# Analysis of differential item functioning on selected items assessing conceptual knowledge of descriptive statistics for Spanish-speaking ELL and non-ELL college students

#### Abstract

Recently, there has been growing interest in promoting conceptual understanding of statistical concepts in the classroom. The Assessment Resource Tools for Improving Statistical Thinking (ARTIST) project is a resource for maintaining and developing scales useful for measuring statistical conceptual knowledge. The focus of this study is to investigate whether items assessing conceptual knowledge of measures of center and variation from the (ARTIST) database show evidence of differential item functioning when administered to English Language Learners (ELLs). This is pertinent topic since the population of English Language Learners (ELL) in the United States has been growing rapidly in the past few years. ^ There is a large body of research about assessment of ELLs in mathematics. However, there is none that focuses just on statistics. Yet, statistics is an important application of mathematics and it requires an expanded vocabulary. In statistics we are not only dealing with numerical answers but also with written responses. For the purpose of this research, we studied assessments for ELL students in statistics focusing on the largest population of ELLs, native Spanish speakers. The items studied focus on measures of center and variability. This is an appropriate focus since all students encounter these concepts and these items are among those that utilize vocabulary that may be diffcult for ELLs. ^ The survey was given to students taking an introductory statistics class at a large urban binational research university located in the Southwest and a large community college system in a large Southwestern urban environment both located by the Mexican border. There was some evidence of Differential Item Functioning (DIF) on some items taken from the ARTIST database on measures of center and variation. For some ability levels, ELLs had a lower probability of answering the item correctly and for other levels of ability that probability was higher for ELLs depending on the type of question. Overall the questions that showed DIF were about mean, median, interquartile range, spread, and average which are common terms that students are expected to understand by the end of an introductory statistics course. Often, these terms are hard to understand even for non-ELLs, but may be even more difficult for ELLs. Students seemed to have issues when moving from the everyday register to the academic register of the word. In addition, ELLs may have a different everyday register of a word than non-ELLs which led them to answer differently. ^

#### Subject Area

Education, Community College|Education, English as a Second Language|Statistics|Education, Higher

#### Recommended Citation

Monarrez, Angelica, "Analysis of differential item functioning on selected items assessing conceptual knowledge of descriptive statistics for Spanish-speaking ELL and non-ELL college students" (2012). ETD Collection for University of Texas, El Paso. AAI1518203.
http://digitalcommons.utep.edu/dissertations/AAI1518203

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