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A mathematical model of how people solve most variants of the number-line task

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Publication details

DateAccepted/In press - 1 Oct 2018
DateE-pub ahead of print - 29 Oct 2018
DatePublished (current) - Nov 2018
Issue number8
Number of pages27
Pages (from-to)2621-2647
Early online date29/10/18
Original languageEnglish


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.

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© 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.

    Research areas

  • Number processing, Number-line, Numerical architecture, Numerical cognition

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