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GELMAN, ROCHEL. Logical Capacity of Very Young Children: Number Invariance Rules. CHILD DEVELOPMENT, 1972, 43, 75-90. Children 3-6 years of age, when given an identification task where number was redundant to length or density, solved the task on the basis of number. Surreptitious subtraction or addition elicited strong surprise as well as search behavior whereas displacements did not. Children who noticed the change in number or length and density gave unambiguous explanations of the nature of the intervening operations and were able to indicate how to reverse the effect. These findings are taken to show young children can treat small numbers as invariant. The results are discussed in terms of why children of the same age fail to conserve number in the standard conservation task and how complex number concepts might develop.
Rochel Gelman (Wed,) studied this question.