In all communications, teachers need to attend to their students, and carefully interpret what the students know from what they say or write. Communication can be used in many ways as a vehichle for assessment and learning. For example, a teacher can ask students what they know about circles at the beginning of a unit of study, then complile a list of the ideas and have students agree or not with each statement, justifying their opinions. This exposes students' misconceptions, and, more importantly, reinforces the expectations that there must be a classroom climate of respectful exchange of ideas, and that students should have reasons for their mathematical positions. Over time, such activities help sharpen students' ideas and their ability to communicate clearly.
Writing is a valuable way of reflecting on and solidifying what one knows.
Problems that require written explanation can be assigned regularly, and the class can discuss and compare the adequacy of any explanations. Such activities also serve as good assessment devices that can help teachers understand student thinking.