Facilitating Mathematics Discussions: Case Study of Attending to Mathematical Language and Mathematical Development and Participation

• In Event: Equity and “Core” Teaching Practices Across Disciplines: Bridging Constructs and Communities to Support Students’ Flourishing

Abstract

With the increased diversity in U.S. classrooms, there is growing attention among educational scholars to classroom mathematical language (e.g., Barwell et al., 2017). Language supports constructing mathematical concepts, positioning of individuals and groups, developing mathematical argumentation, and shaping mathematical communities (Herbel-Eisenmann et al., 2017). However, there is little research on teachers’ thinking about language in their own instruction (Hajer & Norén, 2017). In this paper, we share a case study of a teacher, Olivia, who participated in a job-embedded professional development (PD) focused on the core practice of leading mathematics discussions. We investigate how the PD afforded Olivia attention to ties between both Spanish and mathematical language and mathematical development and participation and access, particularly for Latinx students.

We view the nature of teacher knowledge as embedded in practice where teachers draw from “their own reasoning and decisions, and their own inventions of new knowledge to fit unique and shifting classroom situations” (Cochran-Smith, & Lytle, 1999, p. 267). Based on Gee’s (2005) work, we treat discourse as “language-in-use” or the material of communication such as words and gestures. In this study this applies to heritage languages (e.g., Spanish, English). We also adopt Gee’s definition of Discourse as other “language stuff” that enact specific identities and activities such as ways of acting and believing. This perspective bears on how Olivia thinks about her language use as a marker of not only doing mathematics but also enacting a particular identity.

We used the Learning Labs (LLs) PD environment at Lockwood Elementary, a school situated in an urban area in the U.S., serving about 40% Latinx students. The LLs focused on facilitating mathematics discussions and were structured around participants analyzing and discussing artifacts of practice, collaboratively planning and enacting a lesson, and then debriefing (Kazemi et al., 2021). We collected video/audio recordings and field notes from eight LLs, and teacher interviews and video-stimulated recall interviews (VSRs) from filmed classroom lessons. We focus on Olivia’s case, a bilingual teacher participant who taught in the Dual Language Immersion program where instruction was in both Spanish and English. We analyze how Olivia’s attention to mathematical language intersected with attention to knowing students as people and learners. We also track what Olivia perceived as affordances and tensions in mathematical language.

Our analysis leveraged tensions that Olivia experienced in supporting mathematical language during discussions. One tension was related to content vs. language where Olivia viewed developing language as separate from developing mathematical ideas. As Olivia worked to encourage students to have meaningful discussions, she struggled to find a balance between language socialization and mathematical content, perceiving opposition between them. Olivia also described a disconnect between the language of instruction, Spanish, and students who spoke Spanish. She felt speaking Spanish as something students do but also something empowering. She saw language as part of one’s identity. The paper contributes insights into how learning to facilitate classroom discussions entails learning to establish equitable classroom cultures for mathematics learning through language practices.

Authors

• Eric Cordero-Siy, Boston University

• Sam Prough, University of Delaware

• Hala N. Ghousseini, University of Wisconsin - Madison

• Elzena McVicar, University of Washington