Investigating Links Between Group Interactions and Mathematical Reasoning Among Bilingual Algebra Students

• In Event: High School Students’ Identity, Positioning, and Learning in Mathematics

Abstract

This paper examines how two groups of four bilingual Latino students each used symbolic, linguistic, and social resources to complete algebra tasks focused on generalization and on the relationship between rate and slope. The primary objective is to investigate the link between students’ interactions, their use of social and semiotic resources, and their mathematical reasoning during group discussions.

This study is rooted in a sociocultural approach to learning, where learning is defined as changing patterns of participation in cultural practices across time (Rogoff, 2003) as well as the appropriation of tools for thinking (Wertsch, 1998; Moschkovich, 2004). In the analysis I draw upon methods from sociolinguistics (Schiffrin, 1994; Forman, McCormick, & Donato 1998) and the analysis of mathematical discourse practices (Moschkovich, 2007), focusing on the students’ interactions and reasoning. I examine how each group engaged in mathematical discourse practices (Moschkovich, 2002, 2007), coordinated semiotic tools (Radford, Bardini and Sabena, 2007), and used social resources, in particular the construction of mathematical authority (Esmonde, 2009; Lampert, 1990), in order to complete the given tasks.

The two groups were drawn from a ninth grade bilingual algebra class in a majority Latino/a school in rural California. All of the participating students were bilingual; one group consisted of students who primarily spoke English during their peer interactions, while the other group included recent immigrant students who primarily spoke Spanish, and who were learning English at the time of the study. The teacher was bilingual, and she frequently used group work and reform-oriented curricular materials in her instruction. Data sources included video and field notes from in-class observations, video and student work from out-of-class group problem-solving discussions. This analysis primarily focuses on the students’ discussions during out-of-class problem solving sessions near the start, middle and end of the data collection.

I show that each group used a different array of resources during their joint problem solving discussions, and that these configurations of resources had an impact on each group’s problem solving success. For example, one group relied on geometric patterns and more shared authority when completing a generalization task, while the other group relied on numerical patterns and enacted more traditional forms of mathematical authority. The group that used geometric patterns and shared authority used more time to complete the given tasks, but they were also more likely to provide correct solutions. In the discussion I explore possible sources for these observed differences and consider implications for student learning of critical topics in algebra. This work contributes to current literature by investigating links between group interactions and mathematics learning tied to particular, critical content from school mathematics.

Author

• William Carl Zahner, Boston University