Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/22489
Title: 
Authors: 
Subjects: 
Count list
Infinity
Conceptual change
Successor function
Highest count
Decade+Unit rule
Issue Date: 
2020
Citation: 
Chu, J., Cheung, P., Schneider, R. M., Sullivan, J., & Barner, D. (2020). Counting to infinity: Does learning the syntax of the count list predict knowledge that numbers are infinite? Cognitive Science, 44(8), Article e12875. https://doi.org/10.1111/cogs.12875
Abstract: 
By around the age of 5½, many children in the United States judge that numbers never end, and that it is always possible to add 1 to a set. These same children also generally perform well when asked to label the quantity of a set after one object is added (e.g., judging that a set labeled “five” should now be “six”). These findings suggest that children have implicit knowledge of the “successor function”: Every natural number, n, has a successor, n + 1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language‐specific counting routines (e.g., the rules in English that represent base‐10 structure). We tested 4‐ and 5‐year‐old children’s knowledge of counting with three tasks, which we then related to (a) children’s belief that 1 can always be added to any number (the successor function) and (b) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge was not directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as 4 years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end.
Description: 
This is the original draft, prior to peer-review, of a manuscript published in Cognitive Science. The published version is available online at https://doi.org/10.1111/cogs.12875
URI: 
ISSN: 
0364-0213 (print)
1551-6709 (online)
DOI: 
File Permission: 
Open
File Availability: 
With file
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