Children’s Early Knowledge About Relationships Between Counting and Cardinality

Abstract

Counting and cardinal situations are at first separate and different situations for children. A given situation is either a cardinal situation (to which a single number word is applied, as in “I have five people in my family.”) or it is a counting situation (in which counting is carried out but with no end result). A very important step is taken when children first begin to connect counting and cardinal meanings, when children first indicate that they understand that counting has a result instead of just being an isolated activity. The nature of these first relationships between counting and cardinality, and how these relationships come to be established by children, is the focus of this chapter. The following three chapters continue the exploration of relationships children establish between counting and cardinal meanings of number words. The more complex relationships between counting and cardinality that are established after the first simple ones and that enable children to devise increasingly sophisticated solution procedures for addition and subtraction are discussed in chapter 8. Chapter 9 outlines the roles counting plays in children’s construction of equivalence and order relations on cardinal situations. Chapter 10 presents data on relationships between aspects of children’s ability to say number words, count objects, and relate counting to cardinal meanings. These chapters permit us to follow young children from age 2, when they understand only very small numerosities, to age 8, when they have constructed a general and abstract notion of cardinal number.