Abstract not available. / Thesis (M.Ed.)-University of Kwazulu-Natal, 2008.

Password protected which will not allow abstract to be copied. / Thesis (M.Ed.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

The research conducted in this study is inextricably linked to a larger study of teacher quality and student performance in KwaZulu-Natal. The aim of the larger study was to explore and establish the relationship between teachers’ mathematical content knowledge, teachers’ practice and learner outcomes in grade 6 mathematics classrooms. This meant ascertaining teachers’ mathematical content knowledge, teachers’ pedagogical content knowledge and teachers’ practice in mathematics classrooms. Videos of lessons were analysed for the following aspects: content coverage, mathematical proficiencies facilitated by the teacher, cognitive demand on learners and teachers’ content knowledge. The analyses of all aspects were initiated at the same time, with different researchers/post-graduate students coding for separate aspects. In this study, the notion of mathematical proficiency as originally developed by Kilpatrick and colleagues (Kilpatrick, Swafford, & Findell, 2001) was used to ascertain the promotion of the strands in the district of Umgungundlovu of KwaZulu-Natal. Essentially the larger study hoped to establish the prevalence and quality of these strands by viewing video recordings of lessons obtained from schools. This in turn would present a view on mathematics learning in the district. The larger study used random stratified sampling to identify schools after which the necessary ethical approval and clearance was obtained. Mathematics lessons of the identified schools were then video-taped and questionnaires and both teacher and learner tests were conducted. I have not included examples of test questions due to agreements about not reproducing these. However, analysis of the recordings, in my view required the formulation of a construct that would interrogate the extent to which the strands of mathematical proficiency are promoted. This was necessary since the five strands in the original formulation represent ‘goals of mathematical understanding. ’In order to achieve these goals, tangible evidence of teacher classroom practice must be observable. Using opportunities as a vehicle of identification of such practice, the notion was formulated. The analytical framework entrenches the notion of ‘opportunity to develop mathematical proficiency’ as a construct with its corresponding descriptor table and is the main feature of this study. This in turn informed the design of the instrument which reflected the notion introduced and allowed ease of use. The research was not simply finding instances of what the instrument describes, but also trailing the applicability and strength of the instrument and the underlying notion of ‘opportunities to develop mathematical proficiency’. The findings reflect the current state of the promotion of mathematical proficiency. Not only is the quality of the promotion weak it is also irregular. An important off spin of the results is the alignment of these results to many studies including the recent ‘Report on the Annual National Assessments 2011’ issued by the Department of Basic Education. The notion introduced in this study with its corresponding analytic scoring method indeed proved to be a useful key to unravelling the answers to the questions posed. The results and findings give a detailed description to the aspect of mathematical proficiencies facilitated by the teacher, one of the aspects the larger study aimed to explore and establish. In this respect, it also shows the applicability and relevance of the developed theoretical notion and the related instrument. / Thesis (M.Ed.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

With the introduction in 2006 of the school subject Mathematical Literacy (ML) in the further Education and Training band, there have been expectations that such a subject will develop responsible citizens, contributing workers and self-managing people. The extent to which the subject can meet these aims is dependent on the ways in which the subject is assessed which influences the focus of ML in the classrooms. With this in mind, this study set out to explore the ways in which a class of Grade 12 learners engaged with a preparatory examination designed and administered by the KZN Department of Education. This is a qualitative study carried out with seventy-three grade 12 mathematical literacy learners from an urban school in North Durban. The purpose of this research is to explore the learners’ engagement with the examination tasks, thereby identifying possible factors which influence learners’ success in these items. Data were gathered from a document analysis of the 2009 KZN Trial Examination question paper and marking memorandum; 73 learners’ written responses to the examination tasks, and interviews with ten of these learners. The purpose of the document analysis was to identify contexts in which learners performed well or poorly, as well as to assess the design of the instrument. Semi-structured interviews were conducted individually with ten learners and video recorded. The purpose of the interviews was to explore some of the factors which influenced their written responses. The findings revealed that the task design was problematic for learners in terms of the order of the questions and the placement of the crucial information necessary to answer the questions. Some tasks also contained errors. The complexity of the scenario in terms of the amount of information, the language used, and the presence of distracters further influenced the way in which learners responded to the task. Learners’ personal experience of the context also affected the way they interpreted and responded to the task. Factors that constrained learners’ success in the examination task included poor conceptual understanding, misconceptions and language-related misinterpretation. It was also found that learners did not consider it a priority to make sense of the context: they focused on identifying formulae or information that could be used to present answers with little concern about the reasonableness of their responses. Some strategies used by learners in responding to the task included number grabbing, guessing without checking, scanning for crucial information and assumption-making. The study recommends that provincial examination papers be subject to the same stringent moderation requirements of the national examinations. It also recommends that should diagrams be used, they must be relevant to the context and should not conflict with the subject matter. The use of contexts should cater for alternate answers and multiple approaches and the marking memorandum should be flexible to accommodate these multiple approaches. Care must be taken in the presentation and placement of crucial information, so that learners do not miss the information they need to answer the questions. When familiar contexts are being used, task designers should also consider whether learners’ everyday experiences may conflict with these scenarios. / Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2011.

Proportionality is the content domain of mathematics that is rooted in ratio and proportion. It is believed to be vital for problem solving and reasoning, which are key cognitive domains of mathematics teaching and learning. Hence, ratio and proportion forms part of curricula for all countries. Studies carried out in different parts of the world found that while learners can do simple and routine manipulations of ratio and proportion, they struggle to solve problems that involve these concepts. Researchers apportion the blame for this to the strategies that learners use to solve the problems. Researchers found that learners use flawed strategies due to misconceptions that learners have on ratio and proportion. The purpose of the study is to explore learner errors and misconceptions on ratio and proportion. A test that comprised of questions that are appropriate to the National Curriculum Statement (NCS), for General Education and Training (GET) band, was used to collect data. Items in the instrument were selected and adapted from a tool used in Concepts in Secondary Mathematics and Science (CSMS) study. The participants in the study are 30 Grade 9 learners from a rural school in KwaZulu-Natal (KZN). The findings of the study are that learners have a limited knowledge and understanding of ratio and proportion, hence their performance in items on the topic is poor. A great proportion of the learners have serious misconceptions of ratio and proportion. They use incorrect strategies to solve problems on ratio and proportion that produce errors. The errors and misconceptions they exhibit are not different from those observed by similar studies conducted in other parts of the world. The study recommends a structured focus on ratio and proportion because the topic is fundamental to proportional reasoning. It recommends clarity for teacher trainers, textbook writers and teachers on what learners need to learn on ratio and proportion. It recommends serious exploration of errors and misconceptions on ratio and proportion, and a teaching approach that considers errors and misconceptions as opportunities for learning. / Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2012.

This was a qualitative study carried out with one grade 8 multicultural, multiethnic, mathematics class. This research study began with the idea of finding out whether the learners home language (especially Zulu Xhosa) could be linked to algebraic misconceptions. The 40 learners (participants) in my study had just been introduced to algebra. I chose the school and participants through “convenience sampling”. This made sense since I am an educator at this particular school. I had explained the meaning of the word "variable" in depth. The concepts "like terms" and "unlike terms" had been explained. The index laws for multiplication and division of the same bases had been discussed. It was within this context that the algebra worksheet was given to the learners, in the first cycle. I examined the algebra errors made by the grade 8 learners after marking the worksheets. I linked the errors to past literature on algebraic misconceptions as well as to Bernard's (2002b) error classification list. The conclusion was that the learners were making common errors which were not affected by their home language. I spent time on reflection since the outcome was not exactly what I had anticipated (that is, I had harboured strong suspicions that English second language learners would commit more algebraic errors than the English home language learners). I then considered a possible link between culture and algebraic misconceptions. Videotaped lessons were used for this purpose. However, observations of these videotaped lessons did not produce much data. I honestly could not reach a conclusion. This formed the second cycle of my action research. Prompted by the obvious lack of interaction in the video recordings from my teaching, I changed my focus to what I, the teacher, did during the lessons, and how these actions may or may not have supported some of the algebraic misconceptions. I reflected on my teaching method and recognized the need to change to a more interactive teaching style. I needed to give the learners the space to think for themselves. I would merely facilitate where necessary. In the third cycle, I drew up a set of problems which matched the new teaching style (interactive teaching).The lessons during which the new set of problems were discussed and solved, were videotaped. These videotaped lessons were analyzed and a completely different picture emerged. The learners were absolutely responsive and showed a side of them that I had not seen before! This study came to be an action research study because I went through three cycles of reflecting, planning, acting and observing and then reflecting, re-planning, further implementation, observing and acting etc. / Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2010.

Mathematical Literacy (ML) has only recently been introduced to learners, and research in South Africa concerning learners’ conceptual understanding in ML is not widely available. However an important predictor of learners’ success or difficulties in concepts is the success or difficulties that in-service teachers experience themselves. It is therefore important for us as mathematics educators to identify areas in Mathematical Literacy that teachers are struggling to learn and apply. With this in mind, the study sets to explore teachers’ perceptions about, and performance in Mathematical Literacy tasks based on algebraic concepts. This study is located within the principles of the qualitative research case study approach. The combination of data collection techniques has allowed me to identify broad trends across the group as a whole as well as differences within the participants of the group itself. The participants of the study were a class of 17 students who were completing the ACEML programme at UKZN. Four sources of data were used. Firstly, data was generated from teachers’ reflections about certain tasks, the solution of which required the use of algebra. A second data collection instrument was an open-form questionnaire and the third instrument was two unstructured interviews with two teachers. The final instrument was the analysis of the teachers’ examination scripts. For this study, teachers from this group were classified along the lines of whether they were qualified to teach mathematics or not. The theoretical framework for the study was derived from the OECD/PISA (2003) cycle of mathematisation which specifies 5 aspects of mathematisation, together with the theory of reification. For the purpose of this research, a participant was considered as a “mathematics specialist” if s/he studied mathematics up to tertiary level, while a participant was considered as “non-mathematics teacher” if s/he studied mathematics only up to Grade 12 level. The findings reveal that although the teachers conveyed varying understandings of the ML curriculum, they believed that knowledge of basic algebra was necessary and adequate for them to deal with ML problems. Furthermore the teachers believed mathematical teaching experience contributes to improved problem solving in ML and that ‘practice and familiarity’ helped teachers improve their problem solving skills in ML. They also voiced a concern that the pace of the programme constituted a barrier to their success. Within the group, it was found that Mathematics specialist teachers performed better than the non-Mathematics teachers. All teachers found the mathematisation aspects of solving the mathematical problem and of reinterpreting the mathematical solution to make sense of the real-life problems, challenging, while the non-Mathematics teachers experienced problems with all five aspects of mathematisation. The findings of the study suggest that teachers need help in moving from lower levels to higher levels of mathematisation. Opportunities for mathematical modeling experiences need to be incorporated in the part-time in-service contact courses like ACEML. Further research is needed to inform education authorities about whether the use of teachers with only grade 12 mathematical knowledge to teach ML is advisable. / Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2010.

The purpose of this study was to explore the learning strategies that are used by successful science students. In addressing this purpose, a mixed methods approach was adopted in which both quantitative and qualitative methods of data production were used. The participants were both successful and less successful high school science students from grades ten to twelve inclusive. Quantitative data was collected through questionnaires and analysed. The qualitative data was collected through individual semistructured interviews and focus group interviews. This was analysed using a qualitative thematic approach. The research questions were first about the learning strategies that successful science students seemed to use in order to do well academically, and secondly the question of the factors which influenced these successful students. The findings are that there are differences in the use of strategies between the successful students and their less successful counterparts. The successful students in general reported using more learning strategies more often than the less successful students. Successful students also reported that they engaged in strategies for regulating the effort they applied to work on difficult or boring tasks. They engaged more in cognitive strategies that involved deep processing of information, while the less successful students relied more on rehearsal and more superficial strategies like text underlining. Successful students also engaged more in self-regulatory activities that allowed them to monitor and regulate the way they learn. The findings also revealed that the successful students reported that they are influenced in their studies more by such factors as family support, the love of the subject and their goals or ambitions. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2010.

Over the past years geometry has posed a challenge to most learners in South African schools. The Government, in particular the Department of Basic Education (DBE), have tried and are still trying to implement new innovations and strategies for teaching mathematics more effectively. South Africa has experienced many changes in mathematics curriculum with an aim of placing the country on an equal footing with countries globally. This study was conducted while there was the implementation of the new Curriculum and Assessment Policy Statement (CAPS), which reinstated the geometry section within the curriculum. Geometry was relegated to an optional paper in mathematics in 2006, 2007 and 2008 in Grades 10, 11 and 12 respectively. This study is framed within the theoretical framework lens of social constructivism and situated learning, and is located within the qualitative research paradigm. It takes the form of survey research in one of the universities in KwaZulu-Natal, South Africa. This university is referred to as the University of Hope (UOH) in this study to protect its identity. The main aim of this study was to explore the pre-service teachers' (PSTs) knowledge of proof in geometry. The study used qualitative analysis of data generated through a survey questionnaire, task-based worksheets and semi-structured interviews for both the focus group and individual interviews. In total 180 PSTs completed task-based worksheets. Within this group of 180 students, 47 were 4th year students, 93 were 3rd year and 40 were 2nd year students. After the analysis of a task-based worksheet, a total of 20 participants from the 3rd and 4th year were invited to participate in focus group interviews. The findings of the study exhibit that the PSTs have very little knowledge of proof in geometry. The study revealed that this lack of the knowledge stems from the knowledge proof in geometry the PSTs are exposed to at school level. / Thesis (M. Ed.)-University of KwaZulu-Natal, Durban, 2012.

This research project focuses on Accounting education at tertiary level. There is limited understanding of students' experiences of learning Accounting in higher education institutions. Furthermore, Accounting is generally perceived as a difficult discipline, especially for novice first-year, non-major Accounting students. In this research study the purpose and focus were to explore first-year, non-major Accounting students' experiences when learning Accounting. The study attempts to answer two key research questions pertaining to first-year, non-major Accounting students' experiences when learning Accounting, and to show how their experiences influence their learning of Accounting. The study was conducted at a private higher education institution in South Africa where first-year Accounting is a compulsory element of an undergraduate commerce degree. The research participants sampled for this study were six first-year, non-major Accounting students, some of whom were novice Accounting students while others had studied Accounting in high school up to Grade 12. A qualitative research methodology was adopted to generate data using an interpretive case study approach. Research methods included semi-structured interviews and participant reflective journals. Data were analysed using open coding, and the findings categorised according to themes. Some of the key findings of this study revealed that students' experiences were influenced by teacher/lecturer qualities, students' perceptions and preconceptions of Accounting as a discipline, and the abstract nature of the Accounting discipline and its discourse. Other factors influencing students' learning experiences included their agency, resilience and determination, the effect of Accounting assessments, and ability streaming. This study concludes with a discussion of recommendations based on the findings. These point to the need for staff development workshops for Accounting lecturers, with an emphasis on students' emotions and perceptions when learning Accounting, so that lecturers are more aware of the extent of students' anxieties, insecurities and negative perceptions. Other recommendations include more post-plenary workshops for first-year Accounting students and development of different programmes for novice, non-major and Accounting major students, since these cohorts of students have differing career Accounting competence expectations. / Thesis (M. Ed.)-University of KwaZulu-Natal, Durban, 2012.