L4: Problem-Solving

Problem-Solving

  • Definition: A problem is defined by its Start State (current situation) and Goal State (desired situation). The pathway from start to goal is often unclear.

Types of Problems

  • Well-defined Problems: All aspects (initial state, goal state, possible moves) are clearly defined.

  • Ill-defined Problems: Start state, end state, or possible strategies are unknown (common in everyday situations).

  • Knowledge Lean Problems: Problems that do not require specific knowledge (e.g., puzzles).

  • Knowledge Rich Problems: Problems that require specific knowledge (e.g., expert-level dilemmas).

Theories of Problem-Solving

  • Behaviourist Approach: Focuses on trial-and-error learning. Example: Thorndike's cat experiment demonstrating slow and unsystematic learning.

  • Gestalt Approach: Involves problem restructuring and insights (the "Aha" moment). Example: Kohler’s monkey experiment showing incubation leads to solutions.

  • Information Processing: Developed by Newell & Simon; computational modeling approach focusing on problem space.

Insight and Problem-Solving

  • Gestalt Insight: Insight problems often require restructured representations of the problem, with incubation helping in overcoming impasses.

  • Representational Change Theory: Poor operators (problem-solving actions) are activated from an incorrect representation, but restructuring can lead to insight.

    • Change representation or relax constraints of moves.

Heuristics in Problem-Solving

  • Methods to simplify decision-making:

    • Means-End Analysis: Creates sub-goals to facilitate reaching the main goal.

    • Hill-Climbing: Always choose a move that seems to bring you closer to the goal—but this can lead to dead ends when intermediate steps don't help.

Example Problems

  • Missionaries and Cannibals: Move individuals across a river under specific conditions (no more cannibals than missionaries on either side).

  • Tower of Hanoi: Move discs to a peg under specific constraints (e.g., cannot place a larger disc on a smaller one).

Analogical Problem-Solving

  • Involves learning from previous experiences with similar structural features in problems.

  • Negative Transfer: When previous experiences hinder problem-solving.

  • Positive Transfer: When previous experiences assist.

    • Example: Recognizing the similarity between the problem of a general's army and a surgeon's approach to a tumor.

Expertise in Problem-Solving

  • Expertise Over Time: Accessing knowledge quickly, usually from years of practice. Examples:

    • Chess Experts: Studies by De Groot show that experts remember positions significantly better than novices, focusing on relevant strategies derived from their extensive experience.

    • Medical Experts: Fast recognition of problems (e.g., tumors) due to automatic processes developed through practice.

Summary of Cognitive Approaches

  • Behaviourist Approach: Highlights trial-and-error learning.

  • Gestalt & Representation Theory: Emphasizes insight in problem-solving.

  • Information Processing: Effective for well-defined problems but lacks insight handling.

  • Analogical Problem Solving: Learning from experiences can enhance problem-solving ability.

  • Expertise: Critical for solving knowledge-rich problems, utilizing quick recall of learned information.