| Our research is concerned with understanding how people solve problems in scientific domains such as physics, chemistry, computer science, and related disciplines. Specifically, we are interested in how people use a formal scientific language, such as differential equations or chemical formulae, (i.e. a formal representation) in conjunction with conceptual knowledge of the domain, to solve the wide range of problems of which engineers and scientists are capable.;Many traditional psychological models of these domains suggest that problem solving occurs as an orderly sequence of phases. Shifting from one phase to the next is accompanied by a representational shift.;We investigated the adequacy of this model in accounting for expert problem solving behavior. Suspending two properties of the traditional model suggests two alternative models, the iterative model and the interactive model.;We hypothesize that the traditional model will be adequate to explain the way experts coordinate conceptual and formal knowledge for easy problems in which experts can retrieve a well-practiced schema. However, we suggest that it will not be adequate to explain experts' behavior on more difficult problems.;To address these issues we performed two experiments. In Study One, we asked expert problem solvers to "think aloud" while solving easy and difficult mechanics problems and to give confidence ratings of their solutions. We coded the protocols according to the kind of knowledge subjects were using, and analyzed the ways in which their protocols drew upon conceptual and formal representations. As expected, in the more difficult problems expert behavior could not be adequately characterized by the traditional model. Instead the interactive model was necessary. We also characterize the kinds of representational transitions that occurred and discuss their function.;In Study Two, we examined the generality of the findings by replicating the experiment in a different domain, algorithm design. Again, we found support for the interactive model.;The results of the two studies support the notion that only the interactive model is adequate to account for the kinds behaviors exhibited by expert problem solvers. |
