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Cognitive arithmetic: comparison of operations.

K Miller, M Perlmutter, D Keating

    Journal of Experimental Psychology. Learning, Memory, and Cognition
    |January 1, 1984
    PubMed
    Summary
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    This study on simple arithmetic found that reaction times for addition and multiplication are highly correlated, supporting network models of the brain. A novel "ties" effect was observed, suggesting distinct information processing within these networks.

    Area of Science:

    • Cognitive Psychology
    • Neuroscience
    • Mathematical Cognition

    Background:

    • Mental arithmetic involves complex cognitive processes.
    • Existing models (counting, analog, network) explain aspects of mental addition.
    • Discrepancies arise when comparing model predictions for addition, multiplication, and comparison.

    Purpose of the Study:

    • To test predictions of digital, analog, and network models of arithmetic.
    • To investigate the relationship between reaction times for addition, multiplication, and numerical comparison.
    • To examine the influence of problem size and number 'ties' on performance.

    Main Methods:

    • Adult participants performed simple arithmetic calculations (addition, multiplication, comparison).
    • Reaction times (RTs) were recorded for pairs of single-digit integers.

    Related Experiment Videos

  • A production task was used, contrasting with previous verification tasks.

    • Main Results:

    • A strong correlation was found between RTs for addition and multiplication of the same digits.
    • A "ties" effect was observed, where RTs for doubles (e.g., 2+2) increased more slowly with problem size than non-tie problems.
    • Error probability independently influenced RT, separate from problem size.

    Conclusions:

    • Results support a network model of numerical processing, challenging analog and counting models.
    • The findings suggest a distinction between information location and accessibility within neural networks.
    • The observed "ties" effect and error analysis provide further evidence for network model intricacies.