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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ItemTeacher beliefs about mathematical problem solving in Free Wesleyan Church secondary schools in Tonga( 2001)It is clear from the literature that attention should be paid to teachers' beliefs about how the mathematics classroom operates and about the nature of mathematical problem solving. The introduction of a mathematical problem-solving curriculum which ignores these aspects is likely to be frustrated. This research seeks to learn more about the use of mathematical problem solving by Tongan teachers and what these teachers consider to be good teaching of mathematics and mathematical problem solving. Five mathematics teachers in the Free Wesleyan Church of Tonga education system were interviewed about their beliefs using the Kelly Repertory Grid technique through Enquire Within software. Surveys were also conducted of the material produced for schools by the Tongan Government's Ministry of Education. It was found that the Ministry of Education has implemented a minimal problem-solving curriculum throughout the Kingdom and that the beliefs of the majority of teachers interviewed were compatible with this minimalist model. Recommendations for the Free Wesleyan Church's Education Department are made on possible approaches to fulfilling the Ministry of Education's stated aim of preparing students to apply the principles of mathematics to unfamiliar situations.
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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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ItemThe Wesley College technology enriched graphing project( 1994)Graphics calculators are rapidly becoming more affordable to students of mathematics. In time, it can be expected these calculators will become as essential a tool for mathematics students as scientific calculators are now. This thesis investigates how best to use graphics calculators to improve student achievement and understanding of senior secondary graph-sketching topics. The Wesley College Technology Enriched Graphing Project was an experimental study which involved 180 Year 11 students (8 intact classes) over 15 lessons at two campuses of this large co-educational independent school. Two teaching programs were devised, which differed in the degree of teaching emphasis on issues of scaling and obtaining a complete picture of a graph. The effect of frequency of calculator use was also investigated with a 2 x 2 experimental design. Daily use of the calculator was found to lead to significantly more improvement on general graphing questions than less frequent use. The teaching emphasis on scaling led to significantly more improvement in students' ability to deal with potentially misleading questions where the finite view of a function provided by the calculator omitted important features. Students' attitudes to calculator use were very positive. In the light of these results it is recommended that schools move as quickly as possible to personal ownership of graphics calculators by students and that teaching programs emphasise scaling issues. This approach takes no more time than traditional teaching methods, but confronts student difficulties and leads to better understanding of functions.
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ItemThe effects of trait anxiety, mathematical ability, method of testing, task difficulty, and their interactions, on state anxiety and performance in mathematics at primary school( 1979)A review was made of the theoretical and research literature related to the trait-state concept of anxiety, the relationship of anxiety to academic performance; and some factors confounding the anxiety, performance relationship. A study investigating the differential effect of anxiety on performance under two different methods of testing was reviewed. A study to replicate the findings related to anxiety, performance and varying test precedures was proposed. Data collected in the study made possible an investigation of Spielberger's Trait-State concept of anxiety and Spence's Drive Theory. One hundred and seventy six male, State primary school children drawn from sixteen grade five and six classes took part in the study. All testing was carried out in term I of 1978. As hypothesized the formal method of testing proved to be more anxiety arousing than the informal method of testing and students performed better under the latter testing procedure. Low anxious students performed better than high anxious students under both testing conditions. The study provided further support for Spielberger's Trait-State anxiety theory with high trait anxious students displaying higher levels of state anxiety than law trait anxious students, confirming that the State-A scale is a sensitive device for measuring differential anxiety arousal. The hypotheses related to Spence's Drive Theory were only partially supported by the results. Explanations as to why the interaction between task difficulty, ability and anxiety might not have been significant in this study were discussed. In general this study found evidence confirming the notion that high anxiety hinders performance, particularly for low ability students.
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ItemAttitudes of teachers to the objectives of mathematics education in the junior secondary school( 1976)At the same time as "New Maths" was being gradually introduced, secondary schools in Victoria became largely responsible for their own curriculum. This devolution of responsibility was coupled with a serious questioning of the meaning and purpose of secondary education itself, and an increasing awareness of other relevant factors such as how children learn, but secondary mathematics teachers have been so occupied with the new mathematical content demanded of them that other considerations have tended to be disregarded until very recently. The pressures that have increasingly been acting on secondary mathematics teachers have created confusion about the aims of the subject at the junior secondary level. Some teachers have retained the narrow academic aims of the past, while others have rejected these completely. Most, however, have reached a compromise. Five "innovative" and five "conservative" high schools in the Melbourne Metropolitan area were chosen subjectively by an informed panel. From each of these ten schools, two "junior level" and two "senior level" mathematics teachers were selected. Each of these forty teachers completed a Likert-type attitude questionnaire designed to establish their attitude towards narrow academic objectives at the junior secondary level. It was found that there was no significant difference in attitude between teachers of senior and junior levels, nor between teachers at conservative or innovative schools. There were, however, differences in attitude to the aims of junior secondary mathematics within each school of relatively large proportions. The lack of significant differences in attitude between schools indicates that they may be more alike than their reputation suggests, at least as far as mathematics education is concerned. Perhaps of greater concern is the effect on pupils of teachers with different attitudes towards their teaching. The fear that autonomy of schools has tended to become freedom for individual teachers to act alone in curriculum matters is reinforced by these results.
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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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ItemSelf-perception and academic performance in mathematics: a study of a group of normal technical (nt) students in a girls' school in Singapore( 2008)Self-perceptions of students are determinants of healthy psychological development and school success. Research on the associations between students' self-perceptions and their academic performance is of great importance in the educational realm. There have been limited studies investigating students' self-perceptions in Singapore. Hence, this study aims to examine students' perceptions of Mathematics, academic and general self. It sought to provide insights in relation to how these self-perceptions correlated with each other, and academic achievement with particular focus on Mathematics. Students' sentiments on the Normal Technical stream were also explored. A mixed methods approach was used for data collection. Quantitative data were derived from a questionnaire and students' Mathematics and overall academic results. The self-perception scores were measured by Self-Description Questionnaire - II (SDQII) to yield three scores: Mathematics, Academic-school and General Self-perceptions. Qualitative data was obtained from a group interview using semi-structured questions. The study involved thirty-seven students from the Normal Technical stream in a girls' school in Singapore. Eight students were involved in the group interview. Insights were gained about how students perceived Mathematics, academic school, general self and streaming. Firstly, the study found that Mathematics self-perception correlated strongly with Mathematics performance. Secondly, statistical evidence indicates that students had higher means for self-perceptions than academic achievements. Thirdly, evidence suggests that students' perception of academic-school is strongly correlated to their general self-perception. Finally, students resented the stigma that is attached to the Normal Technical stream, which regarded them negatively. Implications for practice and further research in the three areas of self-perception and academic achievement are also discussed.
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ItemPreparing a bank of mathematical problems for Year 11 students( 1990)The production of a problem bank for Year 11 mathematics students forms the content of this thesis. From an original collection of approximately 100 problems, 30 were chosen representing the areas of algebra, geometry and arithmetic. The RASCH method was used for calibrating the problems using partial credit scoring. There were 452 students in 37 Year 11 classes from 8 Victorian secondary schools that participated. Details of the selection, administration and use of the problems are discussed. Some of the difficulties such as finding problems at the appropriate level of difficulty, establishing a suitable classification for them, defining a marking scheme for their solution and the interpretation of the analysis of the scores are also given. The problem bank in its final form contains 23 problems, and could be used by Year 11 mathematics teachers for assessing students' progress in mathematical problem solving. For ease of use the problems are categorised by area of study and level of difficulty. The methodology involved in developing the problem bank, the processes of selecting and categorising problems and the analysis of student attempts to solve them would also be helpful for these teachers as they incorporate problem solving into their V.C.E. courses.