More precisely defining and measuring the order-irrelevance principle.
R. Gelman and C. Gallistel (1978, Young Children's Understanding of Number, Cambridge, MA: Harvard Univ. Press) use two definitions of the order-irrelevance principle interchangeably: (1) count tags do not have to be assigned in a fixed order and (2) the order in which elements of a set are enumerated does not affect the cardinal designation of the set. A study involving 107 kindergarten and first grade children indicates that the two are actually distinct concepts. Apparently, a willingness to arbitrarily assign tags is a developmentally less sophisticated ability than--and hence does not necessarily imply--an ability to predict that differently ordered counts produce the same cardinal designation. Thus it appears that evidence of the second ability is necessary to infer a full understanding of the order-irrelevance principle. The first ability alone implies what might better be termed an "order-indifferent tagging scheme." Suggestions for measuring and further researching the order-irrelevance principle are discussed.
D002648:Child; D002657:Child Development; D002675:Child, Preschool; D003071:Cognition; D005260:Female; D006801:Humans; D008297:Male; D008433:Mathematics; D012106:Research; D012718:Set, Psychology