Faculty of Education - Theses
Permanent URI for this collection
Search Results
1 - 10 of 16
-
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).
-
ItemAn investigation of Australian OECD Pisa trend results( 2009)This thesis investigates a range of equating-related issues for the Australian data collected under the Organisation for Economic Co-operation and Development (OECD) Programme for International Student Assessment (PISA). The implications for Australia's reported trend results are considered in detail. Following the exploration of differential item functioning (DIE) and dimensionality of the Australian PISA scales, a single scale, over all three PISA cycles (namely 2000, 2003 and 2006) for each major PISA domain (namely Reading, Mathematics and Science) was constructed. Previous published PISA results have employed a common reporting scale across all cycles for Reading, however scales common to all cycles have not been utilised for Mathematics or Science. Two further classes of equating issues are considered in this paper. First four different approaches to equating were used - two different treatments of missing data as well as two different item sets (all items and link items only) were estimated for each scale - and for each approach the implications for trends were discussed. Second, the equating approaches studied here used item parameters which are set at the country level rather than at the international level, thus allowing an examination of the impact of country DIF on the Australian trend results. Australian PISA trends were first explored in terms of means and standard deviations, and then in terms of the overall shape of the estimated performance distribution. This was achieved through the use of Q-Q (Quantile-Quantile) plots. Where applicable, comparisons were made with published trends. While results showed many similarities between models and published results, some differences were found. Australian PISA Reading means were statistically significantly lower when treating all omitted (or missing) responses as not administered at the item calibration stage compared to treating embedded omitted responses as incorrect and trailing omitted responses as not administered in PISA cycles 2003 and 2006. Between 2003 and 2006, published Australian Mathematics means were significantly lower than those found in this study. The published results showed a decline in means between 2003 and 2006, whereas the results reported here showed no change in the Australian means between these two cycles. Published Australian Reading distributions reported a decline from 2000 to 2003 and 2003 to 2006 in the number of Australian students located at the top end of the performance distribution. Between cycles 2000 and 2003 there was a decline from around the 70th percentile onwards and between cycles 2003 and 2006, the decline was even more severe; the higher the ability group the higher the decline from around the 20th percentile onwards. These estimated changes in the distribution shape were not replicated here, where the Australian data is analysed independently of the international data. The reanalysis undertaken here found a decline between the first two PISA cycles, but remarkably in the bottom 15 per cent of the distribution only. Between cycles 2003 and 2006 an almost constant decline across the whole proficiency distribution was found and not a decline that was limited to the top end of the distribution. The reported results highlight some of the potentially important differences that can occur when different analysis methods are used.
-
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.
-
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.
-
ItemMontessori mathematics education : its contribution to contemporary mathematics theory and curriculum( 1987)Montessori education has a long and continuing tradition. The mathematics education component is founded upon an extensive sensory education programme developed by Dr Maria Montessori and implemented in schools throughout the world. This thesis traces the historical precedents that provided the framework for the development of an educational programme firmly premised on the need for a sensorial education. The translation of the first part of Montessori's 'Psicoaritmetica' provides an illustration of an introductory mathematics programme using structured manipulative materials. This programme develops as a direct extension of the sensory-motor emphasis of Montessori pre-school education. Finally, the Montessori mathematics programme, developed initially over fifty years ago is considered in relation to contemporary mathematics education theories, many of which have reiterated principles and practices first developed by Montessori.
-
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.
-
ItemAn investigation of the effects of a graphics calculator based approach on the learning and teaching of year 8 equation solving( 2001)In the middle years of schooling, the topic of equation solving generally begins teaching students how to find solutions to linear equations using traditional by-hand techniques. This is a student's first formal introduction to algebraic equation solving and many master the techniques involved, however, few students acquire a conceptual understanding of the notion of a solution or the solution process. A graphics calculator is capable of plotting a function, generating a table of values and testing whether a number is a solution to an equation, all in a matter of moments. They are currently used in VCE mathematical studies and examinations. The aim of this investigation is to study the effects of a graphics calculator based approach on the learning and teaching of equation solving. This approach involved constant access, by an experimental group, to a TI-83 graphics calculator. A graphics calculator based approach to equation solving may assist students in developing a better understanding of the key concepts and solving techniques, and the application of these to the solution of problems. Constant access to graphics calculators in the classroom may allow students who lack pen-and-paper techniques the opportunity to reason mathematically about problems and mathematical ideas. To accomplish this aim a classroom-based study was conducted in a Melbourne metropolitan school. An experimental-control design was used with the four year eight classes of two teachers. Each teacher taught a control and experimental (graphics calculator) class. The study examined the achievement of the two treatment groups with pre and post-tests. Test performances of all students were compared and analysed to determine the benefits from the various instructional techniques. It was found that there were no significant differences between treatment groups and the only significant difference was between the teachers of the study. It was also found that low ability students, from the graphics calculator environment, made the largest gains. Although no statistical differences were found, students in the experimental group were more successful with questions involving graphs and tables while the students in the control group were better at solving equations by hand.
-
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.
-
ItemStudents' attitudes concerning mathematics: a study of the opinions and views concerning mathematics and mathematics teaching held by students in the upper primary and lower secondary schools of New South Wales and Victoria( 1966)From an examination of the relevant courses of study in mathematics and the associated published writings hypotheses were proposed to examine the influence of an emphasis on an inquiry and discovery approach to the teaching of mathematics on the attitudes concerning mathematics of students in the upper primary and lower secondary schools of New South Wales and Victoria (each N = 1000). Emphasis on the use of inquiry methods at the lower secondary school level was found to be associated with students' views that mathematics teaching involved more inquiry and discovery, with students' opinions that mathematics was an open and creative process and with the students' greater interest in mathematics. At the upper primary school level a strong influence of curricular factors was not detected, however, the evidence suggested that the classroom teacher played an important part in the development of attitudes concerning mathematics. The data collected was examined for the influence of several non-curricular factors including the sex of the pupil, and the occupation and the place of residence of the students' father. The sex of the student and differences in the scientific nature and the socio-economic status of the father's occupation were found to be linked with some differences in the opinions expressed by the students concerning mathematics.
-
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.