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Published on: August 28, 2021
Moving along the number line: operational momentum in nonsymbolic arithmetic
Koleen McCrink1, Stanislas Dehaene, Ghislaine Dehaene-Lambertz
1Department of Psychology, Harvard University, Cambridge, Massachusetts 02138, USA. mccrink@wjh.harvard.edu
Abstract:
Can human adults perform arithmetic operations with large approximate numbers, and what effect, if any, does an internal spatial-numerical representation of numerical magnitude have on their responses? We conducted a psychophysical study in which subjects viewed several hundred short videos of sets of objects being added or subtracted from one another and judged whether the final numerosity was correct or incorrect. Over a wide range of possible outcomes, the subjects' responses peaked at the approximate location of the true numerical outcome and gradually tapered off as a function of the ratio of the true and proposed outcomes (Weber's law). Furthermore, an operational momentum effect was observed, whereby addition problems were overestimated and subtraction problems were underestimated. The results show that approximate arithmetic operates according to precise quantitative rules, perhaps analogous to those characterizing movement on an internal continuum.
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