| The purpose of this study is to investigate the language-mathematics interactions that hinder middle school English learners (ELs) when responding to algebraic tasks about a linear pattern. Specifically, this investigation focuses on how well students, both ELs and fluent English speakers (Non-ELs), understood task instructions, performed mathematically, and communicated their responses. Two hundred twenty-one students from twenty classrooms in two low-performing southern California middle schools chose to participate. There was a 60/40 split between ELs and Non-ELs and a similar split between 6th graders and 8th graders. While the majority of students were Latinos, almost all ELs were Spanish-speakers. Both quantitative and qualitative methods were used to gather and analyze data.;All students engaged a mathematics activity centered on the development and multiple representations of a visually-based linear function. The activity was comprised of nine related written tasks and made available both in English and Spanish. Students had to work silently, alone, and without notes. The investigator administered and evaluated the activity for all students. Soon thereafter, the investigator conducted one-on-one interviews with twenty-four of the students, encouraging them to explain their thinking in their own words. The data was transcribed, coded, and analyzed for identifying language-mathematics interactions and exploring their composition.;Many interactions are identified, explored, and catalogued within the mathematics register (Spanos et al., 1988). However, other interactions necessitated calling for the addition of three new semantic categories to the Mathematics Register: Words used to describe or define mathematical vocabulary, Levels of linguistic conceptual abstraction, and Recognizable forms. Comparing the performance of Non-ELs and ELs, some linguistic difficulties affected Non-ELs to a lesser degree (e.g. not recognizing pattern), some affected both groups to the same extent (e.g., misinterpreting Figure number (n)), and a few affected Non-ELs to a greater degree (e.g., double bar confusion).;In terms of the number of correct responses to the tasks, there is an English proficiency effect, as Non-ELs outperformed ELs. There is a smaller grade effect as 8th graders slightly outperformed 6 th graders. There is no gender effect. On average, Non-ELs attempt more tasks than ELs, as they typically encounter fewer language difficulties. |
