J. A. Easley, Jr.
Piaget's objections to tests as ways of identifying cognitive structures and processes appear to have been largely ignored in most of the replication studies of his work conducted by English and American psychologists. Piaget ( 1929) pointed out that tests cannot provide enough information to decide what structures are involved in a child's thinking, and Piaget and Inhelder later characterized tests as giving only the "results of efficiency of mental activity without grasping the psychological operations in themselves." ( Piaget, 1947) What we wish to argue here is that there is a basic conflict between the general scientific paradigms for structural analysis and for measurement and that the identification of cognitive structure requires the former. To replicate the determination of a population parameter like the mean age of appearance of conservation of substance, a clear conception of the underlying structure is required. It is our claim that cognitive structures in Piaget's sense, and indeed structures underlying phenomena in many other branches of science (e.g. electron, cell, tectonic plate), cannot be treated like measurable quantities or given so-called operational definitions in the sense in which Bridgman defined length and mass by specifying the operations of measurement. Because of the interest which Piaget's studies of children's thinking have for science and mathematics educators, understanding the appropriate paradigm for analysis of cognitive structures and disengaging structural analysis from the confusions of the measurement paradigm is a task that could be pursued fruitfully by researchers in science and mathematics teaching, who have training in the conceptual theories of the natural sciences in which these paradigms are clearly discernable.
The point has been suggested by Smedslund ( 1969) who argued that "the constructs involved (in Piaget tasks) are anchored neither to distal or proximal physical stimuli, nor to physical response categories, but to the meanings of the subjects' acts." (emphasis added) The problem then is to discover a structural theory of meaning rather than of phenomena. It has not often been noted in the literature on scientific thought that measurement and structural analysis paradigms in science are quite distinct and that they may be appropriate in quite different circumstances, but those familiar with the appropriate sciences will testify that electrons, benzine rings, fault zones, the jet stream, and DNA are concepts that are not defined operationally in Bridgman's sense. That is, they are not initially "framed in terms of operations which can be unequivocally performed." ( Bridgman, 1938, p 114) Furthermore, they do not function as in-____________________