How do you establish a classroom culture in which students routinely conjecture and think mathematically? How do you establish a way of working with teachers, using video, in which discussion supports professional development? The present book offers answers to these questions through an in depth (enactivist) study of one exceptional teacher in one innovative mathematics department in the UK. The book reveals some striking parallels between working to support students’ mathematical thinking and working to support teacher learning. A case is made for the importance of meta communication in both contexts - communication about the communications that are occurring. For example, there is compelling evidence from a classroom that metacommunication, linked to the words ‘conjecture’ and ‘becoming a mathematician’, supports student metacognition and mathematical thinking. In working with teachers or students, offering these powerful metacommunications seems to require a heightened listening. With a heightened listening, attention is placed not just in what is said, but in what kind of a thing is said, with the teacher or facilitator being alongside the individuals in the wider group.