[Learning Mathematics Through Worked Out Examples]

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Acknowledgement

I would take this opportunity to thank my research supervisor, family and friends for their support and guidance without which this research would not have been possible

Declaration

I, [type your full first names and surname here], declare that the contents of this dissertation/thesis represent my own unaided work, and that the dissertation/thesis has not previously been submitted for academic examination towards any qualification. Furthermore, it represents my own opinions and not necessarily those of the University (Hoyles, 2003,, 323).

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Abstract

It is difficult to examine the effectiveness of technology-based courses (TBC) without understanding the design and application in classrooms. There is evidence of disconnects among the theory for designing, the theory used to apply TBCs in classrooms, and the theory used to research and evaluate TBCs [Hickey, D. T. (1997). Motivation and contemporary socio-constructivist instructional perspectives. Educational Psychologist, 32(3), 175-193]. Comments provided by administrators, teachers and students may lead researchers to determine whether or not the original TBC course goals have been attained. In this paper, we first discuss examples of theoretical disconnects found in other technology-based research [Aleven, V. E., Stahl, E., Schworm, S., Fischer, F., & Wallace, R. (2003). Help seeking and help design in interactive learning environments. Review of Educational Research, 73(3), 277-320; Hickey, D. T., & McCaslin, M. (2001). A comparative, sociocultural analysis of context and motivation. In S. Volet, & S. Järvelä (Eds.), Motivation in learning contexts: Theoretical advances and methodological implications (pp. 33-55). Elmsford, NY: Pergamon Press]. Then, we describe the course design of the mathematics TBC used in this study, the reasons the principal and the teacher's believe the software will benefit their mathematics students, and the perceptions of mathematics students regarding the effectiveness of the technology in their classroom. In conclusion, we will discuss how this preliminary qualitative data shaped our future research questions.

Table of Contents

ACKNOWLEDGEMENTII

DECLARATIONIII

ABSTRACTIV

CHAPTER 1: INTRODUCTIONVI

CHAPTER 2: POPULATION AND METHODSVIII

CHAPTER 3: COURSE DESIGNX

CHAPTER 4: COMMON THREADSXIII

CHAPTER 5: CONCLUSIONS & FUTURE RESEARCHXX

REFERENCESXXIV

Chapter 1: Introduction

Many students struggle with high school mathematics courses. Researchers and practitioners continue to explore alternative strategies and approaches that motivate and engage students in rich mathematics and allow conceptual learning to occur. One of these alternatives is technology -based courses (TBC). Although TBCs vary in format and learning objectives, this study examined an environment in which students are using a research-based TBC. (Hoyles, 2003) The course design elements focus on both motivation and cognition. The courses use a real-world approach to teaching and learning and a flexible course design to motivate students. From a cognitive perspective, the course was designed to help learners relate to the content through real-world applications and gain a better understanding of difficult concepts. (Galbraith, 2002)

There is evidence of disconnects among the design theory and the theory used to apply TBCs in classrooms (Hickey, 1997). Some TBC designers consider how theoretical principles influence a classroom environment, and others do not (Aleven, Stahl, Schworm, Fischer, & Wallace, 2003). Despite these theoretical intentions, or the lack thereof in some ...