ABSTRACT
Mathematics occupies about one-eighth of the secondary schools curriculum, and in primary schools perhaps slightly more. The expectations will have to be interpreted for each individual according to his or her need, ability and personality but the aims are virtually common for the whole group. In early years everyone expects that there will be verbal communication between pupil and teacher, between pupil and pupil, and between a pupil and himself. Few people would disagree with the statement that one expectation from teaching and learning mathematics is that pupils shall learn to communicate mathematics to others. Mathematical insight occurs when all the various elements of a mathematical situation are grasped in their relation to each other and to the whole situation. That mathematics uses a special language, or at least that it uses language in a special way, is completely obvious.
