Chapters

Chapter 1: Introduction

Version 0.92, 13 Nov. 2009
This chapter begins with some thoughts that inspired and motivated my study. It then presents the central questions and themes of the thesis, lists its settings, process and methods, identifies its aims and surveys its structure.

This chapter argues for a design science perspective in technology enhanced mathematics educational research. It presents the principles and origins of such an approach, and identifies methodological weaknesses which need to be addressed. The emerging issues are formulated as concrete aims in the following chapter

Chapter 3: Aims and Method of Enquiry

This chapter revisits the aims outlined in Chapter one, in light of the review presented in Chapter 2. These aims are elaborated to propose a programme of research, and consequently characterise the overarching method of enquiry.

Chapter 4: A pattern based approach to design research in technology-enhanced mathematics education

Version 0.92, 13 Nov, 2009
This chapter responds to Aim 1 identified in Chapter three: To identify potential elements of an epistemic infrastructure for a design science of technology enhanced mathematics education. The proposed elements include a cycle of enquiry, design narratives, and design patterns. These constructs are reviewed and critiqued. The next chapter uses them as a basis for a methodological framework.

Chapter 5: Methodological Framework, Methods and Settings

Version 0.92, 13 Nov, 2009
This chapter describes the methodological framework and the set of methods used in the demonstrator study defined by Aim 3 in Chapter Three. The framework and methods are derived by projecting the approach detailed in Chapters Two and Four onto the specific research settings. These settings are specified in this chapter as well.


Chapter 6: The Problem Domain - Number Sequences

Version 0.92, 13 Nov., 2009

The purpose of this chapter is to inform theoretically the demonstrator study defined by Aim 3 in Chapter Three. It provides the motivation for number sequences as a curricular topic, considers some of the known challenges in this domain, and proposes some possible causes and remedies for them. The focus of this review is pragmatic: although it does aim to offer a theoretical contribution in this field, the main objective is to guide educational design. The resulting tools and activities are evaluated in Chapter Seven and systematised in Chapter Eight.


Chapter 7: Design Narratives

Version 0.92, 13 Nov., 2009
This chapter responds to Aim 3 identified in Chapter three: to apply the methodology in the problem domain and demonstrate its potential by producing a contribution towards a pattern language for technology enhanced mathematics education. This chapter presents a series of design narratives, as a first tier of interpretation of the empirical work. These narratives are the basis for the design patterns in Chapter 8, but also provide direct insights into the practice of techno-pedagogic design.

Version 0.92, 13 Nov. 2009
This chapter responds to Aim 3 identified in Chapter three: to apply the methodology in the problem domain and demonstrate its potential by producing a contribution towards a pattern language for technology enhanced mathematics education. This chapter presents a collection of design patterns, and the links between them, as derived from the design narratives in Chapter 7.

Chapter 9: Summary and Conclusions

Version 0.92, 12 Nov. 09

This chapter concludes the thesis. It sets off by reviewing the main findings and associating them with the three aims defined in Chapter Three. These are followed by notes on the limitations of this study, directions for future research and some final comments.