In-Depth Problem Solving Notes

Problem Solving Overview

• Cognitive Effort: To solve problems, one must engage cognitively and restructure their thinking if they feel stuck.
• Representation: Effective problem solving often requires clear mental representation of the problem elements; ineffective representation can hinder finding solutions.

Insight vs Analytical Problems

• Insight Problems: Characterized by a sudden realization or 'eureka' moment; warmth ratings (perceived closeness to solution) increase rapidly once the correct way of thinking is adopted. Examples:

  • Cheap necklace problem
  • Kohler's circle problem

• Analytical Problems: Warmth ratings increase gradually as one works step by step towards a solution.

Functional Fixedness

• Definition: The tendency to perceive objects only in terms of their typical use, which can limit creative problem solving.
• Examples: Using a clicker only as a presentation device instead of other potential uses.

Candle Problem (Duncker)

• Setup: Candle, box of thumbtacks, and matches are presented as a problem. Solutions become easier when the box is seen as a shelf (changing representation).
• Relevance: Changing the presentation of objects can enhance problem-solving capacity by breaking functional fixedness.

Two String Problem (Meyer)

• Setup: Two strings hanging from the ceiling, with a chair and pliers as tools.
• Objective: Tie the two strings together without taking them down, which is impossible without using innovative strategies (
  • Use pliers as a weight to swing one string and catch it with the other).
• Effect of Movement: A chance accidental brush against a string resulted in higher solution rates among participants, indicating a mental shift in considering dynamic properties of objects.

Mental Sets

• Definition: Preconceived notions on how to approach problems based on previous experiences.
• Benefits and Drawbacks: Helps with familiar tasks but can blind individuals to simpler or more effective solutions.

Water Jug Problems

• Format: Participants are tasked with measuring specific amounts of water using different sized jugs, often following successful strategies learned from previous problems.
• Examples: Participants often initially replicate familiar strategies (e.g., subtraction-based formulas) despite simpler alternatives possibly existing.

Research Findings

• Influencing Factors: The way a problem is presented can significantly impact solution ease; irrelevant information can also affect problem-solving performance.
• Experiment: Changes in experimental instructions (like a reminder not to be blind to possibilities) can alter the effectiveness of problem-solving strategies.