Origin of number sense

Origin of number sense - PSYCHOLOGICAL SCIENCE Research...

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Unformatted text preview: PSYCHOLOGICAL SCIENCE Research Article 396 Copyright 2003 American Psychological Society VOL. 14, NO. 5, SEPTEMBER 2003 ORIGINS OF NUMBER SENSE: Large-Number Discrimination in Human Infants Jennifer S. Lipton and Elizabeth S. Spelke Massachusetts Institute of Technology Abstract Four experiments investigated infants sensitivity to large, approximate numerosities in auditory sequences. Prior studies pro- vided evidence that 6-month-old infants discriminate large numerosi- ties that differ by a ratio of 2.0, but not 1.5, when presented with arrays of visual forms in which many continuous variables are con- trolled. The present studies used a head-turn preference procedure to test for infants numerosity discrimination with auditory sequences designed to control for element duration, sequence duration, interele- ment interval, and amount of acoustic energy. Six-month-old infants discriminated 16 from 8 sounds but failed to discriminate 12 from 8 sounds, providing evidence that the same 2.0 ratio limits numerosity discrimination in auditory-temporal sequences and visual-spatial ar- rays. Nine-month-old infants, in contrast, successfully discriminated 12 from 8 sounds, but not 10 from 8 sounds, providing evidence that numerosity discrimination increases in precision over development, prior to the emergence of language or symbolic counting. An important issue in human cognition concerns the origins and nature of the capacity to represent number. Is there an innate, core sys- tem of knowledge that underlies the number abilities seen in human children and adults? If so, how does this system emerge in infants, how is it transformed over development, and how does it compare to the numerical abilities of nonhuman animals? A number of investigators have proposed that human adults num- ber representations and mathematical thinking depend, in part, on a sense of approximate numerical magnitudes, or number sense (De- haene, 1997; Gallistel & Gelman, 1992). When adults are prevented from counting, they still are able to estimate large numerosities (Cordes, Gelman, Gallistel, & Whalen, 2001; see also Balakrishnan & Ashby, 1992), as do many nonhuman animals (Gallistel, 1990). Al- though the natural number concepts expressed by symbols such as 7 and 34 specify number exactly, these symbols also evoke a sense of approximate numerosity that adults use in reasoning about them (see Dehaene, 1997). Thus, adults are quicker to compare numbers the more distant they are from one another (e.g., subjects judge more rap- idly that 9 . 5 than that 6 . 5; Dehaene, Dupoux, & Mehler, 1990; Moyer & Landauer, 1967), and quicker to reject false answers to arith- metic problems the more distant they are from the true answer (e.g., subjects are quicker to reject 19 than 13 as the sum of 7 1 5; Ashcraft, 1992). In neuroimaging experiments, adults who perform mental arithmetic activate regions of parietal cortex that are implicated in the processing of approximate numerical magnitudes (Pinel, Dehaene,...
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Origin of number sense - PSYCHOLOGICAL SCIENCE Research...

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