Syntactic embedding of cardinal numbers

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

Integrative Statement

Understanding the meaning of cardinal numbers requires not only the comprehension of the lexical class of digits (i.e., one, two, …, nine) and its local successor function but also the use of the Merge operations among digits, multipliers (e.g., -ty, hundred), and phrases (e.g., two hundred nine) (Hurford, 1975). We propose that understanding the syntactic rules underlying these operations is at the heart of comprehending the discretely combinatorial properties of natural numbers expressed in a base-10 system. In this study, we developed a novel task to assess this syntactic knowledge in representing cardinal numbers, examined the age at which children acquire this knowledge, and tested how it relates to other types of numerical knowledge.
This novel task (Give-a-number-base-10 or Give-N10) is much alike the give-a-number task (Wynn, 1990) as children are asked to give a specific number of items to the experimenter. Critically, however, the task utilizes four spatially distinct groups of ten items, and the children are asked to give a large number of items expressed in complex numerals such as sixteen, twenty-seven, and thirty-two. Importantly, prior to testing, the experimenter models a case of retrieving 31 items by grabbing three groups of ten items one at a time and then grabbing a single item from the last group, illustrating the embedded nature of the numeral thirty-one, [[three -ty] one]. A total of 33 cardinal principle knowers (ages 5.0-9.4 y) completed this novel task as well as the Unit task (Sarnecka & Carey, 2008; Davidson et al., 2012) that assessed children’s semantic induction over a local successor function in the decades. Two other tasks measured children’s abstract counting knowledge and their comprehension of number phrases built from syntactic operations of digits and multipliers using an open abacus.
We found that children’s ability to infer the next number is necessary but not sufficient for understanding the syntactic structure of cardinal numbers. Specifically, many 5-year-old children who pass the Unit task failed to retrieve, for example, 27 or 32 items using groups of ten items, but everyone who passed this Give-N10 task passed the Unit task (mid-P McNemar test, p < .001). On average, it was not until 6 years of age when children passed the Give-N10 task. In addition, children’s performance in Give-N10, while controlling for school grade, was associated with their abstract counting ability (p < .001) and with their comprehension of the numerical sequence in the abacus task (p < .05). These results indicate that Give-N10 taps into the syntactic knowledge underlying the formation of complex numerals, although unlike the other two tasks Give-N10 requires cardinal numerical representations. Thus, Give-N10 potentially provides a unique opportunity to evaluate children’s knowledge about the meaning of natural numbers. In sum, the findings indicate that semantic induction over a local counting sequence is not sufficient for a child to grasp the discretely combinatorial properties of natural numbers in a base-10 system, and that the acquisition of the principles underlying the natural numbers (partially tested in Give-N10) is much protracted than previously thought.

Authors

• Diego Guerrero, University of Massachusetts
  Presenting Author

• Brynn Boutin, University of Massachusetts
  Non-Presenting Author

• Tom Roeper, University of Massachusetts
  Non-Presenting Author

• Joonkoo Park, University of Massachusetts
  Non-Presenting Author