Ordinal Knowledge: Number Names and Number Concepts in Chinese and English

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Abstract Previous research has demonstrated cross-language variation in early counting associated with linguistic differences in number-naming systems. Ordinal number names are typically learned later than cardinal names, but languages also differ in the regularity with which they form these names. Elementary school children in China and the U.S. showed differences in the acquisition and use of ordinal numbers corresponding to linguistic differences in ordinal names in their native languages. On tasks assessing children's conceptual knowledge of ordinal relations, a more complicated picture emerged. These results suggest that (a) children induce their language's set of ordinal number names by generalization based on rules sanctioned by early examples, and (b) the relation between ordinal names and ordinal concepts is a complex one, with language only one source of difficulty in understanding ordinal relations. Implications for studies of the relation between linguistic structure and cognitive development are discussed, in particular the possibility that effects of linguistic differences may vary for different levels of development and for different aspects of cognition.

Becoming a skilled user of symbols is at the heart of what it means to be an educated person. We think about the world in terms of a variety of culturally transmitted symbol systems - the calendars, numbers, and writing systems that we use to form and express our thoughts. Much of cognitive development involves children's struggle to master and then productively use symbolic tools.

Learning any kind of symbolic system is difficult. Some of the problems children have in mastering symbol systems stem from the fact that symbolic representations are inherently complex Deloache, Miller, & Pierroutsakos, 1998) or from general limitations in children's conceptual development (Case, 1992). Others, however, result from the structure of the symbol systems children are acquiring and the match between that structure and the ideas that children bring to the process of acquisition.

Because children within a culture typically learn a common set of symbol systems, distinguishing universal aspects of cognitive development from those that are contingent upon a particular culture or language requires cross-cultural comparisons. Cross-cultural comparisons, in turn, present obstacles of their own to the task of identifying factors that might account for differences that have been found. For example, studies have found quite dramatic differences in mathematical achievement between Englishspeaking children growing up in North American and their Chinese-speaking peers (e.g., Stevenson & Stigler, 1992). Many factors may account for these differences - differences in educational practices in schools (Stevenson & Stigler, 1992), differences in student and parental attitudes toward education (Chen & Uttal, 1988), differences in parental practices (Huntsinger, Jose, Liaw, & Ching, 1997), in addition to differences in the way in which concepts are represented in the different languages.

The research reported here focuses on the last source of cross-cultural differences. To the extent that children must figure out the underlying structure of the symbol systems they are learning, then differences in the organization of those systems and in the fit between that structure and children's pre-existing concepts should have an effect on the ease with which they acquire particular symbol systems (Miller & Paredes, 1996). Yet to maintain that the organization of symbol systems can affect children's learning is not to deny that the various social factors described in the preceding paragraph can have a profound effect on children's learning. Furthermore, in the absence of experiments in which children could be randomly assigned to languages or cultures, it is impossible to draw firm conclusions about the causes of observed cross-cultural differences. …