involving the ability to use symbols and reason about quantities, classifications, and the perspective of others. From Piaget’s point of view, the main accomplishments of the preschool (or “pre-operational”) period involve the development of symbolic abilities, language, imitation, symbolic play, and drawing. There is no doubt that there is a great deal of learning in these symbolic abilities. Still, for Piaget, the young child’s thoughts take place in the here and now and on the perceptual level. Preschool children therefore do not have the conceptual structures that enable hierarchical classification skills or sophisticated quantitative reasoning.

This side of Piaget’s theory of preschool thought is shared by two other prominent child development thinkers, Jerome Bruner and Lev Vygotsky. Despite their differences, all converge on the premise that preschool children’s conceptual abilities are perception-bound. The influence on preschool pedagogy of this confluence was straightforward. It was appropriate to provide children with concrete materials to explore and categorize. However, it was developmentally inappropriate to include learning opportunities about abstract categories, measurement, and advanced arithmetic, for doing so was asking children to deal with tasks for which they lacked the conceptual capabilities.

This assumption continues to be prevalent in the world of practice, especially as regards some interpretations of the notions of “readiness” and what is “developmentally appropriate.” However, the very definitions of these terms are being redefined as new research on the abilities and potential competencies of young children emerges. It has now been shown, for example, that whether or not young children use abstract classification schemes is very dependent on what they know about the materials to be sorted.

Beyond Piaget

The kinds of data that stage theorists of cognitive development obtained are reliable across a wide range of conditions and domains. However, those data coexist with evidence that, when they have accumulated substantial knowledge, children can perform in a particular domain at a level of development beyond

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