Pathways to Number: Children's Developing Numerical Abilities

By Jacqueline Bideaud; Claire Meljac et al. | Go to book overview

6 Relationships Between Counting and Cardinality From Age 2 to Age 8

Karen C. Fuson Northwestern University

Young children begin to understand and to use number words in seven different kinds of contexts (see Fig. 6.1). Three of these contexts are mathematical ones: a cardinal context, in which the number word refers to a whole set of entities (a discrete quantity) and describes the manyness of the set ("I want two cookies"); an ordinal context, in which the number word refers to one entity within an ordered set of entities and describes the relative position of that entity ("I was second"); and a measure context, in which the number word refers to a continuous quantity and describes the manyness of the units that cover (or fill) the quantity ("I am two years old," perhaps with two fingers showing, making it also a cardinal context). Two other contexts, sequence and counting, provide cultural tools for ascertaining the correct number word to be used in cardinal, ordinal, or measure contexts. The sequence context is a recitation context in which number words are said in their correct order but no entities are present, and the number words refer to nothing; this context is originally like reciting the alphabet or the days of the week. In the counting context, number words are put into a one-to-one correspondence with entities; each number word refers to a single entity but describes nothing about it (it is just a count label, or tag, for the entity). Number words are also used to say written numerals. This symbolic context (or perhaps better, a numeral context) originally elicits a number word with no accompanying meaning and no reference beyond the numeral itself ("That's a six" upon seeing 6). Later on, written numerals themselves can take on cardinal, ordinal, measure, counting, or sequence meanings. Finally, number words are also used in non-numerical (or at least quasi-numerical) contexts, such as telephone numbers, television channels, zip codes, house addresses, and bus numbers.

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