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Given the controversy surrounding the theoretical concept of mathematical literacy within mathematics education community around the world and, in particular, its introduction as a new subject of study in the South Africa’s FET curriculum as part of a social transformation process, it seemed necessary and appropriate that a study of this nature had to be undertaken. Thus the study explored perceptions of the notion of ‘mathematical literacy’ as a competence and as a subject of study. It focused on a group of first-year in-service teachers who were part-time students in the faculty of education at Edgewood Campus in the University of KwaZulu-Natal, as well as the documentary analysis of some of the South African curriculum policy documents. The guiding research questions for this study were: (a) what understandings or notions of mathematical literacy are evident in the South African curriculum documents? (b) What are mathematics educators’ perceptions of the competencies of a mathematically literate person? (c) What are their perceptions of, beliefs and views, and initial experiences about mathematical literacy as a subject of study? (d) How do these perceptions and/or understandings play out in the implementation of the new Mathematical Literacy curriculum? In an attempt to answer these questions, I began by, first, exploring the wider theoretical perspectives (both locally and internationally) in extant literature within the domain of mathematics education, and which underpins the debate about mathematical literacy and its related terms as well as informing the recent curriculum change, particularly in South Africa. In the process I discussed the different connotations that were used to describe mathematical literacy and its related terms, as well as the arguments in favour of and against its introduction as a subject of study. Secondly, I explored teachers’ understandings of the concept of mathematical literacy both as a competence and as a subject of study in relation to the NCS documents, as well as the problems associated with its implementation and the importance of understanding the interplay between content and context used for its development. It is argued, however, that re-framing of ‘mathematical literacy’ as a subject of study rather than a competence proves to be problematic in terms of the distinction that could be drawn between epistemology and pedagogy. Finally I have discussed the implications which the findings of this study have for policy and practice, and for further research. Data on the understandings and teachers’ perceptions about mathematical literacy as a competence and a subject of study were obtained using both qualitative and quantitative styles of research as a mixed-mode approach. The major findings of this study are that (1) teachers generally perceived mathematical literacy as a subject of study (2) the South African curriculum documents portray ML as a subject, and therefore framed as such; (3) teachers generally consider a person mathematically literate if that person could do basic arithmetical calculations in everyday life (4) from the international perspective, there are variations on the interpretation of ML, and finally (5) the study has revealed that teachers had difficulties pertaining to their own pedagogical content knowledge of the new subject. Based on these findings it can be concluded that there is need for a sustained monitoring of the implementation process, reviewing of policy documents, and professional development of teachers involved with the teaching of mathematical literacy. / Thesis (M.Ed.)-University of Kwazulu-Natal, 2007.

This was an evaluative study undertaken to unpack some of the factors which could explain Transkei matriculation students' apparent poor conceptual understanding of Mathematics and to throw some light on possible solutions to their problems. In addition the study attempted to examine how Mathematics as well as the learning and teaching of Mathematics, were viewed by Transkei teachers and students at the high school level. The theory of quadratic equations, inequalities and their graphs constituted the mathematical content research area of this study. This topic was chosen because of the key role that it plays in the matriculation Mathematics syllabus. There were 8 research questions which led to 8 hypotheses. The research sample comprised 311 matriculation students taking higher grade Mathematics and their 10 Mathematics teachers from 10 schools in the Umtata education circuit. Four researcher-designed instruments, namely: a diagnostic test (students'), a student interview schedule, a teachers' questionnaire, and a teacher interview schedule were used. The diagnostic test consisted of 38 items aimed at addressing the first 7 research questions. Students' mean scores for each group of items of the test addressing a particular research question were computed and compared against a criterion score of 60%, using the "Z” statistic. In addition, an analysis of students' scripts was carried out and clinical interviews on a sample of the subjects (students) were conducted to find out their conceptual difficulties/misconceptions. The teachers' questionnaire and interview schedule were used to ascertain the teachers' disposition towards Mathematics teaching. Accordingly, teachers were divided into two groups A and B on the basis of their scores in relation to the median for the whole group. This enabled the testing of hypothesis 8. In this regard, means for the students taught by the two respective groups of teachers were comared by using "Z" statistic to establish if they were statistically different from each other. Teachers' reasons for their responses to some of the items in the questionnaire were analyzed and discussed with a view to finding out their favourite teaching styles and some of the difficulties they faced in order to be as effective as they wished to be. Analysis of data for research questions 1-7 showed that students did not have sufficient pre-requisite knowledge, and did not display a satisfactory level of mastery in solving quadratic equations and inequalities, and interpretation of graphs for quadratic equations and inequalities. Students' difficulties identified from the findings of this study were classified into 7 categories, namely: mathematical terms, mathematical symbolic language, mathematical skills, form in mathematics, over generalisations, translation and conceptual difficulties. The "Z" test for hypothesis 8 showed that students taught by teachers whose teaching strategies were more student-centred performed better than those who were taught by teachers whose teaching was inclined towards teacher-centredness. Finally, recommendations for teachers, curriculum planners, education authorities and other researchers are also made. / Thesis (M.Ed.)-University of Durban-Westville, 1994.

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 explored the teaching processes in mathematics education for adults and how they are shaped by certain social and institutional forces. Teaching processes included the selection and ordering of content to be taught; the choice of such techniques as lectures or groupwork; the expectations, procedures and norms of the classroom; and the complex web of interactions between teachers and learners, and between learners themselves. The study addressed three broad questions: (1) What happens in adult mathematics classrooms? (2) What do these phenomena mean for those involved as teachers or learners? and (3) In what ways do certain factors beyond the teachers’ control affect teaching processes? The theoretical framework linked macro and micro approaches to the study of teaching, and offered an analytical perspective that showed how teachers’ thoughts and actions can be influenced and circumscribed by external factors. Further, it provided a framework for an analysis of the ways in which teaching processes were viewed, described, chosen, developed, and constrained by certain “frame” factors. The study was based in a typical setting for adult mathematics education: a community college providing a range of ABE-level mathematics courses for adults. Three introductory-level courses were selected and data collected from teachers and students in these courses, as well as material that related to the teaching and learning of mathematics within the college. The study used a variety of data collection methods in addition to document collection: surveys of teachers’ and adult learners’ attitudes, repeated semi-structured interviews with teachers and learners, and extensive ethnographic observations in several mathematics classes. The teaching of mathematics was dominated by the transmission of facts and procedures, and largely consisted of repetitious activities and tests. Teachers were pivotal in the classroom, making all the decisions that related in any way to mathematics education. They rigidly followed the set textbooks, allowing them to determine both the content and the process of mathematics education. Teachers claimed that they wished to develop motivation and responsibility for learning in their adult students, yet provided few practical opportunities for such development to occur. Few attempts were made to encourage students, or to check whether they understood what they were being asked to do. Mathematical problems were often repetitious and largely irrelevant to adult students’ daily lives. Finally, teachers “piloted” students through problem-solving situations, via a series of simple questions, designed to elicit a specific “correct” method of solution, and a single correct calculation. One major consequence of these predominant patterns was that the overall approach to mathematics education was seen as appropriate, valid, and successful. The notion of success, however, can be questioned. In sum, mathematics teaching can best be understood as situationally- constrained choice. Within their classrooms, teachers have some autonomy to act yet their actions are influenced by certain external factors. These influences act as frames, bounding and constraining classroom teaching processes and forcing teachers to adopt a conservative approach towards education. As a result, the cumulative effects of all of frame factors reproduced the status quo and ensured that the form and provision of mathematics education remained essentially unchanged.

This dissertation describes the personal problem-solving language used by grade five students as they solve mathematical problems. Student classroom interactions were audio-taped and filmed during the course of the 199711998 school year. Ethnographic methods and a qualitative research approach were used for gathering, analyzing and interpreting the data. The questions that guided the study were: (1) how children solve problems and (2) what tools and symbols systems do they use. The purpose was to understand the problem-solving process better. The underlying assumptions were that: (1) most students can generate their own strategies and problem-solving theories; (2) many students can solve complex mathematical problems. The findings revealed that students generate problem-solving strategies and symbol systems that resemble the tools that they chose to use and their individual learning styles. Most students needed to talk about their proceedings and often used a personalized language form and nomenclatures that were uniquely creative as place holders for the more exact terminology, which replaced the invented language. The data also captured highly creative moments when the students experienced a heightened sense of awareness and sensibility while they explored their problem spaces. It was also evident that there is a transfer from the child's personal problem-solving style, choice of tools and creative symbol systems into his unique representation of the problem's solution. This transfer supports Vygotskian notions that language mediates thought and that social interaction mediates language.

Mathematics 436 is the advanced mathematics course offered to students in secondary IV in the province of Quebec. Although the course is designed to challenge students in the advanced stream, it has produced a high number of failures. This study examines the relationship between mathematics anxiety and achievement in Mathematics 436. Fifty-six students from an English high school on the island of Montreal took part in the study. The Mathematics Anxiety Rating Scale for Adolescents was used to measure the level of mathematics anxiety experienced by the students. In addition, grades from the previous year in mathematics were obtained, as well as grades from the present year, and the final examination. The results of the study suggest that students enrolled in Mathematics 436 experience a high level of mathematics anxiety. As well, higher levels of mathematics anxiety experienced by the students are associated with poor performance in mathematics.

Over the last decade or two, there has been a discernible move to include modeling in the mathematics curricula in schools. This has come as the result of the demand that society is making on educational institutions to provide workers that are capable of relating theoretical knowledge to that of the real world. Successful industries are those that are able to effectively overcome the complexities of real world problems they encounter on a daily basis. This research study focused, to some extent, on the different definitions of modeling and some of the processes involved. Various examples are given to illustrate some of the methods employed in the process of modeling. More importantly, this work attempted to build on existing research and tested some of these ideas in a teaching environment. This was done in order to investigate the feasibility of introducing mathematical concepts within the context of dynamic geometry. Learners, who had not been introduced to specific concepts, such as concurrency, equidistant, and so on, were interviewed using Sketchpad and their responses were analyzed. The research focused on a few aspects. It attempted to determine whether learners were able to use modeling to solve a given real world problem. It also attempted to establish whether learners developed a better understanding when using Sketchpad. Several useful implications have evolved from this work that may influence both the teaching and learning of geometry in school. Initially these learners showed that, to a large extent, they could not relate mathematics to the real world and vice versa. But a pertinent finding of this research showed that, with guidance, these learners could apply themselves creatively. Furthermore it reaffirmed the idea that learners can be taught from the general to the more specific, enabling them to develop a better understanding of concepts being taught. Perhaps the findings and suggestions may be useful to pre-service and in-service educators, as well as curriculum developers. / Thesis (Ph.D.)-University of Durban-Westville, 2004.

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 research investigates the translatability of English Academic Discourse into isiZulu with specific reference to the discourse of Mathematics. The focus is on the translation processes and strategies used in the translations to maintain the core meaning of concepts. The reason for the research is that African-language speaking learners experience problems in understanding and using crucial academic concepts in English and the language that contextualizes them. The research thus analyses translated texts from the mathematics and mathematical literacy learning areas selected from a Multilingual Teachers’ Resource Book written for learners at the GET Level (Grade 7-9) in order to explore the process of translation by examining the isiZulu translated texts (target texts) of English source texts, and their subsequent back-translations. The main focus is on the quality of the translation and the strategies translators use in order to retain the core meaning of the original text, especially when languages are non-cognate. The study found that although formal equivalence between non-cognate languages is difficult to achieve, functional or near-equivalence is not always appropriate either, especially in specialized discourses of a scientific or technical nature. The solution lies in building up the technical discourse in the African Languages. This research also explores possible limitations in the translator-training offered for bilingual translators of English and isiZulu and leads to recommendations as to what the translator-training should focus on in the long term. Findings from this research should contribute to the language policy debate on isiZulu as a viable medium of instruction as well as to the process of terminology development. / Thesis (M.A.)-University of KwaZulu-Natal, Pietermaritzburg, 2009.