title: When three is less than two: early developments in children's understanding of fractional quantities.
abstract: Four experiments examined young children's understanding of the inverse relation between the number of parts into which a quantity is to be divided and the size of each part. In Experiment 1 5-, 6-, and 7-year-old children tended to judge, incorrectly, that bigger shares would result from sharing with more, rather than fewer, recipients. In Experiment 2, 5-year-olds correctly recognized the inverse effect of additional recipients when the sharing was based on subtraction rather than on equal partitioning. In Experiment 3, a modification of the equal-sharing task from Experiment 1 designed to reduce cognitive complexity successfully elicited correct performance from 7-year-olds but not from 5-year-olds. However, 5-year-olds markedly improved when they were given a chance to compare the outcomes of sharing with different numbers of recipients. Experiment 4 corroborated and extended this evidence of learning.
authors.affiliation: Department of Psychology, University of Hawaii at Manoa, Honolulu 96822, USA. csophian@hawaii.edu
authors.forename: C
authors.initials: C
authors.lastname: Sophian
authors.forename: D
authors.initials: D
authors.lastname: Garyantes
authors.forename: C
authors.initials: C
authors.lastname: Chang
mesh_terms: D000367:Age Factors; D016009:Chi-Square Distribution; D002648:Child; D002657:Child Development; D002675:Child, Preschool; D003210:Concept Formation; D003430:Cross-Sectional Studies; D005260:Female; D006801:Humans; D007858:Learning; D008137:Longitudinal Studies; D008297:Male; D008433:Mathematics; D002666:Psychology, Child