Ordinal knowledge: Number names and number concepts in Chinese and English

Canadian Journal of Experimental Psychology,  Jun 2000  by Kevin Miller,  Susan M Major,  Hua Shu,  Houcan Zhang

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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. While crosscultural research shares this problem with other areas of psychological research in which participants cannot be randomly assigned to conditions, such as research on gender differences or age-related differences, it greatly complicates the task of drawing firm causal conclusions about the origins of observed cross-cultural differences.

One way to increase the plausibility of language-based explanations for cross-cultural differences in cognitive development is to make specific, linguistically based predictions about the timing and nature of expected cross-cultural differences. Many of the cultural factors listed previously lead to directional predictions that children in a particular culture should out-perform those growing up in a different environment. A language-based explanation is bolstered to the extent that it leads to stronger predictions about the kinds of tasks, the points in acquisition, and the nature of the problems that should distinguish children learning one symbol system from those learning another.

Research on differences in learning to count in Chinese and English provides an example of how linguistic analysis can lead to specific predictions about the timing and nature of cross-linguistic differences in a particular domain. Number name formation for both cardinal and ordinal numbers are presented in Figure 1. Research on the acquisition of cardinal numbers in the two languages will be discussed first, before predictions about the acquisition of ordinal numbers are described. Comparing the two languages, four portions of the number-naming sequence are particularly relevant: (a) Counting to 10 in either Chinese or English requires mastering an unordered set of names (i.e., one cannot predict that "nine" follows "eight" or that "jiu" follows "ba"). (b) After ten, the languages diverge. English names for "eleven' and "twelve" bear only an historical relation to "one" and "two" (Menninger, 1969), and names for "teen" numbers are formed by a different rule than are higher number names, with the unit value named before the decade value. Chinese number names above 10 follow a consistent base-ten rule (e.g., a literal translation of the Chinese name for 11 is "ten one"). (c) In the range 20-99, both systems converge on roughly isomorphic rules: a decade unit (e.g., "six") + "-ty" or "ten"+ a unit value, if any, in the range 1-9. The only morphological difference between Chinese and English names for numbers from 20-99 is that Chinese uses unit values for decade names (instead of modifying them as in English "twen" or "thir") and uses the unmodified name for 10 to designate decades (instead of the English "-ty"). (d) Finally, above 100, both Chinese and English form hundred names by using unit values in the range 1-9 plus a term for the unit (hundred/bai). With one exception, names for the last two digits of numbers above 100 (e.g., the "12" of "112") are not affected by being incorporated into a larger number. The single exception is that Chinese number names in the range 100-109 (and 200-209, etc.) interpose a term (ling) to represent the absent tens value, a feature unique to Chinese and related languages (Hurford, 1975, 198. In general, however, both languages converge after 20 on a regular base-ten system for forming number names.