Metacognition and physics problem solving
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)
Problems (Duncker 1945); complex problems (Complex Problem Solvi...); problem solving (Newell 1972); problem solving and neurobiology (citation not found: Anderson2012); defining problem solving; heuristics (Polya 1945, Martinez 1998); problem solving in education in general (Dewey); problem solving in physics education (Reif 1976, Larkin 1979); what is unique about physics problem solving.
Novice and expert studies (Larkin 1979, Larkin 1980, Dhillon 1998, Snyder 2000); novice and expert studies in other fields – mathematics, computer science, astronomy, engineering, chemistry, biology, medicine, scientific writing, language learning, education, political science, economics, music, theater, physical education; limitations of novice and expert studies; instructors’ ideas about problem solving (citation not found: Henderson2001) Kuo 2004).
Knowledge structures (Reif 1995, National Research Council 2000, Snyder 2000, Sabella 2007); knowledge structures and preconceptions (Arons 1997, Mazur 1997); metacognition and awareness of knowledge structures; neuroscientific correspondence; local and global coherence (Sabella 2007); multiple local coherences (Frank 2012).
Problem solving and self-explanations (Chi 1991).
Physics problem solving was first investigated by comparing the problem-solving strategies of novices (students in introductory physics classes) and experts (physics professors).
Metacognition (Flavell 1976, Fox 2008, Lai 2011); defining metacognition (Jacobs 1987, Nelson 1990, Veenman 2006); metacognition, self-regulation, executive function (McCormick 2013); assessing metacognition (McCormick 2013); metacognition and neurobiology (citation not found: Anderson2011); importance of teaching metacognition (National Research Council 2000).
Analyses of the knowledge and skills underlying the notion of metacognition originated in the work of James, Piaget, and Vygotsky (Fox 2008). The term metacognition was first introduced by Flavell as “knowledge concerning one’s own cognitive processes and products or anything related to them” (Flavell 1976) or “cognition about cognition” (Flavell 1985). Despite these seemingly straightforward definitions, the literature abounds with different working definitions of the term. In general, however, the literature points to two facets of metacognition: knowledge about cognition and regulation of cognition (Schraw 1998, Veenman 2006).
Constructivism; social learning.
History and philosophy of science; understanding basics of cognitive science (McCabe 2011); extrinsic motivation (grades and assessment).