The teacher's mathematical discourse: How is it produced in the classroom and how can it be researched?

How can we examine if a teacher's discourse in the mathematics classroom is effective according to the goals of communicating a culture of school mathematics and producing opportunities for students to learn contents of this culture? In this paper, we present the construction of a notion of local coherence applied to the oral mathematical discourse in the classroom. We create indicators of coherence and relate them to the generation of mathematics learning opportunities. We illustrate the process with data from two teachers and the characterization of their discourse - its coherence - when teaching with examples. The discussion of grades of coherence and learning opportunities serves to distinguish the teachers' discourses. Drawing on this finding, we evaluate the notion of local coherence.