Changing my own and my students' attitudes to calculus through working on Mathematical Thinking

Abstract

Over the years, I have seen my students struggle to move from elementary to advanced mathematical thinking. I believe there is a need for an effective mathematical pedagogy in the learning of advanced mathematics that explicitly promotes mathematical thinking. Researches in mathematics education have contributed much towards providing theoretical perspectives for understanding thinking, learning, and teaching. It has also provided description on aspects of cognition as well as evidence on the viability and consequences of various kinds of instruction. In this study, I will describe my experience in translating some of the theories into classroom practice appropriate to both my students' and my own circumstances. The purpose of my research was to bring about improvements to the teaching of Advanced Calculus (Engineering Mathematics) to engineering undergraduates with the aim that it would also bring about changes on how students think about the mathematics. A framework that guides the design of classroom instruction and activities to support and encourage students' use of their own thinking powers will also be highlighted. A model of teaching was finally adapted based on various approaches designed to invoke students' ability to use their own thinking powers, enhance their problem solving skills and promote soft (generic) skills that can contribute towards students' acquirement of necessary attributes as an engineer. The researcher will also be the teacher and thus the study was implemented using an action research and case study perspectives as various methods within these stances will ensure flexibility in responding to the dynamics of interaction between the teacher and her students. Every encounter with my students, within and beyond, the classroom, was considered and contributed to my reflection about my teaching, review of the strategies and consequently, changing the way I teach or interact with the students. The thesis will present a description of the challenges and obstacles to making changes from my own and my students' point of views. Analysis of the research findings will also add knowledge about the factors that influence students' learning. A model that depicts the process of change will be proposed.