3. Electronic Theses and Dissertations (ETDs) - All submissions

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    The scattering problem on two half-lines with transfer-matrix condition at the origin
    (2009-05-06T10:26:54Z) Emmett, Richard John
    Abstract The mathematical analysis of scattering theory has been a major area of interest in mathematics and physics research since the latter half of the twentieth century. The aim of this work is to examine, in a functional analytic setting, properties of the differential operator L and solutions involved for scattering on the line −∞ < x < ∞. The characterisation of the spectrum of L will provide insight into the physical interpretation of the problem. The study of scattering theory will proceed with the major results in the field being presented with particular focus on reflectionless scattering. Attention is then directed to the inverse reflectionless case. We look at scattering on the line with a matrix transfer condition at the origin in addition an overview of the inverse case is presented.
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    Investigating learner experiences and views of learning mathematics in the context of HIV and AIDS
    (2008-11-24T11:26:18Z) Ndhlovu, Vincent Tebogo
    In order to investigate mathematics learning where a context of HIV and AIDS is used, I chose a case study research method. The method includes interviews, questionnaires, classroom observations, video recording of teacher lessons, participant observation and field notes. I focused on one grade 9 class with 25 learners and one mathematics educator. The study shows that context assists learners to participate meaningfully in the classroom, while motivating them and making learning fun. Secondly, in activities that foregrounds mathematics, learners shifted from the application of their general knowledge of context to focus on mathematical knowledge. Learners tend to ignore factors that are significant to real life or context of the task. When the researcher probed learners their responses shifted towards establishing an authentic connection between mathematics and application of mathematics in everyday lives. In other words in this case study context enables learners to see the value of solving problems within and outside mathematics. Furthermore, in this study context assisted learners to develop positive values and attitudes, and appropriate the role of mathematics in responding to social, political and economical issues.
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    Mathematical knowledge for teaching: a focus on the mathematical work of a grade 8 teacher when introducing algebra
    (2008-10-20T13:17:01Z) Talasi, Tatolo
    This study investigates mathematical knowledge for teaching. One Grade 8 teacher was interviewed and observed for one week while teaching algebra to 8th graders. I focused on mathematical problems that confronted her as she went about her work, the mathematical work of teaching she grappled with, the knowledge resources she called on as well as the algebraic activities that she presented to her learners. The analysis shows that she wrestled with explaining, representing, questioning, defining, working with learners’ ideas while restructuring tasks was entirely absent in this practice. It was interesting to see that learners were exposed to representational, transformational and reading activities of algebra and not the generalizing and justifying activities of algebra. The analysis further shows that this teacher drew on mathematics, curriculum and her experience in order to sustain her practice. Based on the findings of this study I argue that mathematical knowledge for teaching in this practice is empirical, with a strong focus on conventions as well as terminology; and is characterized by representational, transformational and reading activities.
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    Learners' competencies in new forms of assessment: A case study
    (2007-02-28T13:30:19Z) Rodwell, Lynn
    This small-scale case study researches the importance of analysing the mathematics competencies assessed by a selection of tasks developed for a portfolio in Grade 9 during 2003. The tasks are analysed according to the cognitive demand placed on the learners, plus their open-ended versus closed nature. This research reveals that the weaker ability learners experience a greater apparent benefit, compared to the stronger ability mathematics learners. Although there are other mathematical competencies assessed in this research report, those of ‘thinking and reasoning mathematically’ and ‘representing and explaining mathematical entities’ are most problematic, compared to the more traditional competencies of ‘memorisation’ and ‘manipulation of mathematical symbols and formalisms’. Assessing the tasks from the perspective of mathematical competencies, may serve to provide an alternative framework for analysing the appropriateness or not of tasks used in the development of portfolios and thus improve the practises of mathematics teachers in general.
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