A confluence of findings related to early childhood counting and conservation...
Well and good. Piaget's conclusions that development of this awareness typically does not occur before the age of 6 or 7, as children enter the operational stage, have been confirmed numerous times. Even children's ability to match objects in one set to objects in another in order to determine the relative size of each set, a relatively advanced application of one-to-one correspondence, is a fairly late accomplishment (Brainerd, 1979). However, programs that have made conscious efforts to delay young children's exposure to number concepts until they can fully grasp the principle of conservation and its sidekicksintegrated formal understanding of one-to-one correspondence and rational countinghave over-interpreted Piaget's findings and intent. Research has shown, and Piaget's findings do not refute, that even though young children still will rely largely on visual perception, they can and do make use of reasoned counting during the preschool years (Piaget's preoperational stage). Not only have young children exhibited the ability to count in any order (Aubrey, 1993), and correct counting errors such as skipping numbers or double-counting even when the numbers used are beyond their ceiling of known numerals or number words (Gelman & Meck, 1983), but they have done so before exhibiting an operational understanding of quantity. Though there is a difference between operational understanding and the ability to develop fundamental implicit understandings of such important concepts as one-to-one correspondence (see Early Childhood Numeracy), Piaget would further concur that counting is an excellent exercise for helping children develop pre-formal number concepts that eventually lead to an enhanced ability to apply one-to-one correspondence and rational counting in an integrated and cogent manner, as well as to conserve number. Evidence supports the notion that children who fail Piagetian conservation tasks still often operate quite successfully when making judgment of equivalence between sets with small numbers of objects through counting (Gelman & Gallistel, 1978), to the extent that some suggest that equality of sets based on numbers counted occurs earlier than when based on one-to-one correspondence (Thompson, 1989). As a final precaution regarding over-analysis, noteworthy given the backdrop: Even the phrase "number concept" itself is misleading because of the existence of a variety of number concepts, and the usefulness of the idea of one-to-one correspondence is no justification for its use as a criterion for judging a young child's grasp of number (Freudenthal, 1973).
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Jedrysek, E. (2000). Number concept development in young children. In S. Vig, & R. Kaminer (Eds.), Early Intervention Training Institute Newsletter (pp. 1-3). Bronx, NY: Rose F. Kennedy Center.
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