This conversation is playful, urgent, and mathematical. The students are exchanging their observations, clarifying their own and each other's ideas, agreeing, disagreeing, and challenging one another. The Talking Mathematics videotapes contain numerous examples of mathematical discourse that were captured in a variety of contexts and settings. The role of discourse in children's mathematical development in schools has been underrated. Classroom talk plays many roles and needs to be seen as much more complex and varied than previously thought.
Talk is both individual and social.
It is a major way to develop and negotiate shared meanings. In elementary mathematics classrooms, talk may serve many purposes. These include forming ideas, internalizing ideas, thinking aloud, and assessing learning. We discuss each of these in the following section. As far back as any of us can remember, our mathematics teachers seemed to express only clear, complete, and unhesitant ideas.