We aim to open up discussion about the intertwined roles of teachers and tasks that involve students communicating about mathematics when working in groups. Over many years we have observed, researched and ourselves have taught students working on mathematics in groups and find that it is often easier to pay attention to the forms of communication rather than its mathematical content. The notion of 'groupworthy' tasks has become a popular focus and communication an explicit component of curricula in many countries; it is timely to consider further the mathematical content of communication while working in groups on such tasks.