Faculty of Education - Theses
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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.
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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.
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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.
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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.
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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.
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ItemThe effects of single-sex classes on students' confidence and participation in mathematics( 1995)The issue of females' lack of participation in high level mathematics at the senior levels of schooling has been one which has caused much debate. In Australia and overseas, females are less likely than males to participate in mathematics and science in the senior years of secondary education. One of the strategies which has been proposed to redress this imbalance has been the use of single-sex mathematics classes within the school. The subjects of this study were a cohort of students (n=110) at four different campuses of one school. At one campus, students were allocated to single-sex mathematics classes for year 10, and then returned to mixed-sex mathematics classes in Years 11 and 12. At the other campuses, students were always taught in mixed-sex classes. Comparisons were made with students from the other campuses and students from the same campus in other years. The research explored the hypothesis that being in a single-sex mathematics class would improve the confidence of the female students in Year 10, which would in turn lead to an increase in the participation rate of females in high level mathematics in Years 11 and 12. The findings indicated that the experience of single-sex mathematics classes in year 10 did not enhance the confidence levels. There was no increase in the participation rate in high level mathematics of either females or males from the Experimental Group. As this group of students was the first at their school to experience single-sex classes in a co-educational school, it might be that problems of implementation made the intervention unsuccessful.
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ItemMathematical modelling in the Year 9 mathematics curriculum( 1996)This thesis is a report on research conducted in relation to the introduction of mathematical modelling at the Victorian year 9 level. The research attempted to introduce educational mathematical modelling activities into what was then the normal mathematical curriculum of the secondary college and focused on changes to modelling ability, student affective variables, teacher concerns, and learning which might take place. The study was conducted over one school year at a country secondary college. Two experimental and four control classes of year 9 students completed a pre and post test consisting of an attitudinal measurement instrument and a modelling problem. As well, qualitative data was collected from class observations and discussions and interviews with the teachers. During the year, the experimental classes spent approximately 14% of their class time working on educational mathematical modelling activities. The results from the pre and post test did not produce any statistically significant changes leading to a rejection of the hypotheses of the study. However, the qualitative data collected did provide useful results. The teachers in the study reported concerns and problems similar to those reported in the literature. Observations of a class at work on a modelling activity provided insight into issues of motivation and relationships between mathematical achievement and modelling persistence. The results also highlighted a number of issues for future research. Despite the rejection of the hypotheses, this researcher and the teachers of the experimental classes concluded modelling was a worthwhile activity.
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ItemThe influence of cognitive style on student performance and preferences in mathematical assessment( 2003)This study examined the influence of cognitive style on student performance and preferences in mathematics assessment. Two dimensions of cognitive style are: the wholistic-analytic style dimension and the verbal-imagery style dimension. This study investigated the comparative influence of these dimensions, students' _display of mathematics knowledge, specifically, a fractions test, in different assessment and their preferences toward mathematical assessment. A sample of 74 year seven students aged eleven to fourteen (n = 49 males and n = 25 females) with a mean age of twelve years and one month completed an assessment of their knowledge of fractions. Test items were presented verbally, symbolically and in pictorial formats. As well, students' preferences to aspects of mathematics learning and assessment were examined using a questionnaire. A Cognitive Styles Analysis (CSA) instrument was used to assess students' cognitive styles. These protocols were formed as the basis for the research. Cognitive style was found, to some extent, to influence student preferences in mathematical assessment more than student performance in mathematics. There was a significant partial correlation between a cognitive style and student preferences in mathematics assessment; analytic learners preferred the common test and wholistic learners preferred the project. Specifically, (i) analytic learners preferred the common test to the project, as a way of seeing themselves making progress and as a way of thinking about learning mathematics; and (ii) wholistic learners preferred the project to the common test, as a way of identifying the degree they feel pressured and as a way of thinking about learning mathematics. There was indefinite correlation between cognitive style and student performance in mathematics; analytic learners did not perform better than wholistic learners in the fractions test. Further, analytic learners did not perform better on pictorial tasks than on symbolic tasks. Similarly, wholistic learners did not perform better on symbolic tasks than on pictorial tasks. The implication of these findings for teaching is that cognitive style does not influence students' performance in mathematics. This study allowed the author to glimpse at the influence of cognitive style on students' preferred ways of being assessed, through the windows of ways of learning, mathematics knowledge and mathematics assessment.