Correspondences and Numerical Differences between Disjoint Sets

HUDSON, TOM. Correspondences and Numerical Differences between Disjoint Sets. CHILD DEVELOPMENT, 1983, 54, 84-90. Young children's understanding of correspondences and numerical differences between disjoint sets was studied in a series of 3 experiments. In the first 2 experiments, 64 children between 4 and 8 years of age were shown pairs of sets and were asked both standard (How many more birds than worms are there?) and nonstandard (How many birds won't get a worm?) numerical difference questions. The children's observed success in answering the Won't Get questions indicates that many young children are skillful at establishing correspondences and determining exact numerical differences between disjoint sets; their poor performance on the standard questions apparently reflects a misinterpretation or inadequate comprehension of comparative constructions of the general form How many . . . comparative term . . than . .. ? The final experiment, involving 30 additional kindergarten children, dealt with children's solution strategies in answering Won't Get questions. The most frequently observed solution strategy was a sophisticated indirect counting strategy rather than a perceptually guided pairing strategy. Taken together, the present findings restrict the domain of applicability of the theory that young children are limited to perceptually based forms of mathematical reasoning.