Other meanings of Problem solving
Cognitive Psychology
Problem solving is the cognitive process of finding solutions to difficult or complex issues, involving the identification of a discrepancy between a current state and a desired goal, and the deployment of strategies to bridge that gap. It is a fundamental human activity studied across psychology, artificial intelligence, and education, with roots in early 20th-century behaviorism and Gestalt psychology. The field has evolved from trial-and-error and insight theories to information-processing models and modern computational approaches, encompassing both well-defined problems (e.g., a math puzzle) and ill-defined ones (e.g., career decisions).
Problem solving is typically defined as a goal-directed cognitive process that involves overcoming obstacles to reach a solution. Classic models, such as that proposed by John Dewey in 1910, outline stages: recognizing the problem, defining it, generating possible solutions, evaluating alternatives, and implementing the chosen solution. Later information-processing theories, notably by Allen Newell and Herbert Simon, conceptualized problem solving as a search through a problem space, where the solver uses heuristics like means-end analysis to reduce the difference between the current state and the goal state. These models distinguish between well-defined problems, which have clear goals and constraints, and ill-defined problems, which lack such clarity, requiring the solver to structure the problem itself. The stage-based view has been criticized for being too linear, as real-world problem solving often involves iterative loops and backtracking.
Problem solving relies on a variety of cognitive mechanisms, including working memory, attention, and executive functions. Strategies range from algorithmic approaches, which guarantee a solution if correctly applied, to heuristic shortcuts that are faster but fallible. Common heuristics include trial-and-error, hill-climbing, and means-end analysis. Insight, a sudden realization of a solution, contrasts with incremental analysis and has been linked to restructuring of the problem representation, as demonstrated in Gestalt psychology experiments by Karl Duncker and others. Functional fixedness, the tendency to see objects only in their usual roles, can impede problem solving, as shown in Duncker's candle problem. More recently, research has explored the role of incubation, where taking a break can facilitate insight, and the influence of emotions and motivation on problem-solving performance.
Problem solving is central to education, where it is a key competency in curricula worldwide, and to fields like engineering, medicine, and business. In artificial intelligence, problem solving is modeled through search algorithms and planning systems, with applications in robotics and game playing. Individual differences in problem-solving ability are associated with general intelligence, working memory capacity, and domain-specific expertise. Experts differ from novices in their ability to recognize deep structural patterns and to use efficient strategies. Creativity, often considered a subset of problem solving, involves generating novel and useful solutions, and has been studied in relation to divergent thinking. Environmental factors, such as time pressure and social context, also affect performance, with collaboration sometimes enhancing but sometimes hindering problem solving.
Beyond mainstream research, problem solving has niche dimensions. The 'Einstellung effect' describes how prior experience can blind solvers to simpler alternatives, a phenomenon demonstrated in water-jug experiments. The 'candle problem' by Duncker is a classic example of functional fixedness, but it also illustrates the role of motivation and reward, as later studies by Sam Glucksberg showed that incentives can impair performance by increasing anxiety. In mathematics, the 'four-color theorem' was the first major theorem proven using a computer, highlighting the role of computational problem solving. Cross-cultural studies suggest that problem-solving strategies vary, with some cultures emphasizing holistic approaches over analytic ones. Additionally, the 'problem of induction' in philosophy poses a fundamental challenge to problem solving, questioning the validity of generalizing from past experiences.
This entry focuses on the cognitive process of problem solving, distinct from mathematical or computational problem-solving as a discipline.
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