The Development of Computational Estimation: A Neo-Piagetian Analysis

Estimating sums requires the coordination of two qualitatively different sorts of component activities: (a) using nearness judgment to select appropriate substitutes for the addends and (b) mentally computing the sum of the substitute numbers. According to Case's (1985) theory of intellectual development, children are not able to achieve this sort of coordination until they reach the level of vectorial thought, at about 11 or 12 years of age. The present study used a top-down approach to make predictions, based on this theory, about the developmental levels at which children should be able to solve tasks involving first one and then both of the component activities that estimating sums entails. Twelve children at each of Grades K, 2, 4, 7, 9, and 11/12 were then asked to solve tasks at their predicted achievement level and at the next highest level. All predictions were borne out. The framework for the study offers the potential for organizing other developmental data on computational estimation and may also carry important implications for curricular design.