Even more precisely assessing children's understanding of the order irrelevance principle

There are conflicting views of when children understand that the cardinality of a set is independent of the order in which the objects are counted. Some discrepancies between studies using similar tests may be due to children interpreting the experimenter as questioning the accuracy of their counting. Three studies are reported of children between 3 and 6 years old. In Experiments 1 and 2, more expected a count in a different order to yield the same number when they did not have to do any counting than when they had to count or monitor a puppet's counting. However, some also expected subtraction not to affect cardinality. In Experiment 3 substantially more children predicted correctly whether a recount would yield the same number than what the number would be. These variations may reflect the power of forms of questioning to orient the child toward principles or practice