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Engaging students in mathematical argumentation supports language development and conceptual understanding because students use verbal and written language in coordination with mathematical representations to notice patterns, make claims, and create and revise explanations. This study adds to the limited research base on how teachers learn to facilitate discussions specifically aimed to develop students' capacities to engage in argumentation. We analyze teachers' sensemaking about supporting argumentation in the classroom through their participation in an adaptive professional development (PD) design. The PD was embedded in two elementary schools with upper grade teachers which enabled them to engage in iterative cycles of investigation and enactment within their own classrooms. Through collaborative lesson design and inquiry into students' experiences, teachers attended to the language students produced as they tried to formulate conjectures and produce explanations and the classroom participation structures that supported them. Our results suggest shifts in how teachers understood their role. Both cases speak to the complexities teachers face as they try to realize the recommendations for enhancing language learning and provide insight into what "rich" discourse means.

Mathematical modeling is a high-leverage topic; it is critical to students' participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary level has been underemphasized, particularly research on supports and challenges for teachers who engage in designing authentic modeling tasks. In this study, we employed qualitative case study methods to investigate how elementary teachers designed and implemented authentic mathematical modeling tasks, with an explicit focus on how their tasks evidenced different dimensions of authenticity. We analyzed three cases of teams of elementary teachers as they developed modeling tasks connected to school and community contexts. The three cases were: 1) a student-driven modeling task related to paper and plastic waste in a school cafeteria, 2) a modeling task based on authentic situations at a community-run resource center, and 3) a modeling task focused on designing and monitoring a school community-building art project. Our cases illustrate that elementary teachers can successfully design and implement modeling activities that utilize different entry points and evidence multiple dimensions of authenticity. Furthermore, we found that the specific dimensions of authenticity may vary depending on the design supports and curriculum challenges within each context. [ABSTRACT FROM AUTHOR]