Abstract
Previous research amply showed the importance of a good fraction understanding but also people’s lack of fraction understanding. It is therefore important to investigate the cognitive processes that underlie reasoning with fractions. The present study investigated the role of inhibition and switch costs in fraction comparison tasks. Participants solved a fraction comparison task that alternated between 4 items congruent and 4 items incongruent with natural number reasoning. This allowed to not only investigate congruency switch effects, but also inhibition, given that inhibition was experimentally increased by the prolonged exposure to incongruent trials. Based on data of seventh graders, the present study showed that inhibition does not only play a role in learners’ general mathematics achievement, but also in specific areas of mathematics, such as fractions. Moreover, a switch cost was found in the lower accuracy rates and higher reaction times needed to correctly solve switch items compared to non-switch items.
Highlights
IntroductionTwiss-Garrity, 2014; Siegler et al, 2012)
Fraction UnderstandingThe acquisition of a good understanding of fractions is of crucial importance for learners’ mathematical development (Bailey, Hoard, Nugent, & Geary, 2012; Booth, Newton, &Twiss-Garrity, 2014; Siegler et al, 2012)
Most of the studies linking inhibitory control with mathematics achievement are correlational in nature; research showing the causal relation between inhibition and mathematics achievement is still missing
Summary
Twiss-Garrity, 2014; Siegler et al, 2012) It forms the basis for a good understanding of later mathematical contents, such as algebra, proportional reasoning, probability, and calculus (see for example Behr, Lesh, Post, & Silver, 1983; Booth et al, 2014). One reason received a lot of research attention in the last two decades, namely learners’ tendency to apply natural number properties to rational numbers. This phenomenon is known as the natural number bias (for an overview, see Van Hoof et al, 2017). Several longitudinal studies found that a good understanding of the numerical magnitude of fractions is of crucial importance. It forms a first step and is necessary to understand other aspects of fractions, such as doing operations with fractions (Van Hoof et al, 2018; McMullen et al, 2015; McMullen & Van Hoof, 2020)
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