Problem solving occurs when an organism has a goal but the path to achieving it is not immediately obvious. It encompasses a vast range of cognitive activities, from solving a jigsaw puzzle to diagnosing a disease to resolving a diplomatic crisis. Research has identified both general strategies that apply across domains and domain-specific knowledge structures that enable expert problem solving.
Problem Space Theory
Newell and Simon's (1972) problem space theory, the foundational framework for problem-solving research, proposes that problem solving involves searching through a problem space — the set of all possible states from the initial state to the goal state. Operators are actions that transform one state into another. The solver navigates the problem space using strategies (heuristics) that reduce the search, since exhaustive search is impractical for all but the simplest problems.
Barriers to Problem Solving
Several cognitive barriers impede problem solving. Mental set — the tendency to apply familiar strategies even when they are suboptimal — was demonstrated by Luchins' water jug experiments. Functional fixedness — the inability to see objects as serving functions other than their typical use — was demonstrated by Duncker's candle problem. Both reflect the costs of well-learned knowledge: expertise can paradoxically create inflexibility when novel approaches are required.
Chi, Feltovich, and Glaser (1981) showed that physics experts and novices categorize problems differently. Novices sort by surface features (inclined plane problems, pulley problems), while experts sort by deep structural features (conservation of energy problems, Newton's second law problems). This deep structural representation allows experts to rapidly identify the appropriate solution schema, bypassing the laborious search through problem space that novices must perform.