# Analysis of ell student reasoning about measures of center and variation: A triangulation of quantitative and qualitative data

#### Abstract

The population of Spanish-speaking English Language Learner (ELL) students has been growing rapidly in the past 20 years. It has been estimated that by the year 2018, 1 out of 4 students in grades K-12 will be an ELL. There is a large body of research about assessment of Spanish-speaking ELL students in mathematics; however, there is little that focuses on statistics only. Statistics courses are frequently confused and/or classified under mathematics courses. However, students taking an introductory statistic course are required to know a new set of concepts, words and vocabulary that are not always used in mathematics courses. Statistics is not focused on numbers or formulas but rather a more complex set of words, such as mean, median, standard deviation, range, variance, among others. In introductory statistics courses students are often asked to provide a written response and/ or choose from multiple choice answers, both of which require a deep understanding of statistical terminology. This study is focused on understanding the thought process students utilize to answer questions about measures of center and variation and analyzes the possible nature of difficulties English Language Learner students encounter when dealing with concepts about measures of center and variation that are commonly encountered in introductory level statistics courses. The approach of this study was to perform a triangulation of quantitative and qualitative data about the responses of Spanish-speaking ELL and those who are not ELLs (non-ELL) students about measures of center and variation. This is an appropriate focus since all students entering an introductory statistics course will encounter and utilize these new concepts and terminologies. A survey consisting of ten questions was constructed during the Fall 2011 and Spring 2012 semesters. The questions, about measures of center and variation, are presented at a variety of complexity levels and were classified as direct, context-heavy and graphical. The study analyzes not only the final selection of answers provided by students, but also the explanation students provided on how and why they came up with their answers for each specific question. The analysis indicated that ELL students have a harder time answering context-heavy questions correctly, that both populations of students seem to perform well when it comes to direct questions, and that graphical questions seem to benefit ELL students. These results were consistent with those findings from the qualitative part of the data. From the triangulation we can say that there is some evidence to say that Spanish-speaking ELL students have greater difficulty answering context-heavy questions correctly even if these involve terms that are usually known by them in a simpler context. We can also say that both ELL and non-ELL seems to perform better when questions are asked in a direct way and finally, there is some evidence to say that the usage of graphical representations may be beneficial to ELL students. There is also some evidence to say that scaffolding difficulty on the questions presented on an assessment may play an important role on studentsâ€™ performance.

#### Subject Area

Mathematics education|English as a Second Language|Science education

#### Recommended Citation

Galvan, Lorena, "Analysis of ell student reasoning about measures of center and variation: A triangulation of quantitative and qualitative data" (2016). ETD Collection for University of Texas, El Paso. AAI10118245.
https://scholarworks.utep.edu/dissertations/AAI10118245

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