WHEN 3 IS LESS-THAN 2 - EARLY DEVELOPMENTS IN CHILDRENS UNDERSTANDINGOF FRACTIONAL QUANTITIES

Four experiments examined young children's understanding of the invers e 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 r esult from sharing with more, rather than fewer, recipients. In Experi ment 2, 5-year-olds correctly recognized the inverse effect of additio nal recipients when the sharing was based on subtraction rather than o n equal partitioning. In Experiment 3, a modification of the equal-sha ring task from Experiment 1 designed to reduce cognitive complexity su ccessfully elicited correct performance from 7-year-olds but not from 5-year-olds. However, 5-year-olds markedly improved when they were giv en a chance to compare the outcomes of sharing with different numbers of recipients. Experiment 4 corroborated and extended this evidence of learning.