Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation




Education Sciences

First Advisor

Dr. Kelly D. Bradley


English language learner (ELL) is a term to describe students who are still acquiring English proficiency. In recent decades, ELLs are a very rapidly growing student group in United States. In school classrooms, ELLs are learning English and their academic subjects simultaneously. It is challenging for them to hear lectures, read textbooks, and complete tests in English despite of their inadequate English language proficiency (Ilich, 2013). As a result, the increasing number of ELLs in public schools has paralleled the increase in ELLs’ low mathematics performance (NCES, 2016).

Due to the popularization of international large-scale assessments in the recent decade, it is necessary to analyze their psychometric properties (e.g., reliability, validity) so that those results can provide with evidence-based implications for policymakers. Educational researchers need to assess the validity for subgroups within each country. The Programme for International Student Assessment (PISA), as one of the influential large-scale assessments, allows researchers to investigate academic achievement and group membership from a variety of different viewpoints.

The current study was to understand the nature and potential sources of the gaps in mathematics achievement between ELLs and non-ELLs. The nature of achievement gap was examined using three DIF methodologies including Mantel-Haenszel procedure, Rasch analysis, and Hierarchical Generalized Linear Model (HGLM) at the item level instead of total test level. Amon the three methods, HGLM was utilized to examine the potential sources of DIF. This method can take into account of the nested structure of data where items are nested within students, and students nested within schools. At the student level, sources of DIF were investigated through students’ variations in mathematics self-efficacy, language proficiency, and student socioeconomic status. At the school level, school type and school educational resource were investigated as potential sources of DIF after controlling for the student variables. The U.S. sample from PISA 2012 was used, and 76 dichotomously coded items from PISA 2012 mathematics assessment were included to detect DIF effects.

Results revealed that ten common items are identified with DIF effects using MH procedure, Rasch analysis, and HGLM. These ten items are all in favor of non-ELLs.The decreasing number of items showing DIF effects in HGLM after controlling for student-level variables revealed mathematics self-efficacy, language proficiency, and SES are potential sources of DIF between ELLs and non-ELLs. In addition, the number of DIF items continued to decrease after controlling for both student and school-level variables. This finding proved that school type and school educational resources were also potential sources of DIF between ELLs and non-ELLs.

Findings from this study can help educational researchers, administrators, and policymakers understand the nature of the gap at item level instead of the total test level so that United States can be competitive in middle school mathematics education. This study can also help guide item writers and test developers in the construction of more linguistically accessible assessments for students who are still learning English. The significance of this study lies in the empirical investigation of the gap between ELLs and non-ELLs in mathematics achievement at an item level and from perspectives of both students and schools.

Digital Object Identifier (DOI)