Identifying Concrete and Formal Operational Children.

This paper presents a study designed to determine if groups of concrete and formal operational children can be identified through the technique of cluster analysis, using a battery of Piagetian tasks. A Total of 64 subjects, 8 boys and 8 girls from each of the second, fourth, sixth, and eighth grade levels, were selected from a public elementary and middle school in suburban upstate New York. Subjects were given five concrete tasks, representing each of the logical groupings studied extensively by Piaget and Irhelder: (1) primary addition of classes (class inclusion), (2) secondary addition of classes, (3) multiplication of classes, (4) asymmetrical addition of relations (seriation), and (5) multiplication of relations. Five formal tasks, representing the integrated group and lattice, were also given: (1) flexibility of rods, (2) oscillation of a pendulum, (3) equilibrium in the balance, (4) hauling weight on an inclined plane, and (5) projection of shadows. It was tentatively concluded that cluster analysis, using these Piagetian tasks, is an effective way to identify concrete and formal operational children. Results suggest that it is possible to form groups of children which are relatively homogeneous, from a Piagetian point of view. (CS)