Faculty of Education - Theses
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ItemRemediating the elementary mathematics of prospective primary school teachers( 1980)Three areas are reviewed: the knowledge of prospective primary teachers of basic mathematics, remediation programs in mathematics and the use of calculators as a learning aid in mathematics. A remediation program is described involving a diagnostic pre-test and consequent assignment to one of three treatments: self-study, group tutorials or individual tutorials. The purpose of the 10 week program is to help prospective primary teachers meet a competency requirement in mathematics which is mandatory for progress beyond the third semester of a six-semester course of primary teacher training at a Victorian university. The program covers understanding and knowledge of place value, whole number decimals and fraction operations, percentages, averages and measurement including metrics. The group tutorials were given one of two treatments: the use of calculators during the remedial program, or the same program without calculators. Seven hypotheses related to the effects of the program are described. Post-testing after the 10 weeks of the program showed very large gains by each of the three groups. However the calculator group showed no difference from the non-calculator group, a finding consistent with the literature. Discussion of the results and pointers for future study conclude the study, with one recommendation being that mathematics specialists be appointed to primary schools.
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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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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.