Numerical Magnitude Representations Influence Arithmetic Learning

Authors

  • Julie L. Booth,

    Corresponding author
    1. Carnegie Mellon University
      concerning this article should be addressed to Julie L. Booth, Human Computer Interaction Institute, Carnegie Mellon University, Pittsburgh, PA 15213, or to Robert S. Siegler, Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213. Electronic mail may be sent to juliebooth@cmu.edu or rs7k@andrew.cmu.edu.
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  • Robert S. Siegler

    1. Carnegie Mellon University
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  • Funding for this research was provided by the National Institutes of Health Grant HD 19011 and the Office of Educational Research and Instruction Grant R305H020060. Thanks are also due to the Hopewell Area School District for allowing us to collect data in their schools and to Mary Wolfson for assistance with data collection.

concerning this article should be addressed to Julie L. Booth, Human Computer Interaction Institute, Carnegie Mellon University, Pittsburgh, PA 15213, or to Robert S. Siegler, Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213. Electronic mail may be sent to juliebooth@cmu.edu or rs7k@andrew.cmu.edu.

Abstract

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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