Problem Solving What is a problem? How do we go about solving problems? How can we be better problem-solvers?
What is a Problem? • A problem occurs when there is a difference between a goal and the present state and it is not immediately obvious how to reach the goal
The Nine-Dot Problem • Connect all nine dots • Draw no more than four straight lines • You may not lift your pen from the paper
One Solution start
Restructuring • Restructuring the mental representation of the problem can lead to a solution • Insight occurs when the problem is restructured and the solution becomes clear (Metcalfe & Wiebe, 1987)
Gestalt Psychology: Insight • Kohler (1925) -chimpanzees showed insight in problem solving
Restructuring • Functional fixedness is the tendency to see only familiar uses for objects • The “candle problem” was solved more often when the problem was restructured (Duncker, 1945) • Mental set is a tendency to respond based on past experience – e.g., water jar problem (Luchins, 1942)
Means-End Analysis • Compare the goal to the initial state, then create subgoals to reach the solution (Newell & Simon, 1972) • Understanding the initial state is often the hardest part, e.g., mutilated checkerboard problem (Kaplan & Simon, 1990)
Use of Analogies • Use the solution to a similar problem to solve a current problem • Steps (Gick & Holyoak, 1983): • Notice the relationship between the source problem and target problem • Map corresponding parts of the problems • Generate a parallel solution
Use of Analogies • A solution is more likely when the person has a good problem schema (Gick & Holyoak, 1983) • A schema can be induced by: • Providing multiple examples • Giving hints
How Experts Solve Problems • Organize knowledge – experts recognize patterns better, but only in their own fields (Chase & Simon, 1973; Bedard & Chi, 1992) • Categorize problems in terms of principles, not surface characteristics (Chi et al., 1981)
Creativity • Investment Theory: creative people buy low and sell high (Sternberg & Lubart, 1996): • Increasing Creativity (Hayes, 1978): • Develop a knowledge base • Remove inhibitions • Look for analogies
Evolutionary Psychology • What types of problems are humans best adapted to solve? • What types of problems do modern humans face?