Andrea A. diSessa
The true meaning of a term is to be found by observing what a man does with it, not what he says about it.
-- P. W. Bridgman
S understands knowledge K if S uses K whenever appropriate.
-- J. Moore and A. Newell
It is now widely agreed, at least in principle, that the educational task is now well modeled as a process of transmission of knowledge. Especially following Piaget, emphasis has shifted away from learning models like Skinner's which assume a great and universal simplicity in the structures of assimilation of knowledge, toward models with a very careful concern for the richness and complexity of the student's "initial state" in terms of capacity to assimilate.
A similar enrichment has taken place in the very notion of knowledge itself. Indeed, the currently prominent concept of representations of knowledge symbolizes the rather recent awareness of the manifold ways of encoding and distributing knowledge in an "intelligent system."
Psychology and artificial intelligence have made a great deal of these parallel and vitally interrelated "booms" in complexity. Unfortunately, comparatively little effort has been expanded in education to exploit the rich variety of concepts and theories becoming available concerning knowledge encoding and assimilation. In the central notion of this paper, that of "learnable representations," I am proposing a program of research and development in pedagogical material which can, I hope, lend to education in usable form some important theoretical insights.
The program is, briefly stated, to transform old or invent new representations of physics, mathematics or whatever subject, which do justice to the powerful logical structure of the subject, but which at the same time mesh properly with the cognitive reality of human beings. This task is made particularly difficult by popular, unstated epistemological assumptions about the simplicity of knowing, for example, knowing "mathematical truths." These assumptions make inventing new mathematics and physics seem a dubious enterprise at best, even (especially!) for pedagogical purposes. I wish to argue against those assumptions.