Orchestrating a mathematical theme: Eleven-year olds discuss the problem of infinity

The article focuses on the process of learning in joint problem solving and the aim is to give an empirical account of how communication can play a vital role when children seek to understand a mathematical content. The article reports a case study where pupils at the intermediate level of the Swedish compulsory school (11 years of age) solve a non-standard mathematics task confronting them with the phenomenon of infinity. The interaction between the children (4 triads) is video and tape-recorded and in the analysis the childrenʹs interpretations of the given task are described and discussed. We show how the children, by varying their interpretations of the task (e.g. by contextualizing it in different ways) can reach a considerable depth in their understanding of the problem posed and how the children, in a collective orchestration of such variations of the mathematical theme, can exceed the limits of their initial understanding of the mathematical content.