is given by some of the attitudes of pupils themselves towards poetry and the poetry lesson (see Chapter Three). Further confirmation is evident at Teachers' Conferences and from examiners' reports that examination questions on poetry are often among the most badly answered and the least popular of all questions set. Even more significant, perhaps. were the responses from two separate graduate student teacher groups (U.E.D. English Method classes, Rhodes University 1965, 1967). When asked at the beginning of the course to name the one type of English lesson they felt least confident in handling, 42 of the 64 student teachers answered, 'The poetry lesson'. Into. p. 1.

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

This mini-thesis documents and analyses an action research project which I conducted with secohdary school teachers. The teachers wished to learn more about environmental education so that they could run their own programmes. I, on the other hand, wanted to improve environmental education programmes offered at the centre where I worked. I hoped that through encouraging teacher participation and involvement, I could begin a process through which the teachers themselves could contribute to, and be in greater control of, their own learning in environmental education. As an introduction to this mini-thesis, I provide some background information on the centre, and state the reasons for having embarked on this project. In addition, I outline the literature and various research findings pertinent to this study. For the purpose of this study, I have selected emancipatory action research as a mode of research, since I believe that emancipatory action research, which embodies processes of reflection and informed action, constitutes the possibility for authentic, emancipatory change in the practice of teachers. The bulk of this thesis, therefore, documents the first two cycles of the action research process and the experiences of those involved in the process. I also briefly comment on some of the claims of action research as a method for research. An important feature of this thesis is that it addresses the possibilities of and constraints to implementing education for the environment in the teachers' practices. The existence of the latter is acknowledged and discussed from my perspective and those of the participating teachers. The study, furthermore, documents teachers' understandings of environmental education, and how this determines the kind of environmental education activities in which they engage. In the final analysis, I argue that the education system we inherited from the apartheid regime has had the effect of producing passive, disempowered and highly demotivated teachers with extremely low levels of self confidence and assertiveness. Despite this fact, I have not only had the opportunity to wltness some positive attitudinal changes occurring in teachers as the study progressed; the project has also enhanced my own understanding of environmental education and the effect the apartheid education system had in shaping my own thoughts and life.

The teaching of geometry has been neglected at the expense of other disciplines of mathematics such as algebra in most secondary schools for Africans in South Africa. The research aimed at establishing the extent to which creativity and divergent thinking enhance the internalisation of geometry concepts using the problem-based approach and on encouraging learners to be creative, divergent thinkers and problem solvers. In the research, Grade 7 learners were guided to discover the meaning of geometric concepts by themselves (self-discovery) and to see concepts in a new and meaningful way for them. This is the situation when learners think like the mathematicians do and re-invent mathematics by going through the process of arriving at the product and not merely learn the product (axioms and theorems), for example, discover properties of two- and three-dimensional shapes by themselves. Furthermore, learners were required to use metaphors and analogies, write poems, essays and posters; compose songs; construct musical instruments and use creative correlations in geometry by using geometric shapes and concepts. They tessellated and coloured polygons and pentominoes in various patterns to produce works of art. Divergent thinking in geometrical problem solving was evidenced by learners using cognitive processes such as, amongst others, conjecturing, experimenting, comparing, applying and critical thinking. The research was of a qualitative and a quantitative nature. The problem-based approach was used in teaching episodes. The following conclusions and recommendations were arrived at: * Geometric shapes in the learner's environment had not been used as a basis for earning formal geometry. * Second language learners of mathematics have a problem expressing themselves in English and should thus be given the opportunity to verbalize their perceptions in vernacular. * Learners should be made to re-invent geometry and develop their own heuristics/strategies to problem solving. * Learners should be trained to be creative by, for example, composing songs using geometric concepts and use geometric shapes to produce works of art, and * Activities of creativity and divergent thinking should be used in the teaching and learning of geometry. These activities enhance the internalisation of geometry concepts. Groupwork should be used during such activities. / Educational Studies / D. Ed. (Didactics)

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.