Teachers facilitate this process when they pose probing questions and invite children to explain their thinking. Teachers also can assess students' knowledge and insight by listening and observing. The idea that children should learn mathematics meaningfully is implicit in this discussion, for meaningful learning is necessary if mathematics is to make sense and if communication is to be possible. Discussion Young children are active, social individuals. Much of the sense they make of the world is derived from their communications with other people.
Communicating helps children to clarify their thinking and sharpen their understandings.
Representing, talking, listening, writing, and reading are key communication skills and should be viewed as integral parts of the mathematics curriculum. Probing questions that encourage children to think and explain their thinking orally or in writing help them to understand more clearly the ideas they are expressing. Representing is an important way of communicating mathematical ideas at all levels, but especially so in K-4. Representing involves translating a problem or an idea into a new form. Translations of this type often are used by adults and children as they converse with others.