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Related Experiment Videos

Individual differences in cognitive arithmetic.

D C Geary, K F Widaman

    Journal of Experimental Psychology. General
    |June 1, 1987
    PubMed
    Summary
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    This study shows that retrieving arithmetic facts and carrying numbers are key mental processes for solving math problems. Individual differences in these cognitive arithmetic skills strongly relate to numerical facility.

    Area of Science:

    • Cognitive Psychology
    • Psychometrics
    • Neuroscience

    Background:

    • Previous research suggests common processes in solving arithmetic problems using factor-analytic and information-processing methods.
    • The study aims to bridge the gap between cognitive arithmetic processes and traditional psychometric factors.

    Purpose of the Study:

    • To investigate the convergence of mental processes in cognitive arithmetic with psychometric measures of Numerical Facility.
    • To identify elementary component processes underlying arithmetic problem-solving using chronometric techniques.

    Main Methods:

    • Employed a reaction-time (RT) verification paradigm with 320 arithmetic problems (addition, multiplication, simple, complex).
    • Administered ability measures for Numerical Facility, Perceptual Speed, and Spatial Relations to 100 undergraduates.

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  • Utilized structural equation modeling to analyze relations between cognitive processes and ability factors.

    • Main Results:

    • Memory network retrieval of arithmetic facts best predicted reaction times across all problem types.
    • Encoding digits and carrying operations were identified as significant elementary processes.
    • A strong direct relation was found between arithmetic fact retrieval/carrying efficiency and the Numerical Facility factor.
    • A moderate relation existed between digit encoding/decision speed and the Perceptual Speed factor.

    Conclusions:

    • Information retrieval from arithmetic fact networks and the carry operation are unique elementary processes in cognitive arithmetic.
    • Individual differences in these elementary processes significantly predict performance on Numerical Facility measures.
    • Cognitive arithmetic processes are distinct from those measured by Spatial Relations ability.