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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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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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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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.
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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.