Sometimes area counts more than number

doi:10.1073/pnas.0609485103

Sometimes area counts more than number

*Deptartment of Linguistics, University of Delaware, Newark, DE 19716; and
^†Rutgers Center for Cognitive Science, Rutgers University, Piscataway, NJ 08854-8020

Communicated by Lila R. Gleitman, University of Pennsylvania, Philadelphia, PA, October 27, 2006 (received for review August 8, 2005)

Abstract

Using an interference paradigm, we show across three experiments that adults' order judgments of numbers, sizes, or combined area of dots in pairs of arrays occur spontaneously and automatically, but at different speeds and levels of accuracy. Experiment 1 used circles whose sizes varied between but not within arrays. Variation in circle size interfered with judgments of which array had more circles. Experiment 2 used displays in which circle size varied within and between arrays. Between-array differences in the amount of “circle stuff” (area occupied by circles) interfered with judgments of number. Experiment 3 examined whether variation in number also interferes with judgments of area. Interference between discrete and continuous stimulus dimensions occurred in both directions, although it was stronger from the continuous to the discrete than vice versa. These results bear on interpretations of studies with infants and preschoolers wherein subjects respond on the basis of continuous quantity rather than discrete quantity. In light of our results with adults, these findings do not license the conclusion that young children cannot represent discrete quantity. Absent data on attentional hierarchies and speed of processing, it is premature to conclude that infant and child quantity processes are fundamentally different from that of adults.

Footnotes

^‡To whom correspondence should be addressed. E-mail: fel{at}udel.edu
Author contributions: F.H., R.G., and B.S. designed research; F.H. and B.S. performed research; B.S. contributed new reagents/analytic tools; F.H. analyzed data; and F.H. and R.G. wrote the paper.
The authors declare no conflict of interest.
↵ § A mixed ANOVA design with target side (2) × gender (2) × congruency (3) was used here and elsewhere, unless otherwise noted.
↵ ¶ This finding, and a similar result in Experiment 2, is not an instance of the Spatial-Numerical Association of Response Codes effect. Dehaene et al. (26) found that subjects from Western countries (with left to right writing systems) were faster to respond to smaller numbers with the left hand, and larger numbers with the right hand, suggesting that subjects mentally order numbers on an imaginary left-to-right number line. We find the opposite effect, perhaps reflecting a left-to-right-scanning preference.
Abbreviation:

RT,

reaction time.