The purpose of this study was to extend our knowledge about mathematical literacy learning with the focus on a foundational preservice teacher education module required for prospective teachers. The construct of mathematical proficiency provided a framework for understanding how successful learning depends on a multiplicity of competences, and in particular to highlight the pivotal role of a productive disposition towards mathematics in becoming mathematically literate. The main questions that guided the study were as follows: What is the nature and strength of the productive disposition strand of mathematical proficiency evident in preservice teachers entering a Mathematical Literacy module and how does this productive disposition change over the course of the module? and What pedagogical practices and learning behaviours best enable preservice teachers to achieve mathematical literacy? The study was undertaken as two overlapping case studies, the first describing the preservice teachers at the onset of their studies in the Mathematical Literacy for Educators module, and in the second, a three part story-telling case study of the unfolding of the module over three years from 2003 to 2005. The mathematics autobiographies of 254 preservice teachers and the data obtained from a premodule questionnaire and introductory class activities contributed to the first case study which was summarised in the form of three fictional letters. Written reflections, final module evaluations and the insights of my co-workers contributed to the second case study which documented the successes and struggles of the preservice teachers as the module unfolded each year. Complementary mixed methods techniques were used to analyse the multiple sources of data and to weave strong ropes of evidence to support the findings. Statistical analysis pointed to themes which were supported or tempered by qualitative evidence reported in the voices of the preservice teachers themselves. The analysis revealed that many of the preservice teachers entering the Mathematical Literacy for Educators module had found their school experience of mathematics to be dispiriting and consequently had developed negative dispositions towards the subject. The change in this disposition depended on their success in the module and the empathy shown by the lecturer. Helpful pedagogical practices were found to be those that supported language difficulties in learning mathematics, assisted in organising learning, remediated for poor schooling background in mathematics and took account of the diversity amongst the students. I argue that many of the lessons learned and insights gained from teaching the Mathematical Literacy for Educators module are relevant to the expanding number of mathematics courses required as part of humanities programmes. In addition, they can inform practices at school level and in both in mathematics and mathematical literacy teacher education. / Thesis (PhD.)-University of KwaZulu-Natal, 2007.

This study had two components: 1) Investigating the conceptual understanding of teachers teaching elementary mathematics at primary schools in the province of KwaZulu-Natal, who had been successful in their mathematics modules in the National Professional Diploma in Education (NPDE) teacher upgrading program, and 2) Investigating the influence of their mathematical lifehistories on their understanding and personal philosophies about mathematics. It firstly required the NPDE students from the University of KwaZulu-Natal to complete a questionnaire adapted from the TELT interview schedule used by Liping Ma (1999). This questionnaire was to assess whether these high scoring teachers had an understanding of basic mathematical concepts that could have been regarded as being profound. The second part of the study was designed in order to get these teachers to examine their mathematical life histories and then to look at how their life histories could have influenced their level of understanding. It was found that these teachers were procedurally capable and were aware of the algorithms that could be used to solve the problems posed, but they lacked deep understanding of the concepts and were thus conceptually weak. None of the teachers demonstrated an understanding of the fundamental mathematics concepts that were assessed, that could be regarded as been ‘profound’. The mathematical life history portion of this study revealed that these teachers, having experienced mathematics education very differently due to their Apartheid influenced education, mentioned that there were definite influences that had a marked effect on their outlook on the subject and thus their belief in their ability to do basic/ fundamental mathematics. / Thesis (M.Ed. (School of Education and Development)) - University of KwaZulu-Natal, Pietermaritzburg, 2007.

Preservice teachers have had a twelve year "apprenticeship of observation" in the practice of teaching and as a consequence have internalised a set of beliefs about Mathematics teaching and learning. These beliefs are usually implicit but nevertheless influence the teaching practice of the preservice teachers to the extent that they "teach as they were taught." A preservice Mathematics Education course, falling as it does between the prospective teachers' experiences as scholars, and their future teaching experience provides an ideal opportunity for preservice teachers to review their personal beliefs prior to carrying them over to teaching practice. In order to facilitate this review, a series of activities was designed as part of a Mathematics Education course for preservice secondary phase Mathematics teachers. These activities provided opportunities for student teachers to examine their beliefs, to discuss and write about these beliefs, to read about the beliefs of others, and finally to decide whether they wished to retain or modify their personal beliefs. Data on the personal theories of the preservice teachers was obtained from the written responses to various critical incidents, from metaphors for the teaching and learning of Mathematics drawn and described by the preservice teachers, and from interviews with selected participants. These theories were classified into qualitatively different categories. After completing several developmental activities and a five week period of classroom teaching, the preservice teachers were invited to reconsider their personal theories and amend their metaphors. This provided evidence of reflection and development in their thinking. It is contended that the personal theories of preservice teachers are not only reflected in their classroom practice but also function as barriers to impede acceptance of novel ideas and innovations. The findings of this study contribute to the understanding of the thinking of preservice teachers and inform the development of a curriculum for the Mathematics Education component of a Professional Studies course. / Thesis (M.Ed.)-University of Natal, 1999.

The aim of this study was to explore the concept of pedagogical content knowledge, or PCK, and its use in the practice of teaching. Teacher knowledge is a significant factor in determining learner gains in all school subjects. However, little is known about the role of the different types of knowledge that teachers are supposed to possess in particular in a developing world context. PCK was introduced by Lee Shulman in 1986 and has since been the subject of much research in teacher education. Pedagogical content knowledge is thought to be a highly specialised form of teacher knowledge that intertwines subject matter (content) knowledge and general pedagogic knowledge. In this study, I examined the levels of PCK of 39 mathematics teachers; I tried to determine how they used PCK in their teaching of mathematics; what determined their PCK; and to what extent PCK influenced the mathematical achievement of their learners. The methodology that I used was lesson observation of 42 video-recorded grade 6 mathematics lessons from various schools in the greater Umgungundlovu district of Pietermaritzburg in KwaZulu-Natal. These schools were selected through random stratified sampling to participate in a larger regional achievement study, designed to investigate the factors which influence learning in schools. I was part of a research team that analysed the videos of the mathematics lessons, with the intention of getting the ‘big picture’ of mathematics teaching and learning in South Africa. Using the data from my observations, I developed a PCK instrument and attempted to measure the teachers’ PCK. I then tried to link these PCK scores to other variables in my study, which included a teacher’s test and learner tests. I tested the consistency of my instrument and the teachers’ PCK scores appeared fairly consistent across lessons, but that more research is needed to interrogate that. My initial findings suggested that all teachers possess PCK in some form, though their observed PCK levels were limited. The opportunity to develop proficiency, the use of examples and some engagement with learners’ prior knowledge though mostly in the form of checking homework were the areas most prevalent. The focus was mostly on procedural aspects. Only a minority of the teachers used representations, showed more than one method, displayed longitudinal coherence or engaged in more substantial ways with learner thinking (misconceptions and errors). Crucially, it emerged that a sound teachers’ knowledge of mathematical content was necessary for a high PCK rating, but there was no significant relationship between teachers’ PCK and learner gains in mathematics. It is likely that there are other factors which have a greater impact on learners’ learning than effective teachers, factors such as the socio-economic backgrounds of the learners. Given the random sampling of the schools in the study, and various attempts to ensure consistency in my coding and analysis, I hoped that these results would be valid for the greater KwaZulu-Natal area. However, because I used mainly the video analysis of lessons, and only a part of the teachers’ test, to determine the teachers’ PCK, it is possible that I may not have been able to get the full picture of the teachers’ PCK as I would have if I had also interviewed them.

The main purpose of the study was to show the necessity of a classroom-based educator in-service support programme. Educators have unique problems being derived from the uniqueness of their school situations. Thus, the feeling that this kind of support could improve the quality of mathematics teaching and learning. / Thesis (M.Ed.)-University of KwaZulu-Natal, 2005.

It is no unknown fact that South African learners underachieve in mathematics. Due to the fact that the quality of mathematics teaching is one possible factor that has an influence on learners' mathematics achievement, there are valid reasons questioning the conceptual mathematical knowledge of mathematics teachers. In order to facilitate conceptual understanding teachers themselves must possess profound mathematical knowledge. Apart from the influence of a teacher's knowledge for teaching, teachers' attitudes and beliefs play a meaningful role in the way they teach mathematics. The deficient nature of prospective and practising teachers' knowledge of school mathematics, as well as their attitudes and beliefs towards mathematics has serious implications for the training of prospective mathematics teachers. Literature reveals that a technologically enhanced environment can improve the conceptual learning of prospective mathematics teachers. The purpose of this study was to determine the influence of a dynamic technologically enhanced environment on the attitudes and beliefs, as well as the conceptualisation of prospective mathematics teachers regarding the function concept. In this study, prospective teachers were exposed to Geometer's Sketchpad®, a dynamic software programme providing a powerful learning context that promotes the investigation of algebraic relationships. In order to answer the research question, an explanatory mixed method design was used. In the quantitative part of the study, the Study Orientation Questionnaire in Mathematics and a function test were administered to prospective teachers. In the latter, conceptualisation of the function concept was measured in terms of four competence components, namely interpretation, modelling, translation and reification. In the qualitative part of the investigation semi-structured and task-based interviews were held with a group of prospective teachers. Analysis of the results revealed that the dynamic technologically enhanced environment did not contribute to an improvement of the prospective teachers' attitudes and beliefs. In fact, these decreased visibly. Regarding their conceptualisation, only the reification component showed a practically significant improvement. It therefore appears as if prospective teachers are not being prepared to benefit from the dynamic technologically enhanced environment. A model is proposed for the effective use of such a learning environment. The model involves that diagnostic assessment be made of prospective teachers' basic knowledge of the function concept, their study habits, their attitudes and beliefs with respect to mathematics, as well as their mathematics anxiety. The second component comprises recommendations made to prospective teachers as a result of the diagnostic assessment, as well as continuous support being offered as an integrated part of the mathematics module. Support is offered with respect to cognitive and meta-cognitive skills, affective factors and the creation of an advantageous technologically enhanced learning environment. Despite the restricted value of generalisation of the findings from this study, I still recommend the expansion, refining and implementation of the model so that prospective mathematics teachers can effectively benefit from a technologically enhanced environment. Key words for indexing: mathematics education, mathematics teacher education, teacher knowledge, prospective mathematics teachers, function concept, conceptual learning, tertiary education. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2009.

It is no unknown fact that South African learners underachieve in mathematics. Due to the fact that the quality of mathematics teaching is one possible factor that has an influence on learners' mathematics achievement, there are valid reasons questioning the conceptual mathematical knowledge of mathematics teachers. In order to facilitate conceptual understanding teachers themselves must possess profound mathematical knowledge. Apart from the influence of a teacher's knowledge for teaching, teachers' attitudes and beliefs play a meaningful role in the way they teach mathematics. The deficient nature of prospective and practising teachers' knowledge of school mathematics, as well as their attitudes and beliefs towards mathematics has serious implications for the training of prospective mathematics teachers. Literature reveals that a technologically enhanced environment can improve the conceptual learning of prospective mathematics teachers. The purpose of this study was to determine the influence of a dynamic technologically enhanced environment on the attitudes and beliefs, as well as the conceptualisation of prospective mathematics teachers regarding the function concept. In this study, prospective teachers were exposed to Geometer's Sketchpad®, a dynamic software programme providing a powerful learning context that promotes the investigation of algebraic relationships. In order to answer the research question, an explanatory mixed method design was used. In the quantitative part of the study, the Study Orientation Questionnaire in Mathematics and a function test were administered to prospective teachers. In the latter, conceptualisation of the function concept was measured in terms of four competence components, namely interpretation, modelling, translation and reification. In the qualitative part of the investigation semi-structured and task-based interviews were held with a group of prospective teachers. Analysis of the results revealed that the dynamic technologically enhanced environment did not contribute to an improvement of the prospective teachers' attitudes and beliefs. In fact, these decreased visibly. Regarding their conceptualisation, only the reification component showed a practically significant improvement. It therefore appears as if prospective teachers are not being prepared to benefit from the dynamic technologically enhanced environment. A model is proposed for the effective use of such a learning environment. The model involves that diagnostic assessment be made of prospective teachers' basic knowledge of the function concept, their study habits, their attitudes and beliefs with respect to mathematics, as well as their mathematics anxiety. The second component comprises recommendations made to prospective teachers as a result of the diagnostic assessment, as well as continuous support being offered as an integrated part of the mathematics module. Support is offered with respect to cognitive and meta-cognitive skills, affective factors and the creation of an advantageous technologically enhanced learning environment. Despite the restricted value of generalisation of the findings from this study, I still recommend the expansion, refining and implementation of the model so that prospective mathematics teachers can effectively benefit from a technologically enhanced environment. Key words for indexing: mathematics education, mathematics teacher education, teacher knowledge, prospective mathematics teachers, function concept, conceptual learning, tertiary education. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2009.

The purpose of this study was to examine the factors affecting preservice mathematics teachers&rsquo / decisions on probability teaching. The sample of the study was 248 preservice mathematics teachers from Gazi University, Hacettepe University, and Middle East Technical University. According to the gender the number of females and males were 170 and 78 respectively. To obtain necessary data for the study, the following measuring instruments were used: (1) Probability Achievement Test (PAT) / (2) Probability Misconception Test (PMT) / (3) Attitude toward Probability Teaching Scale (APTS) / (4) Attitude toward Probability Scale (APS). Only the third measuring instrument was developed and its reliability and validity was tested by the researcher. An interview was done with 12 preservice mathematics teachers from Gazi University, Hacettepe University, and Middle East Technical University. The data of the study were analyzed by using SPSS and with qualitative techniques. The results of the study demonstrated that there are some factors affecting preservice mathematics teachers&rsquo / decisions on probability teaching. These factors were their attitude toward probability, probability achievement and misconceptions. Subjects thought that gender would have no affect on their decision on probability teaching.

Thesis (M.A.)--University of Toronto, 2005. / Includes bibliographical references (leaves 74-81).

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.