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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ItemAn evaluation of a short, intensive mathematics program( 1999)This thesis evaluates a short intensive mathematics program for primary and secondary students that was conducted at the University of Melbourne in April 1997. The methodology of the evaluation can be described as action-research: a collaborative investigation where researchers, teachers and students cooperate in order to gain insights into a specific learning environment. This process is conducive to various improvement and modifications that the participants can apply to their respective practices. The primary aim of the thesis was to explore factors affecting the success of such programs and the learning which results. The findings suggest that while mathematical self-esteem is closely associated with mathematical achievement actual changes in mathematical self-esteem might not be easily detectable in programs of such short duration. The strength of the Program seemed to be the 'learning atmosphere' fostered by the instructors as well as in the choice of non-routine tasks. A possible weakness was the lack of clear focus regarding the pedagogical aims of the Program.
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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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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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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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ItemComprehension of mathematical word problems( 1995)Many students struggle to answer arithmetic word problems correctly. Examination of their mistakes shows that their difficulties are often related to misinterpreting or not understanding the written language of the questions. This thesis is concerned with examining students' reading difficulties in relation to word problems and noting any differences in student performance after the teaching of a specific comprehension unit within the mathematics class. Four classes of Year 7 students were selected: two classes as a control group, and two classes as an experimental group where they were given specific reading for meaning strategies adapted for mathematics from other curriculum areas as a part of the Whole Numbers and Decimals topic. Students' learning was measured by three tests: a pretest, a post test and a delayed post test completed ten weeks after the post test. As well as the tests, interviews with a small number of students were conducted and two questionnaires were completed by all the students in the sample. It was found that the comprehension unit significantly assisted students in the experimental group for the post test, but no difference was found between the two groups for the delayed post test. The study was not able to find conclusive reasons for the improvement of the control group for the delayed post test although possible reasons are offered. Careful reading of all words in a problem and rechecking work were the most successful approaches used by students. The study recommends that students are taught comprehension in their mathematics class in order to help them better understand the language of mathematics.
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ItemAttitudes of teachers to the objectives of mathematics education in the junior secondary school( 1976)At the same time as "New Maths" was being gradually introduced, secondary schools in Victoria became largely responsible for their own curriculum. This devolution of responsibility was coupled with a serious questioning of the meaning and purpose of secondary education itself, and an increasing awareness of other relevant factors such as how children learn, but secondary mathematics teachers have been so occupied with the new mathematical content demanded of them that other considerations have tended to be disregarded until very recently. The pressures that have increasingly been acting on secondary mathematics teachers have created confusion about the aims of the subject at the junior secondary level. Some teachers have retained the narrow academic aims of the past, while others have rejected these completely. Most, however, have reached a compromise. Five "innovative" and five "conservative" high schools in the Melbourne Metropolitan area were chosen subjectively by an informed panel. From each of these ten schools, two "junior level" and two "senior level" mathematics teachers were selected. Each of these forty teachers completed a Likert-type attitude questionnaire designed to establish their attitude towards narrow academic objectives at the junior secondary level. It was found that there was no significant difference in attitude between teachers of senior and junior levels, nor between teachers at conservative or innovative schools. There were, however, differences in attitude to the aims of junior secondary mathematics within each school of relatively large proportions. The lack of significant differences in attitude between schools indicates that they may be more alike than their reputation suggests, at least as far as mathematics education is concerned. Perhaps of greater concern is the effect on pupils of teachers with different attitudes towards their teaching. The fear that autonomy of schools has tended to become freedom for individual teachers to act alone in curriculum matters is reinforced by these results.
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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.