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Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

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Abstract

Whether our general numerical skills and the mathematical knowledge that we acquire at school are entwined is a debated issue, which many researchers are still striving to investigate. The findings reported in the literature are actually inconsistent; some studies emphasized the existence of a relationship between the acuity of the Approximate Number System (ANS) and arithmetic competence, while some others did not observe any significant correlation. One potential explanation of the discrepancy might stem from the evaluation of the ANS itself. In the present study, we correlated two measures used to index ANS acuity with arithmetic performance. These measures were the Weber fraction (w), computed from a numerical comparison task and the coefficient of variation (CV), computed from a numerical estimation task. Arithmetic performance correlated with estimation CV but not with comparison w. We further investigated the meaning of this result by taking the relationship between w and CV into account. We expected a tight relation as both these measures are believed to assess ANS acuity. Crucially, however, w and CV did not correlate with each other. Moreover, the value of w was modulated by the congruity of the relation between numerical magnitude and non-numerical visual cues, potentially accounting for the lack of correlation between the measures. Our findings thus challenge the overuse of w to assess ANS acuity and more generally put into question the relevance of correlating this measure with arithmetic without any deeper understanding of what they are really indexing.

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Notes

  1. Although the coefficient of variation evaluates the variability (or consistency) of numerical estimates, it does not measure their veridicity, that is, their accuracy with regard to the actual true magnitude

  2. The following mathematical expression was used to fit individual proportion correct responses as a function of ratios (r). The parameter w in the equation is the Weber Fraction.

    $$1 - \frac{1}{2}erfc\left[ {\frac{1}{w}\sqrt {\frac{{\left( {r - 1} \right)^{2} }}{{2\left( {r^{2} + 1} \right)}}} } \right]$$

  3. Spearman rho coefficients were preferred due to the positive skewness of some of the measures.

  4. The inclusion or the exclusion of two potential outliers did not change the pattern and interpretation of the results

  5. It should be noted that we assessed arithmetic performance—which is highly related to math ability—through one measure of arithmetic fluency. Further studies should investigate whether other aspects of general math ability (such as problem solving, spatial reasoning, etc.) are related to basic numerical abilities, and whether they are validly assessed

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Acknowledgments

Mathieu Guillaume was supported by a grant from the Belgian Fund for Scientific Research (FRS-FNRS, Belgium). The authors declare no conflict of interest that might be interpreted as influencing the research, and APA ethical standards were followed in the conduct of the study. Authors gratefully thank all the participants for their collaboration with the study. Correspondence and requests for materials should be addressed to Mathieu Guillaume (maguilla@ulb.ac.be).

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  1. Cognitive Science and Assessment Institute (COSA), Department of Education, Culture, Cognition and Society (ECCS), University of Luxembourg, Walferdange, Luxembourg

    Mathieu Guillaume

  2. Centre de Recherche Cognition and Neurosciences (CRCN), ULB Neuroscience Institute (UNI), Université Libre de Bruxelles (ULB), Av. F. Roosevelt 50/191, 1050, Brussels, Belgium

    Mathieu Guillaume, Wim Gevers & Alain Content

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  1. Mathieu Guillaume
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Correspondence to Mathieu Guillaume.

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Guillaume, M., Gevers, W. & Content, A. Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks. Psychological Research 80, 248–258 (2016). https://doi.org/10.1007/s00426-015-0657-x

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