Cognitive Science 41 (8):2053-2088 (2017)

Abstract
Why might it be beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse primes for the equation that immediately followed it. Students with relatively high math ability showed relational priming both with and without high perceptual similarity. Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers. Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers.
Keywords Mathematical cognition  Rational numbers  Relational priming
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DOI 10.1111/cogs.12468
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