A Mathematical Model of How People Solve Most Variants of the Number-Line Task

Autor/inn/en	Cohen, Dale J.; Blanc-Goldhammer, Daryn; Quinlan, Philip T.
Titel	A Mathematical Model of How People Solve Most Variants of the Number-Line Task
Quelle	In: Cognitive Science, 42 (2018) 8, S.2621-2647 (27 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0364-0213
DOI	10.1111/cogs.12698
Schlagwörter	Mathematical Models; Mathematics Skills; Problem Solving; Mathematical Concepts; Learning Strategies; Task Analysis; Bias + Suchen Sie Ihr Suchwort? Mathematical model; Mathematisches Modell; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Problemlösen; Learning methode; Learning techniques; Lernmethode; Lernstrategie; Aufgabenanalyse
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 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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01