ChapterⅠ Introduction

1.1 Statement of the Problem

1.2 Purpose of the Study and Research Questions

1.3 Theoretical Background

1.3.1 English Language Learners and the Inequality in Education

1.3.2 Language Proficiency in Academic Settings

1.3.3 Accommodation for ELLs

1.4 Chapter Summary

1.5 Assumptions of the Study

1.6 Limitations of the Study

ChapterⅡ Literature Review

2.1 Research on the Relationship between Language and Math Achievement

2.1.1 AConfirmed Relationship

2.1.2 AChanging Relationship

2.1.3 Other Variables of Interest

2.2 Limitations of Past Researches

2.2.1 Limitations in Research Designs

2.2.2 Limitations in Statistical Modeling

2.3 Quantile Regression:Basics and Applications

2.3.1 QRM in Equations

2.3.2 QRM Parameter Estimation

2.3.3 QRM Standard Error Calculation and Confidence Interval

2.3.4 Hypothesis Testing

2.3.5 QRM Goodness-of-fit Index

2.3.6 QRM Coefficients as Measures of Location,Scale and Skewness Shifts

2.4 QRM Applications in the Educational Field

2.5 Chapter Summary

ChapterⅢ Data and Modeling

3.1 Research Questions as a Review

3.2 Data

3.3 Models

ChapterⅣ Results

4.1 Grade Level Results

4.1.1 Overall Model Fit

4.1.2 lndividual Variable Effects

4.2 Longitudinal Results

4.2.1 Modeling Building

4.2.2 Results

4.3 Summary

ChapterⅤ Discussion

5.1 Implications

5.2 Limitations and Future Researches

References

Appendix A:Variable Summary

Appendix B:Descriptive and Diagnostic Statistics

Appendix C:Grade Level Model Comparison Statistics

Appendix D:Grade Level Full Model

Appendix E:Full Quantile Process Plot by Grade

Appendix F:Khmaladez Test at Grade Level