Faculty of Education - Theses
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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.