The Relationship between the Order-Irrelevance Principle and Counting Skill

This study was undertaken to reevaluate whether preschoolers understand that counting in different orders yields the same number before they learn tag-reassigning skills. It also provided an opportunity to evaluate the explanations offered by Gelman and her colleagues. To avoid the interpretative difficulties of an earlier prediction task, the revised reverse-count prediction task proposed by Gelman, Meck, and Merkin (1986) was used. Nevertheless, a statistically significant number of subjects successfully implemented tag-reassigning skills but failed to predict that differently ordered counts would produce the same outcome. An error analysis indicated that children did not systematically add or subtract one, which might be expected if the children misinterpreted the tester's question (Gelman & Greeno, 1989). Moreover, the evidence was clearly inconsistent with Gelman and Greeno's conjecture that children may err on the reverse-count prediction task to avoid the social awkwardness of repeating the obvious. Nor is it likely that children erred because they inferred that the experimenter required a different answer or because of fatigue or inattentiveness. The comments and actions of several children did indicate that they were doubtful about the outcome of recounting. In brief, the results seem most consistent with the view that children may not entirely understand the implications of their counting actions.