ABSTRACT
In the search for new and effective ways of teaching children mathematics, the first important step must be to establish what they need to know about the subject. The question is an obvious one, but there is no universally accepted answer to it. In this chapter, we shall argue that from the beginning of their school learning about mathematics, children need to have, and to be able to use, two different types of knowledge. One is knowledge about quantitative relations and the other knowledge of the counting system. Our claim is that the distinction between the two should play a central role in plans for introducing children to arithmetic when they first go to school. We shall also argue that current theories about mathematical development tend to concentrate on one, and to ignore the other, of these two forms of mathematical knowledge.
