In this article I explore the question of how a cosmopolitan perspective on education could be understood from curriculum-based activities in classrooms. Assuming that there is a cosmopolitan potential in curriculum content as such, I draw on David Hansen, Anthony Kwame Appiah and Donald Davidson to argue that cosmopolitanism at the classroom level needs to be understood from both a moral and a communicative perspective. In this article the focus is on the latter. A communicative understanding of cosmopolitanism emphasizes the relational stance to the other and to the social and physical world.  The conditions for cosmopolitan dialogues are understood in the curriculum as shared environment, cosmopolitan curiosity and reciprocal communicative respect based on the recognition on responsibilities towards others in a shared world. The characteristic of cosmopolitan conversation is its potentiality.