How does counting relate to children’s understanding of infinity?

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

Integrative Statement

We understand that natural numbers are infinite, despite experiencing only particular numbers (e.g., three, fifty-seven, two thousand and ninety-one), but how do we acquire infinity? Previous studies have shown that children who can count to large numbers (e.g., a hundred) are more likely to understand infinity than those with limited counting experience (Cheung, Rubenson, & Barner, 2017; Hartnett & Gelman, 1998), but these studies leave open the question of why. On one hypothesis, children understand the infinite nature of numbers by acquiring their syntactic structure. For example, upon knowing that numbers one through nine are repeated iteratively across decades, children may learn that one can always generate the next number for any number, and thus that numbers never end.
In the current study, we examined this hypothesis by asking whether children who show knowledge of the decade structure of counting are more likely to understand infinity. Evidence for decade structure knowledge comes from two sources. First, children who lack knowledge of decade terms (e.g., 30, 40, 50) should nevertheless be able to count higher once decade terms are provided. Second, children who understand the decade structure should be able to generate the next number for any number. We therefore devised a Highest Count with Decade Support task (HC) and a What Comes Next task (WCN) to measure these abilities. In addition, we included an Infinity Task with questions designed to capture two critical components to understanding infinity: (1) that every number has a successor, and (2) that there is no highest number. We asked whether decade knowledge predicted each of these two components of infinity.
We tested 129 children aged between 4;0 and 5;11 (M: 5;0). Children completed three tasks in fixed order: Highest Count with Decade Support (HC), What Comes Next (WCN), and the Infinity task. To begin, children were asked to count as high as they could. Children who made an error at decade transitions (e.g., 29) were provided with decade terms (e.g., 30), and we tested how much higher they could count. Decade terms between 20 and 90 were provided. Children (N=80) were classified as having knowledge of decade structure if they could count at least two decades past their decade transition error or count to 99 on their own. For the WCN Task, we asked children what comes after N, which was a number ranging from 20 to 90.
We found that children who demonstrated decade knowledge on the HC task could, on average, count 30 higher than their first counting error (vs. 4 for those without decade knowledge). These children also performed better on the WCN task than those who did not show decade knowledge on the HC task. Critically, on the Infinity task, we found that children with decade knowledge on the HC task were more likely to understand that there is no highest number, but decade knowledge did not predict children’s understanding that every number has a successor. These results highlight one potential mechanism that may explain how children acquire infinity.

Authors

• Junyi Chu, Massachusetts Institute of Technology
  Presenting Author

• Rose Schneider, University of California San Diego
  Non-Presenting Author

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

• Jess Sullivan, Skidmore College
  Non-Presenting Author

• David Barner, University of California, San Diego
  Non-Presenting Author