Cognitive Psychology: Problem-Solving

• Cognitive Psychology Lecture 6 discusses problem-solving

Definition of Problems

• Problem-solving involves a situation where a living organism has a goal but lacks the knowledge of how to reach it, according to Karl Duncker in 1945.
• Problem-solving is goal-directed, requires cognitive processes like information processing, and faces a lack of relevant knowledge to produce an immediate solution.

Well-Defined vs. Ill-Defined Problems

• Well-defined problems have all aspects specified, give a clear specified goal, and have all information clearly spelled out.
• Ill-defined problems have some aspects unspecified, make it not obvious when the goal has been reached, and do not clearly provide the relevant information.

Knowledge-Rich vs. Knowledge-Lean Problems

• Knowledge-rich problems require specific prior knowledge.
• Examples of knowledge-rich problems include writing a good psychology essay and solving a crossword.
• Knowledge-lean problems requires little prior knowledge.
• An example, solving Sudoku, has all the information needed contained within the problem itself.

Gestalt Approach

• Gestalt Psychology is a theory of perception that emerged in the early 20th century in Austria and Germany.
• Gestalt Psychology emphasizes the processing of entire patterns, viewing the whole as greater than the sum of its individual components.

Reproductive vs Productive Thinking

• Reproductive thinking relies on experience to solve problems, often involving trial and error learning, and can be overt (actual tries) or covert (imagining the consequences).
• Productive thinking involves coming up with new responses, requiring restructuring of the problem through mental simulation, and resulting in insight when the solution suddenly becomes clear.

Insight Learning

• Kohler's (1925) study involved placing Sultan the ape in a cage with a banana out of reach and a box inside.
• Sultan initially tried jumping to reach the banana but failed, then had an "Aha!" moment and used the box as a tool to reach the fruit.
• Birch's (1945) study presented chimpanzees with a food-raking task.
• Initially, only two chimpanzees immediately used sticks to retrieve the food, but after exposure to the sticks without the food present, all chimps succeeded in solving the problem.
• Maier's (1931) "two cord problem" involved participants tying together two cords hanging from the ceiling, with tools available, where the elegant solution involved making one cord swing like a pendulum. Maier would set one of the cords in motion to provide a hint when participants were stuck.

Effect of Experience

• Sultan consistently solved problems through insight rather than trial and error, without needing long exposure.
• If problem solving is primarily trial and error the more experience should lead to better/faster solutions.

Functional Fixedness

• Functional fixedness is a cognitive bias that limits one's ability to use objects in ways other than their traditional or intended purpose.
• People develop specific frameworks for solving problems based on past experiences, which can limit their ability to think outside the box.
• As we gain more experience with objects, association with their typical functions becomes more ingrained
• An example of this concept in practice is "The Candle Box Problem" created by Dunker.

Water Jar Study

• Luchins' (1942) Water Jar Study had participants use jars of different capacities to measure out a specific amount of water.
• An experimental group practiced problems using B - A - 2*C, while a control group directly attempted test problems.
• The Einstellung effect is the tendency to rely on a familiar problem-solving strategy even when a simpler solution is available.
• Participants in the experimental group tended to stick with the B - A - 2*C formula, even when simpler solutions were available (64% failed to solve the problem!), while the control group more readily found the simpler solutions.

Summary and Evaluation of the Gestalt Approach

• The Gestalt approach introduced and investigated insight as a method of solving problems, emphasized restructuring and representational change, and showed that experience does not always help problem solving.
• It focused on knowledge-lean, well-specified problems and was vague about insight and restructuring, describing what happens but not how.

Cognitive Approach to Problem Solving

• Problem-solving involves a series of cognitive operations transforming information from one state to another
• Newell & Simon defines the problem space as representation of a problem, containing the initial state, all possible operations, all possible problem states, and the goal state. Problem-solving is changing the initial state into the goal state via a series of intermediate states called processing information.

Computational Approach to Problem Solving

• Newell & Simon (1972) developed the "General Problem Solver," a computer simulation of human problem solving, based on 'think aloud' paradigms and retrospective interviews.
• Designed to solve well-defined problems with a clear goal state.
• It's assumptions include being serial, having limited short-term memory capacity, and that relevant information can be retrieved from memory.

Tower of Hanoi

• The Tower of Hanoi involves moving a stack of disks from one peg to another, following specific rules: only one disk can be moved at a time, each move involves taking the upper disk, and no larger disk can be placed on top of a smaller disk.
• The player has to think ahead to know how to solve the puzzle.

Heuristics in Selecting Operations

• Newell & Simon (1972) identified two heuristics: means-end analysis and hill-climbing.
• Means-end analysis involves identifying the difference between the current state and the goal, forming a subgoal to reduce this difference, and performing operations to attain the subgoal.
• Hill-climbing involves changing the current state to a state that more closely resembles the goal.

Representational Change Theory

• The Representational Change Theory is a cognitive theory explaining how people overcome impasses and achieve insights in challenging problems.
• It involves constraint relaxation (reducing unnecessary constraints) and chunk decomposition (breaking down knowledge into manageable parts).
• This change is not the result of a deliberate search and happens unconsciously, leading to the "Aha!" experience.