Problem Solving: Cognitive processes aimed at achieving a specific goal (a solution to a problem) Early Research: Wolfgang Kohler (Gestalt Psychologist) work with chimpanzees on Tenerife Island. Insight learning: the “sudden” realization of a knowledge. Fit nicely with Gestalt idea of perceiving whole meaningful pattern or form.

Duncker (1945) “make a lamp” problem Functional fixedness: tendency to think about objects only in term of the conventional uses

Luchin’s (1942) water jar problem: mental or negative set effects Set effect: inappropriately using a previously successful approach when an another approach would be better.

Return to insight learning Insight as release from irrelevant modes of thinking that inhibit problem solving (“getting over” set or functional fixedness effects) EEG shows a spike in alpha and gamma brain waves prior to insight solution Frontal lobe and anterior cingulate gyrus activity associated with insight solution not non-insight solution

Analogy and problem solving Gick and Holyoak (1980) Radiation Problem Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. It is impossible to operate on the patient, but unless the tumor is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumor. If the rays reach it all at once at a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity the healthy tissue the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor, either. What type of procedure might be used to destroy the tumor with the rays and at the same time avoid destroying the healthy tissue? When give this problem cold, less than 10% were able to solve it.

Analogy and problem solving Gick and Holyoak (1980) Military Problem A small country was ruled from a strong fortress by a dictator. The fortress was situated in the middle of the country, surrounded by farms and villages. Many roads led to the fortress through the countryside. A rebel general vowed to capture the fortress. The general knew that an attack by his entire army would capture the fortress. He gathered his army at the head of one of the roads, ready to launch a full-scale direct attack. However, the general then learned that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely, since the dictator needed to move his troops and workers to and from the fortress. However, any large force would detonate the mines. Not only would this blow up the road, but it would also destroy many neighboring villages. It therefore seemed impossible to capture the fortress. The general, however, devised a simple plan. He positioned a small detachments of soldiers at the head of different roads and on his order they march along different roads to the fortress and arrived at the same time, thereby overthrowing the dictator.

Analogy and problem solving Gick and Holyoak (1980) Analogy was not obvious: only 20% solved the radiation problem when first given the military problem. However, this went up to over 90% when subjects were told that the military problem would be applicable to solving the radiation problem.

When are analogies more likely to work? Holyoak and Thagard (1997) multi-constraint theory of problem solving Analogies more effective when: Similarities in content: elements of one event or experience bear resemblance to elements in another (note: military and radiation have little surface similarity which may explain low rate of problem solving in no-hint condition) Parallel structures: elements in one event or experience can be “mapped” onto elements in the other. (e.g. dictator=tumor; troops=rays; different routes=dividing rays, etc.) Similar purposes: goals/purposes of events are similar (e.g. curing a dangerous problem, dictator/tumor)

Analogy and the brain When doing analogical mapping: left prefrontal and inferior parietal, plus medial frontal active When doing insight learning: right frontal

Means-End Analysis General problem solving heuristic strategy. Includes: Initial state: conditions as they exist currently (with problem) Goal state: conditions as they exist with problem solve Problem space: the “territory” that must be traversed to move from initial to goal states Operators: legal “moves” that can be made to navigate through problem space Subgoals: states in problem space that represent progress toward goal state.

Problem space Tower of Hanoi (3 disks fairly simple). Getting largest one on bottom of last pole might be subgoal. More practical example: clearing snow from drive way. Legal moves and subgoals shown

GPS (General Problem Solver) Early attempt at creating AI Problem-solving computer system using means-end analysis Operated using production systems: directional instructions in the form of if-then statements if no stores are open to buy snow-removal equipment then call for snow removal. If no friend available to help with removal then call professionals, etc. Production systems constrained by legal operator “rules” Ex: can’t call if phone lines down. Can’t contract professionals if no money, etc. Limitation of GPS: often got stuck on subgoals. If solving overall problem required making a move that “moved” away from subgoal, GPS got stuck, called stuck at local maximum