Implicit Understanding of Arithmetic with Rational Numbers: The Impact of Expertise

Recent work has shown that undergraduates at a major public university demonstrate implicit understanding of inverse relations between multiplication problems with fractions, as evidenced by the fact that solving one problem facilitates solving its inverse. The present study investigated whether such implicit understanding of mathematical relations is related to overall math ability. We found that low performers showed relational facilitation only when it was supported by perceptual similarity, whereas high performers showed relational facilitation on both perceptually similar and dissimilar problems. These findings are interpreted in terms of novice-expert differences in the representation of mathematical relations.