PART-WHOLE KNOWLEDGE AND EARLY ARITHMETIC PROBLEM-SOLVING

In two experiments, we examined the development of 4- to 6-year-old ch ildren's understanding of part-whole relations. The first experiment t ested the hypothesis that young children do not appreciate the part-wh ole structure of arithmetic problems, focusing on initial-unknown chan ge problems. Five- and 6-year-olds showed a sensitivity to the part-wh ole structure of those problems in that they responded with a number t hat was larger than that given for the final set more often on additio n than on subtraction problems, and they responded with a smaller numb er 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 childre n'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, ev idenced understanding part-whole relations. The older children chose t he 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 tha n when they were asked to identify the set with more objects. The 4-ye ar-olds did not perform reliably in either of these respects on the cl ass inclusion problems, although on control, noninclusion problems, th ey differentiated appropriately between those on which the superordina te versus a basic-level alternative was the correct choice. Both exper iments support the conclusion that an understanding of the relationshi p between a superordinate set and the basic-level sets that comprise i t develops between 4 and 5 years of age.