CHINESE ABSTRACT

ABSTRACT

CHAPTER Ⅰ INTRODUCTION

Background

Statement of the Problem

Theoretical Framework

Research Questions

Definitions of Key Terms

Limitations of the Study

CHAPTER Ⅱ REVIEW OF THE LITERATURE

Aiming at a Conceptual Understanding of Fractions,Decimals and Percents

External Representations and Internal Representations

The Role of Different Forms of External Representations in Developing Conceptual Understanding of Fractions,Decimals and Percents

Relationship between Different Forms of Representation and Achievements

The Role of the Textbooks in Facilitating Learning Fractions,Decimals and Percents

Impact of Instructional Time and Teaching Quality on Student Achievements

Theoretical Foundations and Rationale

CHAPTER Ⅲ METHODOLOGY

Participants

Instruments

Number Test

Quantity Measurement of Instructional Representations

Quality Measurement of Instructional Representations

Measurement of Students'Written Representations

Procedures

Data Coding

Data Analysis

CHAPTER Ⅳ RESULTS

Research Question 1

Addressing the Mathematics Learning Goals

Classroom Interactions

Quantity of Instructional Representations

Case Example of Quality of Teacher Representation

Quality of Instructional Representations

Summary of Results for Research Question 1

Research Question 2

Revised Model 1

Revised Model 2

Revised Model 3

Revised Model 4

Measurement Model of Students'Written Representations

Model 1

Model 2

Research Question 3

Model 1

Revised Model 2

Research Question 4

Model fit

Relationship between Instructional Time and StudentAchievements

Question 14

Question 15

Question 16e

CHAPTER Ⅴ DISCUSSION AND CONCLUSIONS

Quantity and Quality of Instructional Representations

Structures of Instructional Representations and Students'Written Representations

Relationship between the Forms of Representations Students Use and Their Achievements

Relationship between Instructional Representations and Student Achievement

Implications for Future Research

REFERENCES