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It will be clear from these sketchy examples that working out some of the implications of Piagetian theory for an educational program such as ours offers us a continuing challenge. The theory perhaps does more to console us for some of our failures as teachers than to tell us how our failures may be overcome, for if the fault is in the developmental level that our students have attained, then the fault is not in us. Our teaching, Piaget tells us, can play a role in fostering development, but only a fairly limited role. On the other hand if we accept the challenge, we can be more than teachers; we can be the designers of activities that allow students to engage in the spontaneous transformations of objects in thought that are the very essence of knowledge.