Faculty of Education - Theses
Permanent URI for this collection
Search Results
1 - 5 of 5
-
ItemThe evolution of concepts of decimals in primary and secondary students( 1994)This thesis studies children's conceptions about ordering decimals. It builds upon previous work which established three commonly used systematic errors in children's understanding as they encounter decimal notation. Students were categorised according to erroneous rule usage. This work includes a small longitudinal study which showed little change over twelve months in rule usage by an Australian sample of 50 secondary students. The categorising tests were redeveloped to make them suitable for primary students and to have increased reliability. The main study traced the use of rules from Year Four to Year Ten in a sample of 379 students and showed how students with different rules performed on other decimal tasks. It was found that one of the rules, called the whole number rule (in comparing two decimals that with more decimal places is chosen as the larger) was important in earlier years but disappeared with time. The second rule, called the fraction rule (the decimal with fewer decimal places is chosen as the larger), persisted in worrying proportions well into the secondary years and it was shown that significant gaps in knowledge of decimal notation existed which had not corrected themselves with time. The third rule was shown to be not important. Further investigation of a longitudinal nature to examine how individuals actually make the transition to mastery of decimal notation is encouraged by this study.
-
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.
-
ItemA Further investigation of decimal misconceptions held by primary and secondary students( 2005)This study investigates Australian students' thinking about decimals. A Decimal Comparison Test was used to diagnose thousands of Victorian primary and secondary students' misconceptions of decimal notation. Data from 1998 to 1999 were extracted (from a study funded by the Australian Research Council) and analysed. These data were analysed with the use of cross-sectional and longitudinal approaches. The cross-sectional approach adopted in this study focuses on the tests while the longitudinal approach focuses on the students. Analysis of students' decimal misconceptions was conducted at both the coarse level (4 behaviours) and fine level (12 ways of thinking). Firstly, the variability of the prevalence of expertise by class was investigated, as well as the various misconceptions. It was determined that there were large variations especially in the prevalence of expertise by class, in particular Grade 6 (anywhere between 5% and 95%). The second analysis involved tests that do not match any predicted pattern of correct and incorrect responses (referred to as unclass feeds). From the results, there were Grade 6 students who answered the test inconsistently and have a tendency towards choosing the decimal with the most digits as the largest number. Also, there were Grade 10 students who answered the test inconsistently and have a tendency towards choosing the decimal with the fewest digits as the largest number. The third analysis involved 122 students who completed their first test as experts but made more errors in their second test approximately 6 months later. The analysis of responses to individual test items indicated some of these students were consistent in using various incomplete algorithms to choose correctly on many of the decimal comparisons. However, when the incomplete algorithm failed to give a definite answer, they might guess or revert to a latent misconception.
-
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.
-
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.