The distinction between Piaget's concrete and formal stages of intellectual development[ I] may not be as sharp as is suggested by his data. The results of this study suggest that the concrete-formal distinction is relative and that a given student may respond to tasks at one level, then to similar tasks at another, depending on circumstances unrelated to the logical character of the tasks, hence unrelated to what Piaget considers to be the main determinant of task difficulty. It thus becomes possible to assess a student's performance, not as either concrete or formal, but rather as lying on a continuous scale extending from relatively concrete to relatively formal. Such an ordinal assessment scale should provide more useful information than a dichotomous classification, since it is likely that most individuals perform at levels intermediate to Piaget's two stages which are, after all, idealizations by intent [2]. The technique used to establish the scale can be readily applied to any subject matter for which inferential reasoning is appropriate. In this study, as in its predecessor [3], students were asked to critically judge inferences from simple physical data.
RationaleSince at least as early as the time of Immanuel Kant, it has been recognized that the level of critical awareness is inversely related to the degree to which expectations appear to be confirmed. An unexpected event piques one's curiosity as to its causes while apparent confirmation dulls awareness and leads to uncritical acceptance. Piaget has intuitively used this idea in his disequilibrium-equilibration metaphor for the dynamics of development [4]. This idea can also be used to distinguish between relatively concrete and relatively formal understandings of, say, the concept of controlling variables. Relatively formal understanding would be relatively insensitive to context, thus to expectations within a context, since such understanding is further along the way toward attaining a general, hence context free, principle. While relatively formal understanding would not nor could not ignore context, it would give priority to the need for satisfying criteria of valid * Present address: