The child's ability to identify numerousness as a property of a set, distinct from all the other properties of that set, may be a prerequisite to conservation of numerousness of sets. To test this theory, 11 lessons designed to develop the ability to identify properties of objects and of sets of objects and to represent length and numerousness were presented to kindergarten and preschool children. It was hypothesized that this training would help the subjects score higher on a test of conservation of numerousness. The difference, however, between experimental groups, who received the training lessons, and control groups, who received no special training, was not statistically significant. Nevertheless, since there were some noticeable differences between the amount of improvement in the groups, it was concluded that kindergarten and preschool children can be taught with little difficulty to recognize, discriminate and label properties of objects and sets, and that this training can often be enough to increase the children's scores on a test of conservation of numerousness. (Author/MH)