Faculty of Education - Theses
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ItemFrom the general to the particular : connecting international classroom research to four classrooms in Brunei Darussalam( 2009)This doctoral research project set out to investigate whether large-scale international classroom studies have the capacity to connect with and offer insights into the classroom practices of individual teachers in Brunei Darussalam (hereafter, referred to as Brunei). In this study, the categorising scheme and results of the 1998-2000 Third International Mathematics and Science Video Study (TIMSS-99 Video Study) were used to examine the practices of four Grade 8 mathematics classrooms in Brunei. The practices documented in the four Brunei classrooms were then compared with the practices identified in the seven countries that participated in the TIMSS-99 Video Study. The comparative analyses were made possible by the application of the analytical codes of the TIMSS-99 Video Study to the Brunei video data. Adapting the Learner's Perspective Study (LPS) data collection methods (lesson sequences, interviews and an additional questionnaire) in combination with the analytical framework of the TIMSS-99 Video Study, generated a substantial body of detailed data about each of those four classrooms, sufficient to characterise the practices of those classrooms using the TIMSS-99 Video Study coding scheme and to support comparison with the TIMSS-99 Video Study findings. Connecting the generality of the TIMSS-99 Video Study findings to the specificity of the four classrooms studied in Brunei revealed both similarities and differences between the patterns of practice evident in the international and local data sets. In addition, the study addresses the question of how these similarities and differences might be used to inform classroom practice among the four Brunei teachers. Certain characteristics were common to the 20 Brunei lessons analysed: (i) The consistent shortness of the Brunei lessons (about 22 minutes), (ii) The consistent use by the Brunei teachers and their students of short spoken public utterances (typically less than five words); and, (iii) The relatively high "connectedness" of the Brunei mathematics lessons in comparison with those lessons analysed in the TIMSS-99 Video Study. One reading of my findings is that between-teacher variations problematise the usefulness of national typifications of practice. On the other hand, studies such as the TIMSS-99 Video Study can offer us salient dimensions of practice that alert us to characteristics of familiar classrooms that might otherwise go unnoticed.
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ItemUse of computers in mathematics teaching and learning : transition from grade 6 to year 7( 2001)Over the past ten years computer resources within Victorian schools have improved. Adequate level of facilities and resources has enabled teachers and students to use computers in the teaching and learning of mathematics. However it appears that computer skills acquired during primary years are not always the basis for further and continuous development of skills in the early years of secondary schooling. Research shows that during transition from grade 6 to year 7 there is need for stability and a sense of continuity in the adolescents' education and this applies to the area of mathematics as well. To gain further insight, this research investigated the use of computers in mathematics in a group of feeder primary schools and their linked secondary school. The study initially investigates whether the computer skills introduced in primary schools were known or built upon in secondary schools. The research then makes recommendations to the network of schools involved concerning continuity in teaching and using computer skills in the teaching and learning of mathematics during the transition years. This study was qualitative and involved parents, students and teachers. Questionnaires, interviews and classroom observations were used to obtain data. Recommendations include the need for continuous communication between grade 6 and year 7 mathematics teachers to form and maintain links regarding the development of computer skills, the need to develop a common goal for all grade 6 teachers in terms of teaching computer skills to prepare students for secondary school and finally, the need to increase computer literacy of primary and secondary mathematics teachers and make hardware and software available and accessible to all.
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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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ItemEvaluating the foundations for teaching arithmetic CD-ROM: linking theory and practice( 2005)Lack of mathematical content knowledge (MCK), pedagogical content knowledge (PCK) and the ability to translate this knowledge into practice are recognised as major issues for pre-service teacher education today. Multimedia has been suggested as a way of facilitating the transfer of MCK and PCK to the classroom. In this context the Foundations for Teaching Arithmetic (FTA) CD-ROM was developed in 2001. The aim of this study is to evaluate how pre-service teachers in the Faculty of Education, University of Melbourne have used FTA, if at all, to improve their MCK and PCK and to support the translation of these into practice. Also under investigation is what conditions facilitate or obstruct student use of FTA as a self-help resource in improving pre-service teachers' conceptual understanding of, and confidence in, their ability to do and to teach mathematics. Questionnaires designed to find out why students did or did not use FTA and their rating of particular features of the resource were completed by 389 students in various education courses. Forty-four student users and non-users of FTA were interviewed individually or in focus groups about their experience of FTA and the factors that contributed to their decisions to use or not use it. The impact of these factors was determined through the development of a framework which mapped the action profile of each student. A four phase needs-based progression model was proposed to explain the factors which contributed to students being able to make the successful translation of PCK on FTA into practice. The design and content of FTA facilitated students' use of FTA for the purposes under investigation. Factors hindering student use of FTA did evolve from the content of FTA, but were attributed to circumstantial factors.
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ItemThe use of laptop computers in the year 10 mathematics classroom( 2002)Laptop computers have been used in mathematics classrooms for approximately 10 years and there has not been a comprehensive study into how laptop computers are used, teachers' attitudes towards laptop computer use, and perceived student benefits. This study focuses on: i) How laptop computers are used in the mathematics classroom, concentrating on the types of software used and the type and the activities conducted. ii) Teachers' attitudes towards the use of laptop computers in the mathematics classroom, in particular how their attitudes and experiences may effect the use of laptop computers. iii) Teachers' perceptions of student benefits in terms of understanding and performing mathematical tasks using laptop computers. This study shows that there is a wide variety of software used and a large number of activities completed in mathematics classrooms with laptop computers. Teachers favoured using spreadsheets above any other type of software and tended to use the laptop computers for computational, open-ended activities rather than conceptual tasks. Teachers had varying attitudes about how and when laptop computers should be used in the mathematics classroom. There appeared to be connections between a teacher's own use of the computer and the way the teacher used the laptop computer in the classroom. Some teachers used the laptop computer very frequently whilst others used them sparingly. The most valuable type of in-service about using computers came from the teacher's own faculty, through formal and informal discussions. Finally, not all teachers believed there were benefits for their students from using laptop computers. There was no conclusive evidence about whether teachers believed their students had an increased ability to understand mathematics due to using laptop computers, but, there was evidence of increased student motivation.
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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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ItemThe influence of cognitive style on student performance and preferences in mathematical assessment( 2003)This study examined the influence of cognitive style on student performance and preferences in mathematics assessment. Two dimensions of cognitive style are: the wholistic-analytic style dimension and the verbal-imagery style dimension. This study investigated the comparative influence of these dimensions, students' _display of mathematics knowledge, specifically, a fractions test, in different assessment and their preferences toward mathematical assessment. A sample of 74 year seven students aged eleven to fourteen (n = 49 males and n = 25 females) with a mean age of twelve years and one month completed an assessment of their knowledge of fractions. Test items were presented verbally, symbolically and in pictorial formats. As well, students' preferences to aspects of mathematics learning and assessment were examined using a questionnaire. A Cognitive Styles Analysis (CSA) instrument was used to assess students' cognitive styles. These protocols were formed as the basis for the research. Cognitive style was found, to some extent, to influence student preferences in mathematical assessment more than student performance in mathematics. There was a significant partial correlation between a cognitive style and student preferences in mathematics assessment; analytic learners preferred the common test and wholistic learners preferred the project. Specifically, (i) analytic learners preferred the common test to the project, as a way of seeing themselves making progress and as a way of thinking about learning mathematics; and (ii) wholistic learners preferred the project to the common test, as a way of identifying the degree they feel pressured and as a way of thinking about learning mathematics. There was indefinite correlation between cognitive style and student performance in mathematics; analytic learners did not perform better than wholistic learners in the fractions test. Further, analytic learners did not perform better on pictorial tasks than on symbolic tasks. Similarly, wholistic learners did not perform better on symbolic tasks than on pictorial tasks. The implication of these findings for teaching is that cognitive style does not influence students' performance in mathematics. This study allowed the author to glimpse at the influence of cognitive style on students' preferred ways of being assessed, through the windows of ways of learning, mathematics knowledge and mathematics assessment.