This article specifies how the setup, or introduction, of cognitively demanding tasks is a crucial phase of middle-grades mathematics instruction. We report on an empirical study of 165 middle-grades mathematics teachers' instruction that focused on how they introduced tasks and the relationship between how they introduced tasks and the nature of students' opportunities to learn mathematics in the concluding whole-class discussion. Findings suggest that in lessons in which (a) the setup supported students to develop common language to describe contextual features and mathematical relationships specific to the task and (b) the cognitive demand of the task was maintained in the setup, concluding whole-class discussions were characterized by higher quality opportunities to learn.

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In the accountability era, educators are pressed to use evidence-based practice. In this comparative case study, we examine the learning opportunities afforded by teachers' data use conversations. Using situated discourse analysis, we compare two middle school mathematics teacher workgroups interpreting data from the same district assessment. Despite similarities in their contexts, the workgroups invoked different data use logics that shaped teachers' learning opportunities. The first workgroup's instructional management logic linked increasing student achievement to individualization. The second workgroup's instructional improvement logic focused on students' thinking and linked it to instructional changes but was limited by broader instructional management logics. Evidence-based practice cannot be understood apart from the data use logics in teachers' communities, which are shaped by policy constraints.

This article outlines several forms of instructional practice that distinguished middle-grades mathematics classrooms that were organized around conceptually oriented activity and marked by African American students' success on state assessments. We identified these forms of practice based on a comparative analysis of teaching in (a) classrooms in which there was evidence of conceptually oriented instruction and in which African American students performed better than predicted by their previous state assessment scores and (b) classrooms in which there was evidence of conceptually oriented instruction but in which African American students did not perform better than predicted on previous state assessment scores. The resulting forms of practice can inform professional learning for preservice and in-service teachers.

This article reports on a review of the mathematics education research literature 1989-May 2011 specific to K-12 African American students’ opportunities to learn mathematics. Although we identify important developments in the literature, we conclude that the existing research base generally remains at the level of broad principles or orientations to teaching and is therefore inadequate for specifying forms of instructional practice that support African American students’ participation in rigorous mathematical activity. We suggest a research agenda focused on specifying forms of practice that are empirically shown to support African American students’ learning of mathematics and development of productive mathematical identities.