A Mathematical Model of How People Solve Most Variants of the Number‐Line Task Article Swipe
Dale J. Cohen
,
Daryn Blanc‐Goldhammer
,
Philip T. Quinlan
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1111/cogs.12698
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1111/cogs.12698
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 modeled 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.
Related Topics
Concepts
Task (project management)
Bounded function
Equivalence (formal languages)
Representation (politics)
Number line
Computer science
Line (geometry)
Observer (physics)
Cognition
Artificial intelligence
Mathematics
Psychology
Discrete mathematics
Management
Politics
Physics
Geometry
Mathematics education
Law
Mathematical analysis
Neuroscience
Political science
Quantum mechanics
Economics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1111/cogs.12698
- https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/cogs.12698
- OA Status
- bronze
- Cited By
- 18
- References
- 52
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2899291363
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W2899291363Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1111/cogs.12698Digital Object Identifier
- Title
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A Mathematical Model of How People Solve Most Variants of the Number‐Line TaskWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2018Year of publication
- Publication date
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2018-10-29Full publication date if available
- Authors
-
Dale J. Cohen, Daryn Blanc‐Goldhammer, Philip T. QuinlanList of authors in order
- Landing page
-
https://doi.org/10.1111/cogs.12698Publisher landing page
- PDF URL
-
https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/cogs.12698Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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bronzeOpen access status per OpenAlex
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https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/cogs.12698Direct OA link when available
- Concepts
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Task (project management), Bounded function, Equivalence (formal languages), Representation (politics), Number line, Computer science, Line (geometry), Observer (physics), Cognition, Artificial intelligence, Mathematics, Psychology, Discrete mathematics, Management, Politics, Physics, Geometry, Mathematics education, Law, Mathematical analysis, Neuroscience, Political science, Quantum mechanics, EconomicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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18Total citation count in OpenAlex
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2025: 1, 2024: 2, 2023: 3, 2022: 4, 2021: 2Per-year citation counts (last 5 years)
- References (count)
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52Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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