ABSTRACT
This paper reports research into how mathematical explanations are constructed during conversation based on videotapes of pairs of student math teachers collaboratively writing explanations in geometry. In particular, we analyzed how disagreements about parts of their explanations were managed in these conversations. In contrast to research on disagreement in everyday conversation, explanation disagreements were more likely to overlap with preceding turns and to be stated baldly without prefaces, token agreements or qualifications. However, the observed frequencies of different kinds of disagreements were not consistent with a model favoring explicit substantive disgreement either. Instead, it is proposed that both the interpersonal concerns that would motivate a preference for agreement and the conceptual concerns for a quality explanation that would motivate a preference for substantive disagreement are being managed by participants. Disagreements are co-constructed, and conversants are seen to jointly employ complex devices for introducing and managing disagreement across turns that can satisfy both kinds of concerns with much less conflict between them than might have been expected.
