In this book, I have explored the proposition that, when people talk about mathematics, they use language as a means of satisfying a number of communicative ‘wants’. Many of my data are drawn from expert-novice conversations, and my conclusions apply, in the first instance at least, to such discourse contexts. Broadly speaking, communicative wants in mathematics talk are of two kinds. The first kind is co-operative and cognitive, stemming from a desire to share mathematical ideas-to give and receive insights, knowledge and understanding. It is associated with transactional functions of language. This giving and receiving is not one-way information traffic, flowing from teacher to pupil. The teacher needs to know what the pupil knows, what kind of knowledge s/he has constructed. My transcripts amply demonstrate the willingness of pupils to supply such information, and on occasion the pleasure they derive from doing so.