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Front. Psychol. | doi: 10.3389/fpsyg.2019.00596

Individual Differences in Implicit and Explicit Spatial Processing of Fractions

  • 1University of Wisconsin-Madison, United States

Recent studies have explored the foundations of mathematical skills by linking basic numerical processes to formal tests of mathematics achievement. Of particular interest is the relationship between spatial-numerical associations—specifically, the Spatial Numerical Association of Response Codes (SNARC) effect—and various measures of math ability. Thus far, studies investigating this relationship have yielded inconsistent results. Here, we investigate how individual implicit and explicit spatial representations of fractions relate to fraction knowledge and other formal measures of math achievement. Adult participants (n=105) compared the magnitude of single digit, irreducible fractions to ½, a task that has previously produced a reliable SNARC effect. We observed a significant group-level SNARC effect based on overall fraction magnitude, with notable individual variability. While individual SNARC effects were correlated with performance on a fraction number-line estimation (NLE) task, only NLE significantly predicted scores on a fractions test and basic standardized math test, even after controlling for IQ, mean accuracy, and mean reaction time. This suggests that working with an explicit number line is a stronger predictor of math ability than implicit number line processing of fractions. Neither individual SNARC effects nor NLE performance were significant predictors of algebra scores; thus, the mental number line may not be as readily recruited during higher-order mathematical concepts, but rather may be a foundation for thinking about simpler problems involving rational magnitudes. These results not only characterize the variability in adults’ mental representations of fractions, but also detail the relative contributions of implicit (SNARC) and explicit (NLE) spatial representations of fractions to formal math skills.

Keywords: Spatial-numerical associations, SNARC, number line estimation, fractions, individual differences

Received: 15 Sep 2018; Accepted: 04 Mar 2019.

Edited by:

Firat Soylu, University of Alabama, United States

Reviewed by:

Robert Reeve, The University of Melbourne, Australia
Mauro Murgia, University of Trieste, Italy  

Copyright: © 2019 Toomarian, Meng and Hubbard. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Elizabeth Y. Toomarian, University of Wisconsin-Madison, Madison, United States,