Faculty of Education - Theses
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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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ItemTeaching quadratic functions with a graphical calculator( 2000)Graphical calculators have become an integral part of many mathematics programs. This thesis investigates the teaching of quadratic functions using this technology. 'Teaching quadratic functions using the graphical calculator' was an experimental study, which involved three classes of Year 10 students taught within a two to three week period, from three separate independent schools. Two of the sample classes were from different campuses of the same large coeducational independent school and the third was from a smaller independent girls' school. This study compares the improvement in student achievement across three different classes. A curriculum unit was developed: 1. To encourage positive student attitudes towards using the graphical calculator. 2. To encourage greater teacher confidence and positive attitudes towards using the graphical calculator to teach mathematics. 3. To teach the unit on quadratic functions almost entirely using the graphical calculator. 4. To incorporate a "Scale Plus" learning activity at the start of each lesson that encourages students to confront misconceptions involving scale (Steele, 1994). Three teaching programs were devised which differed in the way in which teachers involved in the study emphasized the critical features of quadratic functions, namely no emphasis, verbal emphasis only and strong verbal and written emphasis. 1. Group A experienced no emphasis of the critical features of quadratic functions and no additional curriculum material on critical features was supplied. 2. Group B experienced verbal emphasis of the critical features of quadratic function by the teacher. No additional curriculum material on critical features was supplied. 3. Group C experienced strong teacher emphasis, both verbal and written, of the critical features of quadratic functions and was provided with supporting curriculum material. A pre-test was used to help establish that at the start of the study the three classes were comparable with regard to their background knowledge of linear functions. My research aims were developed to: 1. Investigate aspects of student use of graphical calculators. 2. Compare the success of the three different teaching programs in relation to the overall improvement in student achievement when identifying critical features of quadratic functions. 3. Seek student opinions on, and determine their attitude to using graphical calculators. Also, to investigate the relationship between attitude and achievement. At the conclusion of the study a post-test was used to compare the three teaching programs; to establish whether there was an association between student achievement and the level of emphasis on critical features. A questionnaire was also administered to each group to investigate student attitudes, understanding, the ease of use of the graphical calculator and how demonstrations were used throughout the teaching program. Despite the difficulties inherent in conducting classroom research, namely controlling the variables, this study found that students from Group C, using the graphical calculator every lesson with strong teacher emphasis of the critical features of quadratic functions, had a better understanding of quadratic functions than students from Groups A and B. In particular, students from Group C could draw quadratic functions with a restricted domain and identifying the domain and range of these functions better than students from Groups A and B. Group C was also better able to detect the intersection of two graphs displayed in the [-10, 10] x [-10, 10] viewing window. The questionnaire showed that student attitudes were positive towards using graphical calculators, particularly amongst weaker students (Group B). The difference in student attitude and the perceived simplicity of the graphical calculator as a technological tool were found to be significant at the 5% level amongst this same group of students. Teachers involved in this study acknowledged the changing role of the teacher, the altered classroom dynamics and the more exploratory nature of the learning environment as a result of the student centered approach to learning quadratic functions with a graphical calculator. In consequence, it is important for the mathematics teacher to embrace the graphical calculator as a learning tool for all students but particularly students with a poor mathematical schema. When using this graphing technology the teacher should emphasise the critical features of quadratic functions every lesson and offer their students many opportunities to learn mathematics using the graphical calculator. Students should be confronted with issues of scale and functions displayed outside the standard [-10, 10] x [-10, 10] viewing window each lesson. This is best achieved with specifically written curriculum material to support the use of the graphical calculator.
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ItemStudent interpretation of graphs at the secondary level( 1994)Students at the secondary school level have misconceptions about, and difficulties with, interpreting the graphs used in such mathematics topics as calculus, statistics and variation. This thesis establishes what many of these misconceptions and difficulties are and trials teaching programs for years 8, 9, 10 and 11, that allow students and teachers to confront and deal with them. The teaching programs are designed to require a minimum of student time and teacher preparation. A study of the literature revealed most but not all of the misconceptions and difficulties and enabled the setting up of a list of those to be confronted by the teaching programs. An important student error, not in the literature, was found. The study was extended to include students' understanding of three dimensional graphs, a topic not previously in the literature. The teaching programs were based on sets of pre-drawn graphs with five questions each and were constructed for years 8, 9, 10 and 11. There were approximately 20 graphs for each year level to address these misconceptions and difficulties. Tests were administered to two classes at each year level and were followed by the teaching programs to only one of these classes at each year level. The same test was used immediately afterwards with all the classes as a posttest and then five months later as a delayed posttest. The effect of the teaching program was statistically significant for all year levels on the posttests. The delayed posttests showed that the gains were mostly maintained. The conclusion reached is that most of the misconceptions and difficulties that secondary school students have with interpreting graphs, can be dealt with in a short, focused teaching program at each year level. The teaching programs developed here go a considerable way towards doing this.