 Melbourne Graduate School of Education  Theses
Melbourne Graduate School of Education  Theses
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ItemTeacher beliefs about mathematical problem solving in Free Wesleyan Church secondary schools in TongaSweeney, Damian F ( 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 problemsolving 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 problemsolving 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.

ItemThe Wesley College technology enriched graphing projectSteele, David ( 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 graphsketching 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 coeducational 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.

ItemAttitudes of teachers to the objectives of mathematics education in the junior secondary schoolMcNaughton, Allen E. ( 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 Likerttype 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.

ItemSelfperception and academic performance in mathematics: a study of a group of normal technical (nt) students in a girls' school in SingaporeHo, Su Ching Eunice ( 2008)Selfperceptions of students are determinants of healthy psychological development and school success. Research on the associations between students' selfperceptions and their academic performance is of great importance in the educational realm. There have been limited studies investigating students' selfperceptions 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 selfperceptions 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 selfperception scores were measured by SelfDescription Questionnaire  II (SDQII) to yield three scores: Mathematics, Academicschool and General Selfperceptions. Qualitative data was obtained from a group interview using semistructured questions. The study involved thirtyseven 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 selfperception correlated strongly with Mathematics performance. Secondly, statistical evidence indicates that students had higher means for selfperceptions than academic achievements. Thirdly, evidence suggests that students' perception of academicschool is strongly correlated to their general selfperception. 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 selfperception and academic achievement are also discussed.

ItemPreparing a bank of mathematical problems for Year 11 studentsHeadlam, Wayne V.W. ( 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.

ItemSome determinants of students' course selection in mathematicsFlinn, Christine ( 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 innersuburban .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, courseavailability 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.

ItemA study of the effect of a student's home background and personal feelings on achievement in year 7 mathematicsBarraclough, Michael ( 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 selfconcept. 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 socioeconomic 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 socioeconomic 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.