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Melissa Boston, Jonathan Bostic, Kristin Lesseig and Milan Sherman

In this article, we provide information to assist mathematics teacher educators in selecting classroom observation tools. We review three classroom observation tools: (1) the Reform-Oriented Teaching Observation Protocol (RTOP); (2) the Instructional Quality Assessment (IQA) in Mathematics; and (3) the Mathematical Quality of Instruction (MQI). We begin by describing each tool and providing examples of research studies or program evaluations using each tool. We then look across tools to identify each tool's specific focus, and we discuss how the features of each tool (and the protocol for its use) might serve as affordances or constraints in relation to the goals, purposes, and resources of a specific investigation. We close the article with suggestions for how each tool might be used by mathematics teacher educators to support teachers' learning and instructional change.

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Daniel L. Reinholz and Niral Shah

Equity in mathematics classroom discourse is a pressing concern, but analyzing issues of equity using observational tools remains a challenge. In this article, we propose equity analytics as a quantitative approach to analyzing aspects of equity and inequity in classrooms. We introduce a classroom observation tool that focuses on relatively low-inference dimensions of classroom discourse, which are cross-tabulated with demographic markers (e.g., gender, race) to identify patterns of more and less equitable participation within and across lessons. We argue that equity analytics can support researchers and practitioners in identifying subtle patterns of inequity in classroom discourse. As we show, even in classrooms with highly experienced, equityminded teachers, subtle inequities can emerge that are detectable through this quantitative methodology. To conclude, we discuss how equity analytics can complement qualitative approaches in the study of equity and inequity in classrooms.

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Amber G. Candela, Melissa D. Boston and Juli K. Dixon ( @MBostonMath ), is a professor of mathematics education at Duquesne University in Pittsburgh, Pennsylvania. She is interested in supporting mathematics teachers at all grade levels to use classroom observation tools to reflect on and enhance their practice