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Counting to Infinity: Does Learning the Syntax of the Count List Predict Knowledge That Numbers Are Infinite?
Junyi Chu1, Pierina Cheung2, Rose M Schneider1
1Department of Psychology, University of California, San Diego.
Cognitive Science
|August 8, 2020
Summary
Children develop an understanding of the successor function and infinity around age 5½. Knowledge of productive counting rules is linked to believing numbers are infinite, not necessarily the successor function.
Area of Science:
- Cognitive Development
- Number Cognition
- Mathematical Development
Background:
- Children's understanding of the successor function (n+1) is crucial for mathematical reasoning.
- Investigating the link between discovering productive counting rules and understanding numerical infinity.
Purpose of the Study:
- To explore how children discover the successor function and its relation to language-specific counting rules.
- To examine the connection between productive counting knowledge and beliefs about numerical infinity.
Main Methods:
- Tested 4- and 5-year-old children using three counting tasks.
- Assessed children's understanding of the successor function and numerical infinity.
- Related counting knowledge to beliefs about number systems.
Main Results:
- Children with productive counting rules were more likely to believe numbers are infinite.
- Productive counting knowledge was not directly linked to the successor function.
- 4-year-olds can generate number words beyond their spontaneous range using counting rules.
Conclusions:
- Children's discovery of productive counting rules may support reasoning about numerical infinity.
- Understanding of the successor function and numerical infinity may develop through different pathways.
- Early ability to generate number words supports inferences about the infinite nature of numbers.
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