The goal of this article is to describe a language that formalizes the constituting role of interlocution underlying the discovery of the solution to an arithmetic problem by two children conversing for this purpose. The interaction takes place from the experimental group of an experiment demonstrating that dyads are better than single subjects at solving a division of division problem. The authors propose a formal description of the natural unfolding of the interaction process that leads to the discovery of the solution, by identifying its microgeneses of the solving and the moment when an understanding irrupts. To show how the discourse precedes the calculation, the authors use interlocutory logic (Trognon and Batt, Interlocutory logic: a unified framework for studying conversation interaction. In: Streek J (ed) New adventures in language and interaction. Benjamins, Bruxelles, pp 9–40, 2010), a theory of the logical properties of natural interlocution .