Faculty of Education - Theses
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ItemTeacher beliefs about mathematical problem solving in Free Wesleyan Church secondary schools in Tonga( 2001)It is clear from the literature that attention should be paid to teachers' beliefs about how the mathematics classroom operates and about the nature of mathematical problem solving. The introduction of a mathematical problem-solving curriculum which ignores these aspects is likely to be frustrated. This research seeks to learn more about the use of mathematical problem solving by Tongan teachers and what these teachers consider to be good teaching of mathematics and mathematical problem solving. Five mathematics teachers in the Free Wesleyan Church of Tonga education system were interviewed about their beliefs using the Kelly Repertory Grid technique through Enquire Within software. Surveys were also conducted of the material produced for schools by the Tongan Government's Ministry of Education. It was found that the Ministry of Education has implemented a minimal problem-solving curriculum throughout the Kingdom and that the beliefs of the majority of teachers interviewed were compatible with this minimalist model. Recommendations for the Free Wesleyan Church's Education Department are made on possible approaches to fulfilling the Ministry of Education's stated aim of preparing students to apply the principles of mathematics to unfamiliar situations.
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ItemThe Wesley College technology enriched graphing project( 1994)Graphics calculators are rapidly becoming more affordable to students of mathematics. In time, it can be expected these calculators will become as essential a tool for mathematics students as scientific calculators are now. This thesis investigates how best to use graphics calculators to improve student achievement and understanding of senior secondary graph-sketching topics. The Wesley College Technology Enriched Graphing Project was an experimental study which involved 180 Year 11 students (8 intact classes) over 15 lessons at two campuses of this large co-educational independent school. Two teaching programs were devised, which differed in the degree of teaching emphasis on issues of scaling and obtaining a complete picture of a graph. The effect of frequency of calculator use was also investigated with a 2 x 2 experimental design. Daily use of the calculator was found to lead to significantly more improvement on general graphing questions than less frequent use. The teaching emphasis on scaling led to significantly more improvement in students' ability to deal with potentially misleading questions where the finite view of a function provided by the calculator omitted important features. Students' attitudes to calculator use were very positive. In the light of these results it is recommended that schools move as quickly as possible to personal ownership of graphics calculators by students and that teaching programs emphasise scaling issues. This approach takes no more time than traditional teaching methods, but confronts student difficulties and leads to better understanding of functions.
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ItemSelf-perception and academic performance in mathematics: a study of a group of normal technical (nt) students in a girls' school in Singapore( 2008)Self-perceptions of students are determinants of healthy psychological development and school success. Research on the associations between students' self-perceptions and their academic performance is of great importance in the educational realm. There have been limited studies investigating students' self-perceptions in Singapore. Hence, this study aims to examine students' perceptions of Mathematics, academic and general self. It sought to provide insights in relation to how these self-perceptions correlated with each other, and academic achievement with particular focus on Mathematics. Students' sentiments on the Normal Technical stream were also explored. A mixed methods approach was used for data collection. Quantitative data were derived from a questionnaire and students' Mathematics and overall academic results. The self-perception scores were measured by Self-Description Questionnaire - II (SDQII) to yield three scores: Mathematics, Academic-school and General Self-perceptions. Qualitative data was obtained from a group interview using semi-structured questions. The study involved thirty-seven students from the Normal Technical stream in a girls' school in Singapore. Eight students were involved in the group interview. Insights were gained about how students perceived Mathematics, academic school, general self and streaming. Firstly, the study found that Mathematics self-perception correlated strongly with Mathematics performance. Secondly, statistical evidence indicates that students had higher means for self-perceptions than academic achievements. Thirdly, evidence suggests that students' perception of academic-school is strongly correlated to their general self-perception. Finally, students resented the stigma that is attached to the Normal Technical stream, which regarded them negatively. Implications for practice and further research in the three areas of self-perception and academic achievement are also discussed.
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ItemPreparing a bank of mathematical problems for Year 11 students( 1990)The production of a problem bank for Year 11 mathematics students forms the content of this thesis. From an original collection of approximately 100 problems, 30 were chosen representing the areas of algebra, geometry and arithmetic. The RASCH method was used for calibrating the problems using partial credit scoring. There were 452 students in 37 Year 11 classes from 8 Victorian secondary schools that participated. Details of the selection, administration and use of the problems are discussed. Some of the difficulties such as finding problems at the appropriate level of difficulty, establishing a suitable classification for them, defining a marking scheme for their solution and the interpretation of the analysis of the scores are also given. The problem bank in its final form contains 23 problems, and could be used by Year 11 mathematics teachers for assessing students' progress in mathematical problem solving. For ease of use the problems are categorised by area of study and level of difficulty. The methodology involved in developing the problem bank, the processes of selecting and categorising problems and the analysis of student attempts to solve them would also be helpful for these teachers as they incorporate problem solving into their V.C.E. courses.