Part-Whole Knowledge and Early Arithmetic Problem Solving

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-olds, but not 4-year-olds, evidenced understanding part-whole relations. The older children chose the superordinate set more often when they were asked to identify which set had more objects than when they were asked to identify which set had fewer objects, and they chose the basic-level alternative set more often when they were asked to identify the set with fewer objects than when they were asked to identify the set with more objects. The 4-year-olds did not perform reliably in either of these respects on the class inclusion problems, although on control, noninclusion problems, they differentiated appropriately between those on which the superordinate versus a basic4evel alternative was the correct choice. Both experiments support the conclusion that an understanding of the relationship between a superordinate set and the basic-level sets that comprise it develops between 4 and 5 years of age.