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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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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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.