How does change occur: a microgenetic study of number conservation

Microgenetic methods can illuminate the path, rate, breadth, variability, and sources of change. The present study illustrates the types of information the method can yield in the context of number conservation. Five-year-olds whose pretest performance showed that they had not mastered number conservation were presented four training sessions. Some were just given feedback on their number conservation performance; others were given feedback and asked to explain the reasoning that led to the experimenter's judgment. Being asked to explain the experimenter's reasoning produced considerably more learning than either of the other two procedures. The learning involved two distinct realizations: that relative length did not predict which row had the greater number of objects and that the type of quantitatively relevant transformation did. Individual children generated multiple types of reasoning about conservation, both on the pretest and throughout the training procedure; understanding the importance of the type of transformation did not lead to immediate rejection of less advanced forms of reasoning, even for a single problem presented several times during the experiment. This variability was positively associated with learning; children who showed greater variability of reasoning on the pretest, both within and across trials, learned more. Educational and theoretical implications of children's efforts to understand other people's reasoning were discussed.