Philosophiae Doctor - PhD (Dietetics)

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    Attitudes towards Mathematics, Achievement in Mathematics Aptitude Problems and Concomitant Teacher Practices in Ugandan Secondary Schools
    (University of the Western Cape, 2004) Opolot, Charles; Julie, Cyril
    The purpose of this study was to investigate students' attitudes toward Mathematics, achievements in Mathematics problem-solving, and the nature of teacher practices in Ugandan secondary schools. The study was intended to determine if there are any relationships between students attitudes toward Mathematics and achievements in Mathematics problem-solving. And to explore the nature of teacher practices in high-performing and low-performing schools. The study used a combination of quantitative and qualitative research methods. Two hundred fifty- four students from nine secondary schools and four mathematics teachers participated in the study. The data examined were from (]) senior three (ninth-grade) students' responses to a student's attitude towards mathematics questionnaire modified from the Fennema-Sherman attitudinal Scales ming, High-Performing schools, Lowitudes towards Mathematics, student attitudes towards mathematics, are achievement g and the nature of teacher practices in Ugandan secondary intended to determine if there are any relationships between student attitudes towards mathematics and achievement in mathematics problem-solving. And to explore the nature of teacher practices in high-performing and low-performing schools. The study used a combination of quantitative and qualitative research methods. Two hundred fifty- four students from nine secondary schools and four mathematics teachers participated in the study. The data examined were from (]) senior three (ninth-grade) students' responses to a student's attitude towards mathematics questionnaire modified from the Fennema-Sherman attitudinal Scales and (2) students' solutions to a mathematics problem-solving test that the researcher developed. The reliability of the instrument was examined by computing Cronbach alpha internal reliability coefficient.
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    Prospective Zimbabwean "A" Level mathematics teachers' knowledge of the concept of a function
    (University of the Western Cape, 2006) Nyikahadzoyi, Maroni Runesu; Julie, Cyril
    The purpose of the study was to investigate prospective 'A' level mathematics teachers' knowledge of the concept of a function. The study was a case study of six prospective Zimbabwean teachers who were majoring in mathematics with the intention of completing a programme leading to certification as secondary mathematics teachers. At the time of the study the six prospective teachers were in their final year of study. Prospective teachers' knowledge of the concept of a function was assessed through task-based interviews and reflective interviews. These interviews, which were done over a period of three months, were structured to capture the prospective teachers' subject matter knowledge and pedagogical content knowledge for teaching the concept of a function. The interviews were also meant to capture the prospective teachers' underlining pedagogical reasons for their choices of the examples, representations and teaching approaches when planning to teach the concept. As part of the study a theoretical framework for understanding prospective teachers' knowledge of the concept of a function was developed. The framework, which was developed, was used as an analytical tool in analyzing prospective teachers knowledge of the concept of a function. The results of the study indicated that the prospective teachers had a process conception of a function although some of them had given a set-theoretic definition of a function in which a function is perceived as a mathematical object. They also confined the notion of a function to sets of real numbers. Functions defined on other mathematical objects (for example, the differential operator and the determinant function) were not considered as functions by five of the six prospective teachers.
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    Reconceptualizing mathematics teaching and learning: Teacher learning in a realistic mathematics context
    (University of the Western Cape, 2000) Smith, Edward Charles; Persens, Jan
    In this study the construct of personal theories is used to represent the teacher's conceptions, which are interpreted as the consciously held beliefs. The teacher's personal theories encompass beliefs, images, values and attitudes as well as understanding about teaching and learning. This study investigates the influence of the teacher's conceptions of mathematics, of the teaching and learning of mathematics and of the context before and after a structured learning experience. The interest in the teacher's conceptions is derived from the assumption that these serve as a primary component that influence how teachers think about their professional responsibilities and how they act in their classrooms. Furthermore, the extent of implementation of a new curriculum has been linked to the scope of congruence between the teachers' conceptions and the underpinning philosophy of the intended curriculum. The study of the teacher's conceptions is especially relevant during a time of educational reform, such as the current transition to an Outcomes Based Education curriculum in South Africa. The participants in this study consist of four primary school mathematics teachers with various educational backgrounds, who teach at schools situated in different physical environments. The conceptions that these teachers have of mathematics, of the teaching and learning of mathematics and the influence of the context are investigated using a variety of instruments. Data collection was done with a questionnaire, a repertory grid, a semi-structured interview and lesson observations. The teachers participated in the Teaching Intervention and Support Programme (TISP), as a structured teacher learning experience. The programme is centred on the integration of the developmental and socio-cultural perspectives on teacher learning. With the developmental perspective the focus is on the acquisition of intellectual skills, while the socio-cultural perspective emphasizes participation in social practice. Both are directed at effecting conceptual change. With the developmental approach the process of conceptual change involves the development of new conceptions from existing conceptions. From the socio-cultural perspective the context is paramount and conceptual change is seen as new ways of being and acting within a particular context. The teachers were invited to attend a two-week intervention session, followed by a six months support programme that was aimed at establishing a teacher learning community. The learning experiences provided during the intervention session were drawn mainly from Realistic Mathematics Education. On completion of the programme, the teachers' conceptions of mathematics, of the teaching and learning of mathematics and the influence of the context were again investigated. The results of this study show that two of the participants had highly mechanistic conceptions of mathematics, and the teaching and learning of mathematics. The remaining two had a more empiristic approach with its high focus on environmental activities. After the programme, the teachers with the mechanistic views adopted a mixed. conception with some of the mechanistic conceptions retained, but now interspersed with some empiristic and realistic conceptions. The participants with the empiristic conceptions adopted a more realistic conception, but again to varying degrees. Thompson's (1991) hierarchical structure for the development of conceptions was also used to describe the extent of conceptual change. However, it was found that a concentric, rather than a hierarchical representation is a more appropriate to describe these changes. With regards to the socio-cultural view of conceptual change, all the participants perceived the context differently. The teachers' actions were also more commensurate with the practices associated with teachers that encourage learner autonomy, mathematical investigations and a facilitative role for the teacher.