that while nondynamic models may account for some features of the behavior, dynamic, action scheme models will be needed to account for other features. That is, we must consider the possibility that going through an action vicariously over a period of time and vicariously experiencing its effect, are activities intrinsic to this kind of causal knowledge.
Several factors lead us to consider this possibility. The semiquantitative relations used to model Mark's conceptions are of the form A ∣ → ∣ B, where this means that a change in A leads to a change in B. It is very natural to propose that this A ∣ → ∣ B notation represents an action-based scheme for doing action A and anticipating the direction of change in B. The vicarious operation of such a scheme without external actions could involve internalized actions and kinesthetic and visual imagery. The fact that Mark's statements are accompanied by hand motions and hefting-like manipulations of the equipment also suggests that action- based structures involving kinesthetic feedback are central to Mark's thinking in this interview. This is especially true whenever he talks about the way the added weight will affect the cart's motion by being "a large mass that you have to pull" at the start, and by "helping it keep going" once it gets started. During almost all of the time he gives his explanations he is looking directly at the cart. The hand movements take place over periods of seconds and are often repeated several times. He also tends to redescribe and rephrase several of his explanations as he stares at the cart.
All of these observations suggest the presence of intuitive nonverbal conceptions which become active in Mark over periods of two to 10 seconds and which are responsible for his awareness over these time periods of the visual and kinesthetic effects of some imagined action involving the cart. This suggests that the knowledge structures responsible for Mark's physical intuitions, like overt actions, must function continuously over a period of time and involve the motor-kinesthetic and visual systems at some level in order to be meaningful. If these preliminary indications are confirmed, it will be necessary for theorists to be as creative and open-minded as possible in order to develop more detailed models of physical intuition that account for these aspects of the behavior.
We have tried to show that it is possible to study systematically students' conceptions in physics, specifically in the area of mechanics, by using protocol analysis techniques. This can be done even when the basic concepts that the student uses are physical intuitions that are not equivalent to standard concepts used by the physicist. Such an analysis provides a much richer source of information about students' knowledge structures than do written tests.
With regard to methodology I believe that we are at a stage in the science of studying complex cognitive processes where the primary need is to develop viable qualitative models of cognitive structures. The analysis of many more protocols at various levels of detail should provide a needed background of rich phenomena as a fertile ground for the development of such models. The inclusion of verbatim sections of transcript in such studies provides an important constraint on the model construction process, since the requirement that a proposed model be consistent with as many aspects of the transcript as possible is a demanding one in the case of extended protocols.