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Individual Differences in Implicit and Explicit Spatial Processing of Fractions

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 (SN...

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Autores principales: Toomarian, Elizabeth Y., Meng, Rui, Hubbard, Edward M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6460993/
https://www.ncbi.nlm.nih.gov/pubmed/31024373
http://dx.doi.org/10.3389/fpsyg.2019.00596
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author Toomarian, Elizabeth Y.
Meng, Rui
Hubbard, Edward M.
author_facet Toomarian, Elizabeth Y.
Meng, Rui
Hubbard, Edward M.
author_sort Toomarian, Elizabeth Y.
collection PubMed
description 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.
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spelling pubmed-64609932019-04-25 Individual Differences in Implicit and Explicit Spatial Processing of Fractions Toomarian, Elizabeth Y. Meng, Rui Hubbard, Edward M. Front Psychol Psychology 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. Frontiers Media S.A. 2019-04-05 /pmc/articles/PMC6460993/ /pubmed/31024373 http://dx.doi.org/10.3389/fpsyg.2019.00596 Text en Copyright © 2019 Toomarian, Meng and Hubbard. http://creativecommons.org/licenses/by/4.0/ 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.
spellingShingle Psychology
Toomarian, Elizabeth Y.
Meng, Rui
Hubbard, Edward M.
Individual Differences in Implicit and Explicit Spatial Processing of Fractions
title Individual Differences in Implicit and Explicit Spatial Processing of Fractions
title_full Individual Differences in Implicit and Explicit Spatial Processing of Fractions
title_fullStr Individual Differences in Implicit and Explicit Spatial Processing of Fractions
title_full_unstemmed Individual Differences in Implicit and Explicit Spatial Processing of Fractions
title_short Individual Differences in Implicit and Explicit Spatial Processing of Fractions
title_sort individual differences in implicit and explicit spatial processing of fractions
topic Psychology
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6460993/
https://www.ncbi.nlm.nih.gov/pubmed/31024373
http://dx.doi.org/10.3389/fpsyg.2019.00596
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