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      The Relationship Between Children’s Approximate Number Certainty and Symbolic Mathematics

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      * , a , , a
      Journal of Numerical Cognition
      PsychOpen
      number sense, symbolic mathematics, certainty, metacognition

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          Abstract

          Why do some children excel in mathematics while others struggle? A large body of work has shown positive correlations between children’s Approximate Number System (ANS) and school-taught symbolic mathematical skills, but the mechanism explaining this link remains unknown. One potential mediator of this relationship might be children’s numerical metacognition: children’s ability to evaluate how sure or unsure they are in understanding and manipulating numbers. While previous work has shown that children’s math abilities are uniquely predicted by symbolic numerical metacognition, we focus on the extent to which children’s non-symbolic/ANS numerical metacognition, in particular sensitivity to certainty, might be predictive of math ability, and might mediate the relationship between the ANS and symbolic math. A total of 72 children aged 4–6 years completed measures of ANS precision, ANS metacognition sensitivity, and the Test of Early Mathematical Ability (TEMA-3). Our results replicate many established findings in the literature, including the correlation between ANS precision and the TEMA-3, particularly on the Informal subtype questions. However, we did not find that ANS metacognition sensitivity was related to TEMA-3 performance, nor that it mediated the relationship between the ANS and the TEMA-3. These findings suggest either that metacognitive calibration may play a larger role than metacognitive sensitivity, or that metacognitive differences in the non-symbolic number perception do not robustly contribute to symbolic math performance.

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          Most cited references50

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          The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations.

          In this article, we attempt to distinguish between the properties of moderator and mediator variables at a number of levels. First, we seek to make theorists and researchers aware of the importance of not using the terms moderator and mediator interchangeably by carefully elaborating, both conceptually and strategically, the many ways in which moderators and mediators differ. We then go beyond this largely pedagogical function and delineate the conceptual and strategic implications of making use of such distinctions with regard to a wide range of phenomena, including control and stress, attitudes, and personality traits. We also provide a specific compendium of analytic procedures appropriate for making the most effective use of the moderator and mediator distinction, both separately and in terms of a broader causal system that includes both moderators and mediators.
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              Core systems of number.

              What representations underlie the ability to think and reason about number? Whereas certain numerical concepts, such as the real numbers, are only ever represented by a subset of human adults, other numerical abilities are widespread and can be observed in adults, infants and other animal species. We review recent behavioral and neuropsychological evidence that these ontogenetically and phylogenetically shared abilities rest on two core systems for representing number. Performance signatures common across development and across species implicate one system for representing large, approximate numerical magnitudes, and a second system for the precise representation of small numbers of individual objects. These systems account for our basic numerical intuitions, and serve as the foundation for the more sophisticated numerical concepts that are uniquely human.
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                Author and article information

                Journal
                JNC
                J Numer Cogn
                Journal of Numerical Cognition
                J. Numer. Cogn.
                PsychOpen
                2363-8761
                15 June 2020
                2020
                : 6
                : 1
                : 50-65
                Affiliations
                [1]Department of Psychology, University of British Columbia, Vancouver, Canada
                Author notes
                [* ]Department of Psychology, University of British Columbia, 2136 West Mall, Vancouver, British Columbia, Canada V6T 1Z4. cebaer@ 123456psych.ubc.ca
                Article
                jnc.v6i1.220
                10.5964/jnc.v6i1.220
                46cb84b4-5db0-4628-9dbb-ce27dffe744c
                Copyright @ 2020

                This is an open-access article distributed under the terms of the Creative Commons Attribution (CC BY) 4.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 03 May 2019
                : 26 September 2019
                Categories
                Empirical Research

                Psychology
                number sense,symbolic mathematics,certainty,metacognition
                Psychology
                number sense, symbolic mathematics, certainty, metacognition

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