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Learning a Novel Number System: The Role of Compositional Rules and Counting Procedures.

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Title: Learning a Novel Number System: The Role of Compositional Rules and Counting Procedures.
Authors: Holt, Sebastian1 (AUTHOR) sholt@ucsd.edu, Barner, David1 (AUTHOR)
Source: Cognitive Science. Jun2025, Vol. 49 Issue 6, p1-31. 31p.
Subject Terms: *Artificial languages, *Learning, *Adult students, *Instructional systems, Number systems
Abstract: Humans count to indefinitely large numbers by recycling words from a finite list, and combining them using rules—for example, combining sixty with unit labels to generate sixty‐one, sixty‐two, and so on. Past experimental research has focused on children learning base‐10 systems, and has reported that this rule learning process is highly protracted. This raises the possibility that rules are slow to emerge because they are not needed in order to represent smaller numbers (e.g., up to 20). Here, we investigated this possibility in adult learners by training them on a series of artificial number "languages" that manipulated the availability of rules, by varying the numerical base in each language. We found (1) that the size of a base—for example, base‐2 versus base‐5—had little effect on learning, (2) that learners struggled to acquire multiplicative rules while they learned additive rules more easily, (3) that memory for number words was greater when they were taught as part of a sequential count list, but (4) that learning numbers as part of a rote list may impair the ability to map them to magnitudes. [ABSTRACT FROM AUTHOR]
Copyright of Cognitive Science is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Humans count to indefinitely large numbers by recycling words from a finite list, and combining them using rules—for example, combining sixty with unit labels to generate sixty‐one, sixty‐two, and so on. Past experimental research has focused on children learning base‐10 systems, and has reported that this rule learning process is highly protracted. This raises the possibility that rules are slow to emerge because they are not needed in order to represent smaller numbers (e.g., up to 20). Here, we investigated this possibility in adult learners by training them on a series of artificial number "languages" that manipulated the availability of rules, by varying the numerical base in each language. We found (1) that the size of a base—for example, base‐2 versus base‐5—had little effect on learning, (2) that learners struggled to acquire multiplicative rules while they learned additive rules more easily, (3) that memory for number words was greater when they were taught as part of a sequential count list, but (4) that learning numbers as part of a rote list may impair the ability to map them to magnitudes. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Cognitive Science is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: Jun2025
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