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A new similarity measure to reveal individual differences and growth in implicitnumber conceptions

Abstract

How are numbers represented in peoples minds? Previous work has used pairwise similarity judgments among numeralsto reveal development in individuals conceptions of number, from exclusively encoding magnitude in elementary schoolto including properties like shared factors in adulthood (Miller & Gelman, 1983). We extend this observation to develop anew, expanded measure comprised of two 10-item sets exemplifying multiple mathematical concepts (e.g., squares, prime-ness), which can ultimately be used as a subtle pre- and post-test surrounding concept-specific education or interventions.Initial multidimensional scaling analyses reveal individual differences in clustering of numerals based on mathematicalproperties that are not necessarily concordant with the individuals explicit knowledge of the same properties, which wealso solicited. We thus see this as a promising way to measure implicit number conceptions and track the salience of richmathematical properties in individuals representations of number.

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