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 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.
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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.
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ItemThe march of the calculator into Malaysian classrooms?( 1995)Calculators are used extensively in the workplace and are part of the technological change that is taking place in Malaysian society. However they are not used widely in the classrooms. About 200 primary, secondary and college teachers in Malaysia were surveyed about their attitudes toward the student use of calculators in the classroom and their current teaching practices. As many as 98% of the primary teachers and 83% of the lower secondary teachers have never used calculators in their mathematics lessons. The upper secondary teachers were using calculators in their classrooms because the present Malaysian national mathematics curriculum encourages and allows the use of calculators only at these levels. Most Malaysian teachers held more conservative views on calculator use than the teachers surveyed in Victoria, Australia in 1980. They felt that calculators should only be used after students have mastered basic number facts, acquired paper and pencil skills and understood the meaning of the four operations. About 29% of the teachers surveyed supported the introduction of calculators into primary classes. Although teachers believed that calculator use would enhance mathematics learning, many would not allow calculators to be used in class if they were not allowed on tests or examinations. Teachers also believed that parents would be against calculator use in the classrooms if they were not allowed on tests and examinations. It is recommended that the Malaysian Ministry of Education must allow calculator use on tests and examinations in order to encourage their use in primary and lower secondary classrooms.
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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.
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ItemTeaching negative number operations: a comparative study of the neutralisation model using integer tiles( 1998)The thesis describes an attempt to improve the teaching and learning of negative number concepts and operations. A teaching method based on the neutralisation model and using counters in the form of 'integer tiles' as the manipulative materials was developed and evaluated. The thesis begins with a review of the history and development of negative number. The influence that authors have exerted in embedding the use of the number line in signed number teaching practice was shown by examination of popular textbooks. Testing of classes across Years 8 to 11 revealed negative number skill deficiencies resulting from normal teaching methods. The major component of the research compared the integer tile method with normal teaching methods, in terms of learning outcomes, using a series of four tests of signed number operational skills and applications. Qualitative descriptions of student and teacher reactions and behaviour based on observation, interviews, conversations and examination of students' work by the researcher are also given. The experimental and control groups were shown to be well-matched on the pre-test. The experimental group performed significantly better on the post-test. The difference between the groups widened during the year following initial teaching. However no significant difference between the groups was found two years after the initial teaching. The evidence suggests that the integer tile method was more effective and for a wider range of student ability levels at the time of teaching than the normal method. Subsequently middle ability students in the control group were capable of catching up following application and practice in the use of negative numbers in later topics. However weaker students in both groups who did not fully master operational skills at the time of teaching continued to display skill deficiencies. The conclusion reached is that the integer tile teaching method could be a more effective initial negative number teaching method than normal methods based on the number line for most students. Further research is required to investigate the effectiveness of the integer tile method with weaker students.
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ItemTransition from primary to secondary school maths retention( 1985)In the last decade, a great deal of educational interest has centred on the transition of secondary pupils into post-secondary education or the workforce. This research project undertook an examination of the transition of primary pupils from their current school to be relocated in a nearby secondary school. The basic question addressed by the study was : Does a primary student transferring to a nearby secondary school suffer significant reduction in his mathematical skills within the first two weeks in the new school ? The testing was completed by using a twenty item mathematics test and administered to pupils in year 5 and year 6 in the primary schools in December. The same test was again given the same pupils, now in year 6 and year 7, in the February of the following year. It was because of the potential bias of items being relatively more difficult for the younger group, that the Rasch latent trait model was used to calibrate sample free item difficulties for the two groups of students. Items in the test were then given an estimate of their difficulties and each pupil was given an ability estimate depending on the total number of successful items on the test. It was with these ability estimates that the major questions of this study were examined. The study used a three way analysis of covariance to determine if a significant set back in mathematics skills had occurred during the transition. The major factors were the different year groups, sex differences and schools. Consideration was also taken for the ethnic population in the study. The results suggest a reduction in mathematical skills in the first two weeks in high school, and that this applies equally for male and female students. However an interactive influence can occur due to school differences.
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ItemGirls, maths and schooling: what counts( 1989)This thesis is a critical review of public discourses about the significance of mathematics and of what feminists have had to say, directly or indirectly, about this. There are four main aspects which correspond to the chapters. These are based around the following questions: 1. How is the significance of maths proclaimed? 2. How have feminists analyzed the problem of girls and schooling? 3. What are the issues raised by feminists on the problem of girls and maths? 4. What are the most significant assumptions about gender, education and society implied in the culture of maths? The material used in each chapter is largely literature which includes theoretical literature and empirical investigations. This reflects the dual approach which has been used to tackle the issues. Where it is appropriate, I have included my own experience and observations to substantiate and highlight a case. There are various standpoints within the literature on the problem addressed by this thesis, and I attempt to show that each, historically at least, is significant. I also demonstrate however that there needs to be a more critical appraisal of the girls and maths initiatives currently being explored in our schools.