School of Mathematics and Statistics - Theses

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    Improving intellectual and affective quality in mathematics lessons: how autonomy and spontaneity enable creative and insightful thinking
    WILLIAMS, GAYNOR ( 2005-09)
    The nature of creative mathematical thinking undertaken by students in classroom settings was studied through analysis of the autonomy and spontaneity associated with these processes. The theoretical lens developed enabled simultaneous analysis of cognitive, social, and affective elements of the creative process, and student responses to successes and failures during their exploratory activity (resilience or optimism). Collective case study was employed, with each case progressively informing the analysis of subsequent cases. The classrooms of teachers who were seen by their school communities to display 'good teaching practice' were selected for study. It was anticipated that such classrooms would provide more opportunity to study creative thinking than classrooms chosen at random. During the research period, each student participated individually in post-lesson interviews that were stimulated by lesson video material. To generate data to study student thinking, and the social and personal influences upon it, students were asked to identify parts of the lesson that were important to them, and discuss what was happening, and what they were thinking and feeling. Through this process, students who explored mathematical complexities to generate new mathematical knowledge were identified. (For complete abstract open document)
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    Collaborative problem solving in mathematics: the nature and function of task complexity
    WILLIAMS, GAYNOR ( 2000)
    The nature and function of Task Complexity, in the context of senior secondary mathematics, has been identified through: a search of the research literature; interviews with experts that focused on the nature of task complexity; expert use of the Williams/Clarke Framework of Complexity (1997) as a tool to categorise the complexity of a task, and observation and analysis of the responses of senior secondary mathematics students as they worked in collaborative groups to solve an unfamiliar challenging problem. Although frequently used in the literature to describe tasks, ‘complexity’ has often lacked definition. Expert opinion about the nature of mathematical complexity was ascertained by seeking the opinions of experts in the areas of mathematics, mathematics education, and gifted education. Expert opinion about task complexity was stimulated by questions about the relative complexity of two tasks. The experts then categorised the complexities within each of these tasks using the Williams/Clarke Framework of Complexity. This framework identifies the dimensions of task complexity and was found by experts to be both useful and adequate for this purpose. A theoretical framework was developed to assess student ability to solve challenging problems. This theoretical framework was used to design a test to assess student ability to solve challenging problems. The information this test provided about the problem solving ability of the students in this study informed my analysis of student response to complexity.