Development of linear measurement in five- and six-year-old children.

This study sought to identify the higher level knowledge (e.g., conservation of number) necessary for a child to understand linear measurement and to chart the growth of linear measurement in terms of the development of its components. To assess the presence of these components, a battery of 34 number, length, and distance tasks was developed and administered to 100 children between the ages of 63 and 78 months from kindergarten and Grade 1. Results indicate that there is a substantial delay between acquisition of the necessary components and emergence of a mature grasp of linear measurement. The collection of components for the number and length domains form scaled sets; within each domain, however, the pattern of development is marked by discontinuities. These discontinuities are interpreted as being associated with the need to reorganize number and length concepts. Most elements of the observed sequences of development are predicted by Piagetian theory, although others, such as asynchronies between conservation and transitive inferences of nonequivalence, are more consistent with Gagne's (1968) model of development.