Part-Whole Knowledge and Early Arithmetic Problem Solving

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Abstract
In two experiments, we examined the development of 4- to 6-year-old children's understanding of part-whole relations. The first experiment tested the hypothesis that young children do not appreciate the part-whole structure of arithmetic problems, focusing on initial-unknown change problems. Five- and 6-year-olds showed a sensitivity to the part-whole structure of those problems in that they responded with a number that was larger than that given for the final set more often on addition than on subtraction problems, and they responded with a smaller number than that given for the final set more often on subtraction than on addition problems. In contrast, 4-year-olds tended to choose a small number on both addition and subtraction problems, and their responses were not consistent with the part-whole structure of the problems to a reliable degree. The second experiment further examined young children's appreciation of part-whole relations, using a class inclusion task. Again on these problems, 5- and 6-year...