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• #### Index 441-454

The difficulty preschoolers have in coordinating the process of keeping track of objects and counting them seems to be a universal characteristic of learning to count, with children in different cultures showing comparable rates of recounting or skipping objects.18 Large differences across languages have been found in a second key aspect of procedural fluency in the preschool period, the mastery of the set of number names used in the child’s native language.

##### Language and Early Mathematical Development

One aspect of counting that preschool children find particularly difficult is learning the number names. Learning a list of number names up to 100 is a challenging task for young children. Furthermore, the structure of the number names in a language is a major influence on the difficulties children have in learning to count correctly. These difficulties have important implications for the initial learning of mathematics in elementary school.

The number names used in a language provide children with a readymade representation for number. Counting principles are universal and so do not differ between languages, but number names do differ in sound and structure across languages and influence children’s learning to count.

Linguistic structure of number names. Names for numbers have been generated according to a bewildering variety of systems.19 The Hindu-Arabic system for representing the whole numbers is clearly a base-10 system, with 10 basic symbols (the digits 0–9). These may be freely combined, with the place of a digit indicating the power of 10 that it represents.20 The Hindu-Arabic system is a useful reference point in describing number-naming schemes for two reasons. First, it is a widely used system for writing numbers. Second, it is as consistent and concise as a base-10 system could be.

Box 5–1 shows how spoken names for numbers are formed in three languages: English, Spanish, and Chinese. All of these languages use a base-10 system, but the languages differ in the clarity and consistency with which the base-10 structure is reflected in the number names.

As the first section of the figure shows, representations for numbers from 1 to 9 consist of an unsystematically organized list. There is no way to predict that 5 or five or wu come after 4, four, and si, respectively, in the Arabic numeral, English, and Chinese systems.

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