Abstract

Number systems are a cultural tool for understanding the world; therefore numeracy is as crucial in education as literacy. Numbers have two kinds of meaning: an analytical meaning, defined by the logic of the number system, and a representational meaning, which involves relating numbers to quantities and relations in the world. In general terms, the analytical meaning of numbers can be thought of as arithmetic and the representational meaning is the basis of quantitative reasoning. There is some degree of independence between children’s understanding of arithmetic and quantitative reasoning, but both are necessary when one uses numbers to understand the world. The heuristic value of this analysis will be illustrated in this talk by considering the development of children’s mathematical knowledge.