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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ItemMathematics and the preoperational child : why and how to use stories didactically( 1986)Premathematical concepts such as more/less are important for an understanding of mathematics in the primary school. The literature concerning the preoperational child's acquisition of concepts, their level of intellectual development, and the use of stories to introduce concepts is reviewed along with the literature concerning the way young children form an understanding of the concepts "more/less". Thirty preparatory children from a working class area were divided into two groups - one group was taught mainly with stories and the other group with the activities described in the Boehm Resource Guide for Basic Concept Teaching (1976). They were pre- and posttested with the Boehm Basic Concepts Test (1971). It was found that teaching using selected stories is as effective as using Boehm's special activities and that girls learn better with stories than boys. The children's knowledge of "more/less" and "most/least" was assessed in individual testing sessions using toy cars and sweets as stimuli. Approximately fifty per cent did not know "less", while a majority of the children had a stable knowledge of "more" in the sense of "greater in number". Approximately 65% of the. children understood "most" and approximately 19% understood "least". The Boehm Test was critically analysed and lists of books currently available from children's book shops or libraries, suitable for introducing and reinforcing children's knowledge of concepts of space, quantity and time, and miscellaneous concepts, have been compiled.
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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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ItemComputer-assisted instruction, for elementary school mathematics( 1985)In the 1960s, many educational researchers in the U.S. were attracted to the instructional potential of the computer. In the late 1970s, some of this potential had begun to be realized, as schools gained computing facilities consisting mainly of lower-cost micro-computers. This instructional medium has relatively recently begun to find its way into Australian schools and those of other western countries. Although there are many ways computers may be used to assist the teaching/ learning process, the available educational software tends to consist largely of what is referred to as C.A.I. This is probably the result of the majority of software being of U.S. origin, and of early developmental emphasis placed on this type of program. Programs of this type attempt to perform the function of the teacher by direct instruction of students or examination of their knowledge of a usually elementary topic. (Preferable usage regards the computer as a tool which enables the student to explore or carry out other useful tasks related to learning.) This investigation represents an early attempt at examining the effectiveness and feasibility of this type of instructional computer use in a Victorian primary school. It includes a description of the modes of computerized instruction and learning, together with claimed advantages and perceived drawbacks attaching to this practice. A survey of the use of computers in western countries is included, together with an examination of some of the early C.A.I. research conducted in the U.S. The practical component of the investigation involved the development of a C.A.I. program for the teaching of addition of vulgar fractions. This was subsequently tested with 19 Grade Five children at an independent primary school. The children were tested on the topic before and after exposure to the program, and also received a questionnaire on their attitudes and perceptions. The results were analysed by comparing the performances and responses of children of differing mathematical abilities (measured by prior administration of an achievement test). The program appeared to be only moderately effective. This could have. been because of deficiencies in the program and/or the shortage of student exposure. The effectiveness appeared to be greater for students of "medium" ability. Use of the computer on the other hand proved to be highly motivational to all of the children. There seemed to be some evidence that children of higher ability found the experience easier and more enjoyable, and that some children exhibited somewhat immature perceptions of the computer and of their own computer-related behaviour. The report includes criticisms of the program as tested and recommendations for improvement. Finally, recommendations are included for further research, as well as for any intending educational computer users and programmers. Note: In keeping with the investigational topic, the computer was utilized in the preparation of the report in two ways:- (i) A computerized search of the ERIC educational data base was conducted, to locate reports dealing with C.A.I. in elementary school mathematics. (ii) After experiencing a number of difficulties with typists, the report was produced by the investigator himself, using the WORDSTAR word-processing program. It should be pointed out that the investigator is, at best, a "two-finger" typist! Use of this method of report preparation, although consuming considerable time, is thoroughly recommended to other research 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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ItemSome determinants of students' course selection in mathematics( 1984)In this study some determinants of students' course selection in mathematics. were investigated, with particular attention being given to those factors which may result in differential participation rates between boys and girls. The aim of the study was to assess the relative importance for student decisions of various psychological variables related to achievement attitudes. Such knowledge could then be used in the design of appropriate programs and techniques to increase the likelihood of students continuing to take maths. Questionnaires were administered to the 115 students in Year 9 and to the 107 students in Year 7 at a Melbourne inner-suburban .high school. Specific findings apply to those students in that particular school; without investigation of the effect of such variables as socioeconomic status, ethnic background., administrative structure, course-availability and class size they could not be extrapolated to other students in other schools. Students' estimates of their maths abilities and their expectations for maths performance, decreased with age, as did their perception of their parents' and teachers' beliefs about their ability and expectations for their success. Students' beliefs about the importance of success in maths and their declared interest in and liking'for the subject also decreased with age, while their estimates of the difficulty of maths increased with age. Year 9 boys had higher opinions of their maths ability and were more confident of success in future maths courses, than were Year 9 girls. These girls saw the subject as being more difficult and the cost of the effort required to do well to be higher than did their male classmates. At the Year 7 level, however, the only sex differences were in the stereotyping of the utility of maths for females and in the stereotyping of maths as a male domain. Plans to continue with maths were facilitated by high expectations, by firm beliefs in the value of maths and in one's own ability and by low estimates of the difficulty of maths. Sex differences favouring boys were found on these variables. On the basis of these findings, certain areas for intervention were identified. These areas included the encouragement of positive attitudes towards maths, the provision of career awareness programs, and the attempt to modify parents' and teachers' attitudes as to the maths, ability of girls and the importance of maths for them.
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ItemTrainee-teachers: can attitudes and achievement in mathematics be improved?( 1988)The aim of the investigation was to compare the effects of different class-groupings upon the Attitude to, and Achievement in, Mathematics of Primary Teacher Trainees. The experiment was of the pre-test, post-test design, with students randomly assigned to Experimental or Control classes. Lecturers taking part were assigned one Experimental and one Control group each. The treatment comprised the First Year Mathematics Education Course at Phillip Institute of Technology, with students assigned to classes which were either homogeneous (Experimental) or heterogeneous (Control) with respect to school Mathematics background. The sample was drawn from an entire entry cohort (with depletions), to give a sub-population of about one-third. The experimental conditions extended over ten months (the time between dependent variable measurings) and subjects were not treated as special in other than those (grouping) ways mentioned above. Simple graphical analyses showed results of the treatment to be quite varied. Predicted outcomes were supported in few instances (measured by Effect Sizes) but in the main, hypotheses remain unsupported by this investigation - which matches the results of the majority of studies in this field.
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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.
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ItemA study of the effect of a student's home background and personal feelings on achievement in year 7 mathematics( 1982)Year 7 is a time of considerable change for most students, and in particular for those entering a new- secondary school. It has been suggested that factors external to the school situation can have the most effect in times of greatest change. This study involved all the students who undertook year 7 in two Technical Schools in 1980. At the beginning of the school year the students were given a commercial mathematics test, and a questionnaire on their attitude to mathematics and their self-concept. Identical tests were given 12 months later, together with a questionnaire on their home background and on their feelings towards their future schooling and career expectations. Correlation analysis was used to identify simple relationships existing between the variables. This then formed a basis for mathematical models of the relationships to be drawn up and tested using causal path analysis. The findings showed overall that the socio-economic status of the home, the sex of the student, the student's self concept, and the student's expectations for future education and career, all had some effect on the student's mathematics achievement and/or change in mathematics achievement during the 12 months either directly or indirectly. These variables also affected a student's attitude to. mathematics, however the attitude variable had no effect on the two main variables. The main finding of the study was that the students who had the greater gain in mathematics achievement during the study were those who had lower score. in mathematics at primary school level, who had lower self concepts and came from the lower socio-economic status homes. This finding lends good support to those who would suggest that the Victorian Technical Schools give a great deal of encouragement and a good educational environment for this type of student.