On the Compatibility of Dialogism and Dialectics: The Case of Mathematics Education and Professional Development

We argue that the distinction between dialogue (after Bakhtin) and dialectics
(after Hegel, Marx, Vygotsky), is of key importance to learning-teaching and to
mathematics education. Some followers of Bakhtin have argued that these
concepts are irreconcilable, or incompatible, since dialectics implies and
dialogism implicitly denies the requirement of telos (i.e., a targeted endpoint). On
the contrary, we argue for compatibility; dialogism can allow for the progress
implied by dialectics, but its teleology is inherent in its efficacy in practice rather
than in any pre-defined endpoint. We show how a mathematical or professional
dialogue can involve dialectical negations and supersession, thus providing for
progress or development, without loss of dialogism. Our case is taken from a
lesson study in which progress emerging from classroom and staffroom dialogues
is interpreted in dialectical terms as developmental. The connection with
Vygotsky’s theory of concepts in learning-teaching and the possible
generalization of the argument are discussed. We conclude that the key moments
on which concept development turns are: (1) the negation by multiple, lived
practices, and (2) the creative, speculative, supersession of inadequate concepts,
in appropriate dialogues.