Mapping Multilingual Students’ Mathematical Vocabulary Usage, Cognitive Engagement, and Belonging in Middle-Grades Math Classrooms

• In Event: Straight Talk: Natural Language Processing Approaches to Characterizing Student Opportunities to Learn in Mathematics

Abstract

The importance of mathematical language development for achievement in mathematics has been well documented, particularly for multilingual learners (Erath et al., 2021; Hughes et al., 2016; Moschkovich, 2002). Recent research has demonstrated the promise of natural language processing (NLP) techniques to study student language in math classrooms, and in particular, mathematical vocabulary usage on a larger scale (Author et al., 2024). We expand this emergent research by focusing on multilingual learners’ mathematical vocabulary usage in grades 6-8 and its relation to cognitive engagement and belonging in math class. Drawing from Thompson and colleagues’ (2023) analytic framework for English learner (EL) classification, we examine language groups beyond the EL designation binary. Instead, we analyze mathematical vocabulary among four groups: 1) identified ELs with beginner proficiency, 2) intermediate proficiency, 3) former ELs, and 4) never ELs. These categories offer insight into how student language practices in math classrooms – and their relation to belonging and cognitive engagement – differ for students in various stages of learning English, and how their practices compare to students who have never been identified as ELs. Specifically, we ask: 1) How does students’ mathematical vocabulary usage differ by English language background? 2) Do belonging and cognitive engagement in math class predict student mathematical vocabulary usage?

We employ NLP techniques to measure student mathematical vocabulary usage in approximately 300 middle-grade math lessons over one school year across 12 schools (19 teachers, ~500 students) from a large district. We use speech enrollment to link student utterances to survey data and administrative records. Once class recordings are made, the data team creates transcripts with identifiers for consented students. We classify students’ language background using English proficiency data (WIDA) and EL designation history. We measure cognitive engagement and belonging with factor scores from a lesson-level survey that students took six times over the 2024-25 school year. To answer RQ1, we use multilevel modeling with language background group as a fixed effect to test for group differences in mathematical vocabulary usage at the lesson level. For RQ2, we add belonging and engagement factor scores as predictors, including their interaction terms with language background, to assess variation in the relations between each construct and mathematical vocabulary usage across groups.

We hypothesize that students with emergent English proficiency use less mathematical vocabulary than their more proficient peers and that students formerly and never designated as ELs have similar patterns of mathematical vocabulary usage. Across all language groups, we expect students who report greater belonging and engagement to use more mathematical vocabulary and that this difference is more pronounced in students with beginner/intermediate English proficiency, with implications for belonging and cognitive engagement as mediators of students’ math language practices. Findings contribute a detailed examination of multilingual learners’ mathematical vocabulary usage, cognitive engagement, and belonging in math class beyond the “one size fits all” approach of binary EL classification. Additionally, we offer methodological insights into how a more descriptive multilingual analytic framework can be applied to large-scale quantitative analyses of classroom language practices.

Authors

• Bailey Buchanan, Harvard University

• Jeannette Garcia Coppersmith, Harvard University