Connecting Teaching Routines and Access to Learning Opportunities Using an Observational Tool

• In Event: Equity-Focused Mathematics Instruction: What We Can Learn From Classroom Observational Systems

Abstract

In this paper, we focus on the access to learning opportunities (ALO) dimension of the Math Access Observation Tool (blinded). The tool was created to observe mathematics classrooms for elements of standards-based instruction that support student access, by promoting student engagement in conceptual argumentation and mathematical practices (e.g., Boaler & Staples, 2008; Jackson & Cobb, 2010) and drawing upon instructional practices that support emergent bilinguals (e.g., Moschkovich, 2015; Walqui & Van Lier, 2010). The instructional triangle framing underlies this work which conceptualizes teaching and learning in terms of the relationships and interactions between teacher, student, and content (Thanheiser et al., 2021). We have operationalized teacher and student activity that can support students in accessing tasks, language, and each other’s ideas to promote a classroom culture of justifying and generalizing. We capture teaching routines -- extended ways teachers promote student-centered classrooms, catalytic teaching habits -- particular moves that can engender student engagement in mathematical practices, and habits of mind and interaction -- ways that students engage with mathematics and each other. The observation tool has a distinct temporal component; all activity is marked with a timestamp in order to address calls for instruments that link teacher moves with student responses over time (e.g. Jacobs & Spangler, 2017). For this presentation we focus on the teaching routines as an opportunity to provide access.

As part of an instrument validation study, we analyzed 97 classroom lessons spanning grades 4-8 from three urban school districts in geographically distinct areas of the United States. Lessons were purposefully selected to include variations in instruction as measured by the Mathematical Quality of Instruction (Hill, 2014). A stratified random sample was identified based on strata of low, medium, and high MQI scores. All videos were then analyzed using the observation tool by two coders where disagreements were resolved via discussion.

We focus on three teaching routines that have the potential to promote access and more equitable classrooms: Working with Public Records of Student Thinking, Structuring Student Talk, and Making Meaning of Tasks and Terms (see Table 2 for type of data picked up by the observation tool.) We examined each of these teaching routines with respect to access and the various forms the teaching routine can be enacted across classrooms.

The Math Access Observation Tool, which was designed to support access and argumentation, promotes necessary, but insufficient, instructional practices to promote more equitable learning environments. We consider a trifold lens: potential (access), participation (who gets to participate), and positioning (who is treated as competent). A temporal component can provide additional insight into classroom practices, and how and why promoting access and opportunity for conceptually-driven mathematics is just one step in supporting equitable classrooms.

Authors

• Kathleen Melhuish, Texas State University

• Sharon Kay Strickland, Texas State University-San Marcos

• Elizabeth Wrightsman, Texas State University

• Amanda T. Sugimoto, Portland State University

• Eva Thanheiser, Portland State University

• Brittney Ellis