Learning algebra in a computer algebra environment : design research on the understanding of the concept of parameter

Abstract

It is well known that algebra is a difficult topic in the school mathematics curriculum, and is often experienced as a stumbling-block. One of the directions in which solutions to the problems with the learning of algebra can be sought is the integration of information technology (IT) into mathematics education. Although originally not developed for educational purposes, a computer algebra system is an IT tool that seems promising because of its algebraic power. The basic aim of this study, therefore, is to investigate whether computer algebra use can contribute to the understanding of algebra. This leads to the following main research question: How can the use of computer algebra promote the understanding of algebraic concepts and operations? Chapter 1 contains the research questions and explains the aims and backgrounds of the study. In Chapter 2 the research design and methodology are described. Key words are design research and hypothetical learning trajectory. Chapters 1 and 2 together indicate what the research is about and how it is conducted. Chapters 3, 4 and 5 form the theoretical part of the thesis. They treat the main themes of the study: algebra in general, the concept of parameter in particular and the possible roles of computer algebra. Chapter 3 concerns algebra in general. It sketches different views on algebra and describes the standpoint of this study. The theoretical issues of symbol sense, symbolizing, the process-object duality and Realistic Mathematics Education are addressed. In Chapter 4, we zoom in on the concept of parameter. After a brief historical perspective, a conceptual analysis of the parameter is given. Then we describe what we consider a higher level understanding of the concept of parameter. This is connected to the theoretical notions from Chapter 3. Chapter 5 deals with the tool that students use in this research project: computer algebra. Besides an overview of previous research in this domain, it contains a description of the theory of instrumentation that will be used in Chapter 10 in particular. Chapters 6 - 10 form the empirical part of the dissertation. Chapters 6, 7 and 8 describe the development of the hypothetical learning trajectory and the classroom experiences during the three subsequent research cycles. Chapter 9 concerns the contribution of computer algebra use to the understanding of the concept of parameter. In Chapter 10, the results concerning the instrumentation of computer algebra are presented. Chapter 11, finally, answers the main research question. After that, we look back on the study and discuss the results and the methodology. Also, the relevance of the theoretical framework and the generalizability of the findings are evaluated. The chapter ends with recommendations for teaching, for software design and for further researc