Yeung Pui Lam. / Thesis submitted in: December 2003. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 99-102). / Abstracts in English and Chinese. / Table of Content --- p.i / List of Tables --- p.iv / List of Figures --- p.v / Abstract --- p.vi / Chapter Chapter 1 --- INTRODUCTION / Research Background --- p.1 / Purpose and Significance of Study --- p.6 / Organization of the Thesis --- p.8 / Chapter Chapter 2 --- CONCEPTS OF UNIT / Introduction --- p.10 / Concepts of Unit as Key Concepts for Transforming Learning from Whole Numbers to Rational Numbers --- p.11 / Development of Unit Concepts across Additive and Multiplication Conceptual Fields --- p.11 / Six Aspects of Unit Concepts --- p.15 / Formation of Units in Rational Number Situation by Partitioning --- p.19 / Formation of Singleton and Composition Unit --- p.22 / A Flexible Concept of Measurement Unit --- p.23 / Decomposition and Composition of Unit --- p.23 / Reconstructing the Unit Whole --- p.24 / Fraction Equivalence --- p.24 / Chapter Chapter 3 --- SITUATIONS OF MULTIPLICATION AND DIVISION / Introduction --- p.26 / Semantics of Rational Numbers --- p.27 / Part-whole Subconstruct / Part-whole Comparison --- p.27 / Quotient --- p.28 / Operators --- p.31 / Measures --- p.32 / Ratio --- p.32 / Structures of Multiplication and Division --- p.34 / Vergnaud's Interpretation on Multiplicative Structures- --- p.35 / Isomorphism of measures --- p.35 / Product of measures --- p.38 / Multiple Proportion --- p.39 / Greer's Classification on Multiplication/Division Situations --- p.40 / Relationship between Unit Concepts and Rational Number Multiplication and Division --- p.46 / The Role of Unit in the Scope of Rational Numberśؤ --- p.46 / Children's Implicit Model of Fraction Multiplication / Division --- p.47 / The Role of Unit in Multiplication/Division Situation --- p.49 / Research Question --- p.54 / Influence of Concepts of Unit in Students' Solving Rational Number Multiplication and Division --- p.55 / The Development of Unit Concepts in the Course of Learning --- p.57 / Chapter Chapter 4 --- METHODOLOGY / Design --- p.58 / Participants --- p.58 / Instruments --- p.59 / Unit concept test --- p.60 / Fraction multiplication and division test --- p.61 / Procedures --- p.62 / Research Hypothesis --- p.63 / Chapter Chapter 5 --- RESULTS / Dimensions of the Unit Concepts --- p.67 / Relationship between Various Concepts of Unit and Fraction multiplication and division Performance --- p.68 / Relationship between unit concepts and rational number multiplication and division situational problem --- p.69 / Differentiated relationship between unit concepts and situational vs. symbolic rational number multiplication and division --- p.71 / Relationship between unit concepts and types of situational rational number multiplication and division- --- p.73 / Relationship between Grade Level and Performance on Measures of Unit Concepts and Rational Number Multiplication and Division --- p.83 / Chapter Chapter 6 --- DISCUSSION / Summary of Findings --- p.87 / Importance of Concepts of Unit --- p.88 / Dimension of concepts of unit --- p.88 / Relationship between concepts of unit and situational problems --- p.89 / Differentiated impacts of concepts of unit on situational problems and symbolic problems --- p.90 / Differentiated impacts of concepts of unit between multiplication and division problems --- p.91 / Implications of the Findings for Development of Concepts of Unit and Mathematics Learning --- p.92 / Research Implication --- p.92 / Instructional Implication --- p.93 / Limitations in the Study --- p.94 / Directions for Future Research --- p.96 / Conclusion --- p.97 / References --- p.99 / Appendices / Appendix 1: The questionnaire used in present study --- p.104 / Appendix 2: The characteristics of items in Questionnaire I- --- p.115 / Appendix 3: The characteristics of situational problems of fraction multiplication and divisionin questionnaire II --- p.116 / Appendix 4: The CFA model of concepts of unit --- p.117 / Appendix 5: Sample cases for illustrating strategiesin solving situational problems --- p.118
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324578 |
| Date | January 2004 |
| Contributors | Yeung, Pui Lam., Chinese University of Hong Kong Graduate School. Division of Education. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, ix, 119 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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