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. © 1996 John Wiley & Sons, Inc.