Cohen, Dale, Blanc-Goldhammer, Daryn and Quinlan, Philip Thomas orcid.org/0000-0002-8847-6390 (2018) A mathematical model of how people solve most variants of the number-line task. COGNITIVE SCIENCE. pp. 2621-2647. ISSN 0364-0213
Abstract
Current understanding of the development of quantity representations is based primarily on performance in the number line task. We posit that the data from number line tasks reflect the observer’s underlying representation of quantity, together with the cognitive strategies and skills required to equate line length and quantity. Here, we specify a unified theory linking the underlying psychological representation of quantity and the associated strategies in four variations of the number-line task: the production and estimation variations of the bounded and unbounded number-line tasks. Comparison of performance in the bounded and unbounded number-line tasks provides a unique and direct way to assess the role of strategy in number-line completion. Each task produces a distinct pattern of data, yet each pattern is hypothesized to arise, at least in part, from the same underlying psychological representation of quantity. Our model predicts that the estimated biases from each task should be equivalent if the different completion strategies are modelled appropriately and no other influences are at play. We test this equivalence hypothesis in two experiments. The data reveal all variations of the number-line task produce equivalent biases except for one: the estimation variation of the bounded number-line task. We discuss the important implications of these findings.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Cognitive Science Society, Inc. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details. |
Keywords: | Number processing,Number-line,Numerical architecture,Numerical cognition |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Psychology (York) |
Depositing User: | Pure (York) |
Date Deposited: | 07 Nov 2018 09:49 |
Last Modified: | 26 Mar 2025 00:09 |
Published Version: | https://doi.org/10.1111/cogs.12698 |
Status: | Published |
Refereed: | Yes |
Identification Number: | 10.1111/cogs.12698 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:138200 |