Instructional improvement initiatives in many districts include instructional coaching as a primary form of job-embedded support for teachers. However, the coaching literature provides little guidance about what activities coaches should engage in with teachers to improve instruction. When researchers do propose activities, they rarely justify why those activities might support teacher learning. Drawing on the preservice and inservice teacher education literatures, we present a conceptual analysis of learning activities that have the potential to support mathematics and science teachers to improve practice. We argue that our analysis can inform research on mathematics and science coaching, coaching policies, and the design of professional learning for coaches.

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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Background Research suggests that teachers’ views of their students’ capabilities matter when attempting to accomplish instructional reform, particularly in settings serving historically marginalized groups of students. However, to date, this issue has received minimal attention in the scholarship and practice of mathematics instructional reform. Purpose This study offers a large-scale snapshot of middle-grades teachers’ views of their students’ mathematical capabilities in the context of instructional reform. It contributes to the field's understanding of the learning demands for teachers inherent in achieving a vision of high-quality mathematics instruction and suggests potentially critical foci for professional learning opportunities. Setting The study took place in two large urban districts pursuing ambitious reform in middle-grades mathematics. Participants Participants included 122 middle-grades mathematics teachers. Research Design The study consisted of a qualitative analysis of semistructured interviews conducted with each of 122 teachers regarding their perspectives on the district's reform efforts, including their views of their students’ mathematical capabilities in relation to the reform. Conceptually, we approached our analysis of teachers’ views of their students’ mathematical capabilities by attending to how they framed a common problem of practice—students facing difficulty in mathematics—diagnostically (i.e., how they explained the source of students’ difficulty) and prognostically (i.e., what they described doing to support students facing difficulty). Analysis also focused on patterns in the relations between teachers’ diagnostic and prognostic framings. Findings On the whole, most teachers did not view all of their students as capable of participating in rigorous mathematical activity. Most teachers attributed at least some of their students’ difficulty to inherent traits of the students or deficits in their families or communities, and most described lowering the cognitive demand of an activity if they perceived that students were facing difficulty. Moreover, our analysis of the relations between teachers’ diagnostic and prognostic framing revealed that even when teachers explained students’ difficulty in terms of instructional opportunities, thereby taking responsibility for their students’ learning, they did not necessarily respond in ways that would enable students to participate substantially in rigorous mathematical activity. Conclusions Findings suggest that a significant challenge in accomplishing ambitious reform entails supporting shifts in how teachers view their students’ capabilities along two dimensions: how teachers explain the source of students’ difficulties in mathematics and how they address such difficulties. Implications for designing professional learning opportunities to support productive shifts in teachers’ views of their students’ capabilities are discussed.