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      Is the Long-Term Association Between Symbolic Numerical Magnitude Processing and Arithmetic Bi-Directional?

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      * , a , , a , a
      Journal of Numerical Cognition
      PsychOpen
      6-year longitudinal design, symbolic numerical magnitude processing, arithmetic, bi-directionality

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          Abstract

          By analyzing longitudinal data from the start to the end of primary education, we aimed to investigate whether symbolic numerical magnitude processing at the start of primary education predicted arithmetic at the end, and whether arithmetic at the start of primary education predicted later symbolic numerical magnitude processing skills at the end. In the first grade (start) and sixth grade (end) of primary education, the same group of children’s symbolic numerical magnitude processing skills and arithmetic competence were assessed. We were particularly interested in exploring the direction of the association between symbolic numerical magnitude processing and arithmetic and observed that this association was bi-directional across primary education. Symbolic numerical magnitude processing skills in first grade predicted arithmetic in sixth grade; but also the reversed direction turned out significant: Early arithmetic predicted later symbolic numerical magnitude processing skills. Both directions remained significant after controlling for motor speed and nonverbal reasoning. Critically, when controlling for auto-regressive effects of prior abilities, the symbolic comparison-arithmetic association was no longer significant, the reversed direction became marginally significant. This suggests that children’s arithmetic development across primary education to some extent strengthens their ability to process the numerical meaning of Arabic digits.

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          Specific reading disability (dyslexia): what have we learned in the past four decades?

          We summarize some of the most important findings from research evaluating the hypothesized causes of specific reading disability ('dyslexia') over the past four decades. After outlining components of reading ability, we discuss manifest causes of reading difficulties, in terms of deficiencies in component reading skills that might lead to such difficulties. The evidence suggests that inadequate facility in word identification due, in most cases, to more basic deficits in alphabetic coding is the basic cause of difficulties in learning to read. We next discuss hypothesized deficiencies in reading-related cognitive abilities as underlying causes of deficiencies in component reading skills. The evidence in these areas suggests that, in most cases, phonological skills deficiencies associated with phonological coding deficits are the probable causes of the disorder rather than visual, semantic, or syntactic deficits, although reading difficulties in some children may be associated with general language deficits. Hypothesized deficits in general learning abilities (e.g., attention, association learning, cross-modal transfer etc.) and low-level sensory deficits have weak validity as causal factors in specific reading disability. These inferences are, by and large, supported by research evaluating the biological foundations of dyslexia. Finally, evidence is presented in support of the idea that many poor readers are impaired because of inadequate instruction or other experiential factors. This does not mean that biological factors are not relevant, because the brain and environment interact to produce the neural networks that support reading acquisition. We conclude with a discussion of the clinical implications of the research findings, focusing on the need for enhanced instruction.
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            Default Bayes Factors for Model Selection in Regression.

            In this article, we present a Bayes factor solution for inference in multiple regression. Bayes factors are principled measures of the relative evidence from data for various models or positions, including models that embed null hypotheses. In this regard, they may be used to state positive evidence for a lack of an effect, which is not possible in conventional significance testing. One obstacle to the adoption of Bayes factor in psychological science is a lack of guidance and software. Recently, Liang, Paulo, Molina, Clyde, and Berger (2008) developed computationally attractive default Bayes factors for multiple regression designs. We provide a web applet for convenient computation and guidance and context for use of these priors. We discuss the interpretation and advantages of the advocated Bayes factor evidence measures.
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              Numerical magnitude representations influence arithmetic learning.

              This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be predictive of their learning of answers to unfamiliar arithmetic problems. The relation to learning of unfamiliar problems remained after controlling for prior arithmetic knowledge, short-term memory for numbers, and math achievement test scores. Moreover, presenting randomly chosen children with accurate visual representations of the magnitudes of addends and sums improved their learning of the answers to the problems. Thus, representations of numerical magnitude are both correlationally and causally related to arithmetic learning.
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                Author and article information

                Journal
                JNC
                J Numer Cogn
                Journal of Numerical Cognition
                J. Numer. Cogn.
                PsychOpen
                2363-8761
                20 December 2019
                2019
                : 5
                : 3
                : 358-370
                Affiliations
                [a ]Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, University of Leuven , Leuven, Belgium
                Author notes
                [* ]Parenting and Special Education Research Unit, L. Vanderkelenstraat 32 - box 3765, 3000 Leuven, Belgium. Kiran.Vanbinst@ 123456kuleuven.be
                Article
                jnc.v5i3.202
                10.5964/jnc.v5i3.202
                1c0ae746-7aa8-468f-b249-3d6574bc12e4
                Copyright @ 2019

                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
                : 12 October 2018
                : 07 April 2019
                Categories
                Empirical Research

                Psychology
                bi-directionality,6-year longitudinal design,arithmetic,symbolic numerical magnitude processing

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