This study tested 148 preschoolers between the ages of 48 and 72 months on a Piagetian number conservation task. Children's judgment accuracy, estimation, and response latency were measured. Children were also questioned about the number conservation principle. A four-step developmental sequence was hypothesized: (1) nonconservation; (2) correct judgment without adequate explanation; (3) correct judgment with adequate explanation after extra questioning; and (4) correct judgment and adequate explanation without probing. Some children fell into each of the four groups. Children who made correct judgments and provided adequate explanations only after additional questioning constituted 7 percent of the sample. These children were called "late explainers." Those who never gave adequate explanations, called "transitionals," constituted 16 percent. Half the transitionals and nonconservers were given a training session and were retested 2 weeks later. In the posttest, transitionals had no advantage over nonconservers, and students with training had no advantage over those who did not. Three references are included. (BC)