En route to a gazillion meanings: The acquisition of the syntax and meaning of complex multiplicative numerals in children

• In Event: 1-030 - Linguistic basis of numerical cognition

Integrative Statement

All numerate cultures have numerical composition systems that allow the creation of indefinitely many numerals out of a small number of numerals. According to Hurford (1975), all numerical composition systems are based on two abstract syntactic rules, one for expressing multiplication and one for expressing addition. The present study focuses on the acquisition of the multiplicative rule.
The multiplicative rule states that any numeral that is combined with a numeral from the general category MULTIPLIER is a complex multiplicative numeral. In other words, all complex multiplicative numerals have the same abstract syntactic structure, namely [[NUMERAL][MULTIPLIER]]. In English, the most frequent multipliers are “hundred,” “thousand” and “million.” Thus, in English, “two hundred”, “twenty-five thousand” and “twenty-five thousand million” are all complex multiplicative numerals. The abstract syntactic structure [[NUMERAL][MULTIPLIER]] is mapped onto the abstract meaning Numeral X Multiplier. Thus, the meaning of all complex multiplicative numerals can be derived from their syntactic structure and from the meaning of their constituent parts. For example, “two hundred” means two times one hundred and “twenty-five thousand” means twenty-five times one thousand. This is highly generative because it can also be applied to novel combinations. For example, given knowledge that the novel numeral “dodecaglion” is a multiplier that refers to the number of stars in the Milky Way, one can infer that the complex numeral “two dodecaglion” means two times the number of stars in the Milky Way because it has the abstract syntactic structure [[NUMERAL][MULTIPLIER]]. Using the same principle, one can then go on to infer the meanings of a large number of new numerals such as “five thousand and twenty-three dodecaglion” and so on.
In the present study, we ask when young children begin to represent complex multiplicative numerals in terms of the abstract syntactic structure [[NUMERAL][MULTIPLIER]] and to use it to infer the meaning of novel combinations. To do so, we taught 30 English-speaking 4½ to 6½-year-olds that the novel complex numeral “one gobi” meant one times three by showing them groups of three (e.g., three houses) and referring to them as “one gobi” (e.g., “These are one gobi houses”; see Table 1). To test whether children analyzed “one gobi” as [[NUMERAL][MULTIPLIER]] , we asked whether they were able to infer that two gobi means two times three without any further teaching. 40% of the participants inferred this. To test whether they did so because they had mapped “one gobi” and “two gobi” onto [[NUMERAL][MULTIPLIER]] , we taught a novel number that could not be mapped onto this structure to another group of 30 children of the same age – i.e., these children were taught to map “gobi Xs” onto groups of three (e.g., “These are gobi houses”). Only 10% of the children in this group took two gobi to mean two times three. These findings suggest that at least some children are able to interpret complex numerals using the multiplicative rule, and thus have the capacity to learn the meaning of indefinitely many numerals.

Authors

• Mathieu Le Corre, Centro de Investigación en Ciencias Cognitivas, Universidad Autónoma del Estado de Morelos
  Presenting Author

• Meghan Dale, Queen's University
  Non-Presenting Author

• Pierina Cheung, Nanyang Technological University, National Institute of Education
  Non-Presenting Author