We argue that the distinction between dialogue (after Bakhtin) and dialectic (after Hegel, Marx, Vygotsky), that Matusov has previously highlighted, is of key importance to mathematics education. According to Matusov, for Bakhtin these concepts are incommensurable since dialectics implies and the dialogism denies telos (a target). In this essay we argue that mathematical dialogue can and should have teleology Matusov says is implied by dialectics. Thus a good dialogue might involve mathematical (or professional) negation and sublation, providing the dialectic for mathematical (or professional) 'progress' and development. To make this concrete, we illustrate the argument with a lesson study in which progress emerging from dialogues is interpreted in dialectical terms. [For the complete proceedings, see ED597799.]