Abstract
It is well known that algebra is a difficult topic in the school mathematics curriculum, and is often experienced as a stumblingblock. 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 processobject 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 research
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 processobject 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 research
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  25 Sept 2003 
Place of Publication  Utrecht 
Publisher  
Print ISBNs  907334655X 
Publication status  Published  25 Sept 2003 
Keywords
 Mathematics
 Landbouwwetenschappen
 Natuurwetenschappen
 Wiskunde: algemeen
 mathematics education
 technology
 algebra
 computer algebra
 CAS
 developmental research
 realistic mathematics education