ABSTRACT OF THE DISSERTATION.......................................ii
ACKNOWLEDGEMENTS.............................................................iv
DEDICATIONS................................................................................vi
LIST OF FIGURES...........................................................................x
CHAPTER 1: INTRODUCTION....................................................1
1.1 Nature of the
Study
1.2 The Setting and
the Participants
1.3 The problem
Task
1.4 The Taxicab
problem and its significance
1.5 Research
Purpose and Guiding Question
1.6 Mathematical
Microcultural Norms of the Participants
CHAPTER 2: Review of
literature.................................................13
2.1 Introduction
2.2 Learning
2.3 Discourse
2.3.1 Teacher-to-student discursive interactions
2.3.2 Student-to-student discursive interactions
2.4 Intended
Contribution of the Study
CHAPTER 3: Theoretical
Framework and Analytic Method....32
3.1 Introduction
3.2 Theoretical Framework
3.2.1 Maher's notion of critical events
3.2.2 Inscriptions
3.2.3 Gattegno's contents of mathematical experience
3.2.4 Interlocution
3.3 Analytic Method
3.3.1 Data collection
3.3.2 Data analysis
3.3.2.1 Viewing attentively the video data
3.3.2.2 Describing consecutive time intervals
3.3.2.3 Identifying critical events
3.3.2.4 Transcribing the video record
3.3.2.5 Coding synchronously the transcripts, videotapes, and
inscriptions in an inductive and deductive manner
3.3.2.5.1 Coding transcript
3.3.2.5.2 Coding inscriptions
3.3.2.6 Writing analytical memoranda
3.3.2.6.1 Categorize codes, identifying properties, and
dimensionalizing properties within categories
3.3.2.7 Constructing visual representations of codes and categories
3.3.2.8 Constructing a storyline
3.3.2.9 Composing narrative
3.4 Researcher as
participant interlocutor
CHAPTER 4: DETAIL DESCRIPTION OF DATA......................63
4.1 Notation and
nomenclature of the Problem
4.2 Narrative
Description of Video Data
CHAPTER 5: RESULTS...................................................................103
5.1 Introduction
5.2 Structuring the
investigation
5.3 Understanding
the problem
5.4 Developing
problem-solving strategies, overcoming heuristic hurdles
5.5 Implying,
hypothesizing, and articulating combinatorial algorithms
5.6 Building conjectures,
counterexamples, and justifications
5.7 Building and
clarifying isomorphisms
CHAPTER 6: CONCLUSION..........................................................169
6.1 Introduction
6.2 Limitations of the
study
6.3 Interpretations:
Responding to research questions
6.3.1 The first question
6.3.2 The second question
6.3.3 The third question
6.3.4 The fourth question
6.4 Implications for
Research and pedagogy
6.4.1 Research question
6.4.2 Pedagogical implications
6.5 Summary
APPENDIX A: The problem
task....................................................192
APPENDIX B: Combinatorics problem sequence........................193
APPENDIX C: Transcript of problem-solving session................196
APPENDIX D: Transcription
convention......................................283
APPENDIX E: Participants'
inscriptions........................................284
APPENDIX F: Layered building of inscription (SK)...................309
APPENDIX G: Layered building of inscription (LS)...................316
APPENDIX H: Student-researcher interaction episodes.............323
REFERENCES:
References..............................................................326