A substantial gap exists between the growing body of cognitive science research on physics problem solving and problem-solving instruction in university physics courses. One of the notable findings from problem-solving research suggests that metacognition – awareness of one’s own cognitive processes – plays a critical role in both the development of new problem-solving skills and in the regulative aspects of ongoing problem solving.
Two objectives guide us through this project. First, we use existing research to construct a basic cognitive model for physics problem solving; second, with this model in mind, we will develop a set of instructional tools and techniques aimed at furthering metacognitive development in students in university physics courses.
A problem arises when a living creature has a goal but does not know how this goal is to be reached. (Duncker 1945)
Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable. Henri Poncaré (Hadamard 1945)
One’s knowledge concerning one’s own cognitive processes and products or anything related to them. […] Metacognition refers, among other things, to the active monitoring and consequent regulation and orchestration of these processes in relation to the cognitive objects on which they bear, usually in the service of some concrete goal or objective. (Flavell 1976)
Novices typically begin to solve a problem by plunging into the algebraic and numerical solution – they search for and manipulate equations until they find a combination that yields an answer. All too often they neither use their conceptual knowledge of physics to qualitatively analyze the problem situation, nor do they systematically plan a solution before they begin numerical and algebraic manipulations of equations. When they arrive at a numerical answer, they are usually satisfied – they rarely check to see if the answer makes sense. (Heller 1992)