Faculty of Education - Theses
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ItemPredictors of performance in arithmetic in the middle years of primary school( 2002)While the amount of research into difficulties in mathematics has increased markedly over recent years there continues to be a need for more research into mathematics in the middle years of Primary School. The present study examined the extent to which performance on various maths related processing tasks (e.g. reading numbers, reading number statements, mental arithmetic) and measures of maths understanding (e.g. numeration and counting) predicted maths computation ability as determined by performance on typical Year 3-5 un-timed pen and paper arithmetic tasks. Analysis consisted of a stepwise regression for each of the three year levels. Some of these tasks were found to be highly predictive of achievement in arithmetic. The multiple regression was not only significant at each of the three year levels but accounted for a substantial proportion of achievement criterion variance: Year 3: 61%, Year 4: 59.8% and Year 5: 61.5%. Achievement in arithmetic was best predicted by a combination of factors at each year level with some similarities occurring across levels. The most striking of these is Mental Arithmetic: multiplication which was found to be a predictive factor at all three levels. Other significant predictive factors included Mental Arithmetic: subtraction (Year 3), Numeration: tens of thousands (Years 3 & 4), Processing of 4-digit numerals (Years 4 & 5), and Mental Arithmetic: addition (Year 5).
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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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ItemThe effects of trait anxiety, mathematical ability, method of testing, task difficulty, and their interactions, on state anxiety and performance in mathematics at primary school( 1979)A review was made of the theoretical and research literature related to the trait-state concept of anxiety, the relationship of anxiety to academic performance; and some factors confounding the anxiety, performance relationship. A study investigating the differential effect of anxiety on performance under two different methods of testing was reviewed. A study to replicate the findings related to anxiety, performance and varying test precedures was proposed. Data collected in the study made possible an investigation of Spielberger's Trait-State concept of anxiety and Spence's Drive Theory. One hundred and seventy six male, State primary school children drawn from sixteen grade five and six classes took part in the study. All testing was carried out in term I of 1978. As hypothesized the formal method of testing proved to be more anxiety arousing than the informal method of testing and students performed better under the latter testing procedure. Low anxious students performed better than high anxious students under both testing conditions. The study provided further support for Spielberger's Trait-State anxiety theory with high trait anxious students displaying higher levels of state anxiety than law trait anxious students, confirming that the State-A scale is a sensitive device for measuring differential anxiety arousal. The hypotheses related to Spence's Drive Theory were only partially supported by the results. Explanations as to why the interaction between task difficulty, ability and anxiety might not have been significant in this study were discussed. In general this study found evidence confirming the notion that high anxiety hinders performance, particularly for low ability students.
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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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ItemA case study of the various influences on the development of an educational innovation( 2002)This thesis is a case study describing knowledge creation for education in Queensland. The final CD-ROM product: Space, Measurement, Chance and Data: Improving Learning Outcomes incorporates Common Learning and Teaching Sequences for space, measurement, chance and data. Commonwealth funding for this project was designated for the improvement of literacy and numeracy knowledge and skills in young students. The project brief dictated a consultative approach that would utilise feedback and input from key stakeholders to influence and shape the development of the final product. The study describes this knowledge utilisation and the impact on knowledge creation for education. The study then reflects on the processes adopted and attempts to generalise about processes considered for future innovations. It establishes that the continual involvement with stakeholders should begin at the point of conception of the idea that is, prior to establishing the specific need for the innovation. The need for the innovation should also be influenced and shaped by involvement with stakeholders. This process will ensure that the innovation meets the needs of its end-users and should have a direct influence on the potential for adoption. This thesis provides useful information when establishing processes for knowledge creation in education, which not only will influence and shape the end product but has the potential to improve the rate of adoption after dissemination.
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ItemTrainee-teachers: can attitudes and achievement in mathematics be improved?( 1988)The aim of the investigation was to compare the effects of different class-groupings upon the Attitude to, and Achievement in, Mathematics of Primary Teacher Trainees. The experiment was of the pre-test, post-test design, with students randomly assigned to Experimental or Control classes. Lecturers taking part were assigned one Experimental and one Control group each. The treatment comprised the First Year Mathematics Education Course at Phillip Institute of Technology, with students assigned to classes which were either homogeneous (Experimental) or heterogeneous (Control) with respect to school Mathematics background. The sample was drawn from an entire entry cohort (with depletions), to give a sub-population of about one-third. The experimental conditions extended over ten months (the time between dependent variable measurings) and subjects were not treated as special in other than those (grouping) ways mentioned above. Simple graphical analyses showed results of the treatment to be quite varied. Predicted outcomes were supported in few instances (measured by Effect Sizes) but in the main, hypotheses remain unsupported by this investigation - which matches the results of the majority of studies in this field.
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ItemAn investigation of the effect of teachers' reflection on their development of pedagogical content knowledge for teaching primary mathematics( 2008)In recent years, teachers' pedagogical content knowledge (PCK) has become the subject of an increasing volume of research. Another body of literature has grown around the subject of reflection, and its effect on practice. Although a link between the two has often been assumed, few have attempted to map this link explicitly. This study investigates the possibility of such a link, and explores possible descriptions of the link. This case study compared two primary (elementary) teachers, investigating both their PCK and their reflection. The teachers were asked to complete a written questionnaire about mathematics teaching, including some questions requiring a response to hypothetical classroom situations. They were then interviewed about the questionnaire. The teachers were observed as they taught, and interviewed about those lessons. The questionnaire and first interview were used to investigate the teachers' PCK, and all interviews were used to investigate the teachers' reflection. One teacher was found to have both rich and well-connected PCK, and a strong tendency to reflect. The second teacher was found to have much weaker PCK than the first, and also demonstrated less reflection. Some examples of the first teacher's reflection were examined, to investigate the possibility that the teacher's reflection had an influence on the development of PCK. PCK was observed to develop during reflection, suggesting that reflection influences the development of PCK.
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ItemA comparative survey of the teaching of mathematics in primary schools in South Australia and Victoria( 1976)During the last two decades the teaching of mathematics in Australian primary schools has experienced widespread changes in content and method. These changes were introduced, mainly, in an attempt to overcome certain problems associated with the teaching of the subject. The views of psychologists and mathematicians influenced the new approaches to a greater extent than on any previous occasion. At the outset this thesis discusses some of the problems encountered in the teaching of mathematics and outlines three areas.requiring attention. An overview is given of the place of mathematics in the primary school curriculum in South Australia and Victoria since the middle of the nineteenth century. In tracing this development, an historical setting is given for the current controversies in the teaching of mathematics. A number of important changes in the teaching of mathematics emerge. In particular the changes which have occurred during the last twenty years are considered in some detail. An attempt is made to compare these recent developments and special attention is given to the period since the Australian conference on primary school mathematics in 1964, when a major restructuring of courses was proposed. Finally, it is shown that in attempting to overcome the problems associated with the teaching of mathematics, other factors have emerged which have implications for future developments. The current claim that the 3 R's have been neglected is likely to bring about a change in emphasis.