Individual Differences in Implicit and Explicit Spatial Processing of Fractions.

Elizabeth Y Toomarian,Rui Meng,Edward M Hubbard

doi:10.3389/fpsyg.2019.00596

Abstract

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–for fractions–working with an explicit number line is a stronger predictor of math ability than implicit number line processing. 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.

Highlights

Recent efforts to understand predictors of mathematical achievement have begun to focus on the contribution of spatial skills in addition to numerical abilities
This study aimed to investigate the link between implicit spatial representations of fractions in adults and explicit measures of numerical/mathematical knowledge by focusing on three central questions: (1) which factors predict individual differences in spatial representations of fractions? (2) to what extent is the Spatial Numerical Association of Response Codes (SNARC) effect distinct from other indices of numerical processing and (3) do spatial representations of fractions, as measured by the fractions SNARC and Number Line Estimation (NLE) task, uniquely account for differences in math achievement in university undergraduates?
The overall experiment time would be unreasonably long if we were to collect twenty observations per stimulus per condition and would compromise the integrity of the data. Because this recommendation stems from the desire to control for intra-individual variability, we argue that our wide range of fraction magnitudes serves a similar purpose; by increasing the number of points on the mental number line (MNL) to which participants are asked to respond, we are effectively controlling for this variability in an analogous fashion

Summary

Introduction

Recent efforts to understand predictors of mathematical achievement have begun to focus on the contribution of spatial skills in addition to numerical abilities. One possible account for these relationships is the close behavioral, cognitive, and neural link between numbers and space (e.g., Hubbard et al, 2005; Toomarian and Hubbard, 2018a) These findings highlight just a few of the many factors that contribute to early mathematical understanding. In one specific study, preschool children’s approximate number sense and cardinality knowledge of number words both predicted later math achievement, and cardinality was found to mediate the relationship between approximate number and math achievement (Chu et al, 2015) Further investigation of these factors is certainly needed, as they relate to classes of numbers such as fractions, which are believed to be a critical part of a strong foundation for numerical understanding and uniquely predictive of later algebra-readiness (Booth and Newton, 2012)

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