A Mathematical Model of How People Solve Most Variants of the Number‐Line Task
Autor: | Daryn Blanc-Goldhammer, Philip T. Quinlan, Dale J. Cohen |
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Rok vydání: | 2018 |
Předmět: |
Theoretical computer science
Mathematical model Computer science Concept Formation Cognitive Neuroscience 05 social sciences Numerical cognition Experimental and Cognitive Psychology Cognition Observer (special relativity) Models Theoretical Article 050105 experimental psychology Number line Underlying representation Artificial Intelligence Bounded function Task analysis Humans 0501 psychology and cognitive sciences Comprehension Mathematics Problem Solving 050104 developmental & child psychology |
Zdroj: | Cognitive Science. 42:2621-2647 |
ISSN: | 1551-6709 0364-0213 |
Popis: | 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. |
Databáze: | OpenAIRE |
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