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.