Melbourne Graduate School of Education - Theses

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    The Wesley College technology enriched graphing project
    Steele, 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 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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    Preparing a bank of mathematical problems for Year 11 students
    Headlam, 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.