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  1. Background: The field of mathematics education has made progress toward generating a set of instructional practices that could support improvements in the learning opportunities made available to groups of students who historically have been underserved and marginalized. Studies that contribute to this growing body of work are often conducted in learning environments that are framed as “successful.” As a researcher who is concerned with issues of equity and who acknowledges the importance of closely attending to the quality of the mathematical activity in which students are being asked to engage, my stance on “successful learning environments” pulls from both Gutiérrez’s descriptions of what characterizes classrooms as aiming for equity and the emphasis on the importance of conceptually oriented goals for student learning that is outlined in documents like the Standards. Though as a field we are growing in our knowledge of practices that support these successful learning environments, this knowledge has not yet been reflected in many of the observational tools, rubrics, and protocols used to study these environments. In addition, there is a growing need to develop empirically grounded ways of attending to the extent to which the practices that are being outlined in research literature actually contribute to the “success” of these learning environments. Purpose: The purpose of this article is to explore one way of meeting this growing need by describing the complex work of developing a set of classroom observation rubrics (the Equity and Access Rubrics for Mathematics Instruction, EAR-MI) designed to support efforts in identifying and observing critical features of classrooms characterized as having potential for “success.” In developing the rubrics, I took as my starting place findings from an analysis that compared a set of classrooms that were characterized as demonstrating aspects of successful learning environments and a set of classrooms that were not characterized as successful. This paper not only describes the process of developing the rubrics, but also outlines some of the qualitative differences that distinguished more and less effective examples of the practices the rubrics are designed to capture. Research Design: In designing the rubrics, I engaged in multiple cycles of qualitative analyses of video data collected from a large-scale study. Specifically, I iteratively designed, tested, and revised the developing rubrics while consistently collaborating with, consulting with, and receiving feedback from different experts in the field of education. Conclusions: Although I fully acknowledge and recognize that there are several tensions and limitations of this work, I argue that developing rubrics like the EAR-MI is still worthwhile. One reason that I give for continuing these types of efforts is that it contributes to the work of breaking down forms of practice into components and identifying key aspects of specific practices that are critical for supporting student learning in ways that make potentially productive routines of action visible to and learnable by others, which may ultimately contribute to the development of more successful learning environments. I also argue that rubrics like the EAR-MI have the potential to support researchers in developing stronger evidence of the effectiveness of practices that prior research has identified as critical for marginalized students and in more accurately and concretely identifying and describing learning environments as having potential for “success.” 
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  2. This descriptive study attended to the extent to which we see evidence of the presence of four practices that promote equity and access in 141 grades 3-8 mathematics lessons in the United States. We found that lessons generally showed evidence of some incorporation of the practices but often not at the highest level. Teachers in this sample engaged in social coaching at a relatively high level, across elementary and middle school classrooms. Teachers tended to do less with respect to supporting connection and engagement between student context and the math learning environment. We also found statistically significant differences between elementary and middle school lessons in positioning students as competent and supporting a nurturing environment by proactively building relationships and productive classroom culture. We offer possible interpretations and a few brief implications of these findings. 
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  3. This study examines the utilization of cognitive interviews longitudinally over a one-year period to collectively trace raters’ response processes as they interpreted and scored with observational rubrics designed to measure teaching practices that promote equity and access in elementary and middle school mathematics classrooms. We draw on four rounds of cognitive interviews (totaling 14 interviews) that involved four raters at purposeful time points spread over the year. Findings reported in this study focus on raters’ responses about one rubric, positioning students as competent. The findings point to the complexities of utilizing observational rubrics and the need to track response processes longitudinally at multiple time points during data collection in order to attend to rater calibration and the reliability and validity of resulting rubric scores. 
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