The nature of mathematical activity and discourse that teachers foster in classrooms is likely influenced by their explanations of sources of students' difficulty. Several small-scale qualitative studies suggest that how teachers make sense of student difficulty matters for whether they engage all of their students in rigorous mathematical activity. In this article we extend such work to a sample of 165 teachers in four large urban districts. In particular, we investigated the extent to which teachers' explanations of sources of students' difficulty in mathematics (as due to traits of students or the communities they come from, or as in relation to the opportunities to learn provided in classrooms) are related to students' participation in quality mathematical discourse. We found that they are significantly related and that they depend on the racial and linguistic classroom composition of students they teach.

This study sought to understand how aspects of middle school mathematics teachers' knowledge and conceptions are related to their enactment of cognitively demanding tasks. The author found that teachers' mathematical knowledge for teaching and conceptions of teaching and learning mathematics were contingent on one another and significantly related to teachers' enactment of cognitively demanding tasks.

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.

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Background/Context This article contributes to the literature on how teachers learn on the job and how schools and districts can support teacher learning to improve student learning and incorporate changing standards and curricular materials into instructional practices. The findings in this study are relevant to the implementation of ambitious mathematics instruction reform through changing teachers’ knowledge and instructional practices. Focus of Study This study examines how middle school teachers’ networks influence their mathematical knowledge for teaching (MKT) and instructional practices. We also examined how mathematics coaches’ expertise, in the form of MKT, plays a role in augmenting the extent to which teachers learn through interacting with close colleagues. Research Design The article draws on data from a larger NSF-funded study in four large, urban districts that responded to accountability pressures by attempting to implement ambitious mathematics instruction aligned with the recommendations of the National Council of Teachers of Mathematics (NCTM) and by supporting implementation with a significant investment in teacher learning. The analysis in this paper involves 89 focal participants who were middle school mathematics teachers in 29 schools, the focal participants’ close colleagues, and their instructional coaches. Measures include mathematics teachers’ professional networks, MKT, classroom practices, individual background characteristics, and school factors. We used hierarchical linear models with cross-level interaction effects and in-depth sensitivity analyses of the effects of close colleagues and coaches. Findings/Results Our results show that changes in teachers’ instructional practice were positively related to their access to instructional expertise through interactions with close colleagues. But, we did not find a similar significant relationship between changes in teachers’ MKT and access to their close colleagues’ MKT expertise. Rather, coaches’ MKT expertise positively moderated the extent to which teachers learned MKT from their close colleagues through seeking advice on teaching mathematics; that is, having an expert coach in the school enhanced the MKT learning opportunities that teachers had from interacting with close colleagues. Conclusions/Recommendations Results from this study shed light on how to support teachers’ on-the-job learning and successfully implement ambitious instructional reforms in schools. It is important for schools and districts to consider ways to encourage the development of teacher networks that can promote instructional changes. For example, schools and districts can purposely provide common planning time and common workspaces that facilitate sharing expertise among teachers. They can also support teachers with instructional coaches who have content expertise and know how to facilitate interactions among teachers.