The same cognitive intervention was attempted with children from two schools serving different populations. All children were identified by their teachers as having cognitive difficulties in kindergarten. Within each school, children were randomly assigned to experimental and control groups. Children in the experimental groups received more than 40 short lessons on unidimensional classification (oddity), seriation, and number conservation. These lessons were taught via a learning-set procedure employing 160 kinds of manipulatable objects. Children in the control groups received an equal amount of instruction on verbal and mathematics materials recommended by their teachers. Five months after the instruction was concluded, the experimental group in one school scored significantly better on a psychometric test of reasoning. There was no significant difference in verbal and mathematics achievement. Differences in the significance of outcomes of the intervention at the two schools suggest that children at different stages of cognitive development will benefit differently from cognitive interventions.As Silliphant (1983) has pointed out, kindergarten must in part be a diagnostic period, because of differences in children who are developing normally when they enter school and those who are lagging cognitively but are not mentally retarded.
DiHerences in ReasoningWithin the Piagetian framework, Inhelder and Piaget (1959/1964, p. 53) described classifications by 5-year-olds that are nongraphic but lack the inverse operation of class inclusion. These classifications, identified as an advanced form of the second stage of classification, amount to successful employment of the oddity principle to any one dimension that is relevant. Children who are well along in this transition to concrete operational thought solve oddity problems easily, focusing on the critical feature in spite of irrelevant perceptual similarities and differences (Kemler Nelson, 1990; Sugimura & Taki, 1989; Ward, Vela, & Hass, 1990). Children of the same age and in the same kindergarten, but lagging cognitively, will show partial reversions to the graphic collections of Stage I, or may even be in Stage I. The intrusion of perceptually salient characteristics of stimuli and the complexive nature of their thinking prevent successful and consistent consideration of relevant differences even when only one dimension need be attended.At about the same time some children have become able to conserve simple dimensions of matter, such as number or substance. Piaget (1941/1952, p. 33, 47) described conservation of discontinuous quantities by 5-and 6-year-olds and their recognition that rows of items retain equivalency in number irrespective of the arrangement of their elements. This understanding of reversibility and equivalence, which Piaget defines as a mathematical operation, is not shared by other children of the same age. Some are unable to maintain their intuitive grasp of equivalence in the face of a perceptual conflict. They do not realize that number or q...