Internal Models in Physics Problem Solving

In this paper, we discuss the relations among internal mental models, attentional cues, and knowledge structure in solving elementary physics problems. The notion of semantic sensitivity is introduced as a qualitative measure of problem-solver receptivity to cues for generating, or making a shift to, a new internal model that may lead to the correct answer. Using three physics problems and their variations, the following results were obtained. First, think-aloud protocol data of two experts and one novice, working on those problems, were analyzed to provide empirical examples of internal models, and also to show that generation and shift of internal models generally results from the interplay of two kinds of processes, model construction and model development. Second, protocol data from 15 novices and seven professionals were used to present a more extensive empirical taxonomy of internal models for those problems. Third, seven experiments were used, along with the results from the protocol data, to suggest the following conditions on semantic sensitivity. (1) If the problem solver's present internal model is independent of his knowledge of physics principles underlying the given problem, but if attentional cues are related directly to the knowledge, then his present model is semantically sensitive to the cues, that is, it can be shifted easily to another model that is based on the knowledge. (2) His present model is semantically insensitive, if given cues are encoded based on the same knowledge as used for generating the model. (3) The relevance of cues to knowledge structure is critical for semantic sensitivity of the presently encoded model: Which cues to attend to is guided by the problem solver's knowledge, and if he can focus on those most relevant to the physics principles underlying the problem, then his present model is semantically sensitive to those cues, that is, he is more able to shift the present model to another that would lead to the correct answer.