CHINESE ABSTRACT 1
ABSTRACT 1
CHAPTER Ⅰ INTRODUCTION 1
Background 1
Statement of the Problem 4
Theoretical Framework 6
Research Questions 8
Definitions of Key Terms 8
Limitations of the Study 10
CHAPTER Ⅱ REVIEW OF THE LITERATURE 11
Aiming at a Conceptual Understanding of Fractions,Decimals and Percents 11
External Representations and Internal Representations 14
The Role of Different Forms of External Representations in Developing Conceptual Understanding of Fractions,Decimals and Percents 16
Relationship between Different Forms of Representation and Achievements 19
The Role of the Textbooks in Facilitating Learning Fractions,Decimals and Percents 20
Impact of Instructional Time and Teaching Quality on Student Achievements 21
Theoretical Foundations and Rationale 23
CHAPTER Ⅲ METHODOLOGY 25
Participants 25
Instruments 27
Number Test 28
Quantity Measurement of Instructional Representations 28
Quality Measurement of Instructional Representations 30
Measurement of Students'Written Representations 31
Procedures 32
Data Coding 33
Data Analysis 34
CHAPTER Ⅳ RESULTS 36
Research Question 1 36
Addressing the Mathematics Learning Goals 37
Classroom Interactions 47
Quantity of Instructional Representations 53
Case Example of Quality of Teacher Representation 57
Quality of Instructional Representations 60
Summary of Results for Research Question 1 61
Research Question 2 63
Revised Model 1 69
Revised Model 2 70
Revised Model 3 71
Revised Model 4 72
Measurement Model of Students'Written Representations 75
Model 1 76
Model 2 76
Research Question 3 79
Model 1 79
Revised Model 2 80
Research Question 4 81
Model fit 82
Relationship between Instructional Time and StudentAchievements 83
Question 14 86
Question 15 87
Question 16e 88
CHAPTER Ⅴ DISCUSSION AND CONCLUSIONS 90
Quantity and Quality of Instructional Representations 90
Structures of Instructional Representations and Students'Written Representations 93
Relationship between the Forms of Representations Students Use and Their Achievements 95
Relationship between Instructional Representations and Student Achievement 95
Implications for Future Research 97
REFERENCES 100