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In-Depth Notes on Problem Solving and Cognitive Processes

  • Understanding Hose Location in Problem-Solving

  • When a dishwashing hose is not in its expected place, problem-solving can become difficult.

  • Key takeaway: Cultivate the ability to generalize solutions from specific experiences.

  • Generalization of Knowledge and Concepts

  • Store knowledge in a generalized way for adaptability across different situations.

  • This allows for problem-solving adaptability, applying learned solutions to new contexts.

  • Well-Defined vs. Ill-Defined Problems

  • Well-Defined Problems:

    • Clear goals, unambiguous paths to solutions.
    • All information needed for the solution is present.
    • Example: Cooking pasta follows a clear script of steps.

  • Ill-Defined Problems:

    • Ambiguous goals and multiple possible paths to solutions.
    • Requires deeper cognitive engagement to navigate.
    • Example: Planning a vacation involves various interpretations of what constitutes relaxation.

  • Examples of Problem Types

  • Well-Defined Problems are typically associated with games and puzzles like Sudoku:

    • Clear rules, task constraints (e.g., no repeated numbers in rows or columns).

  • Ill-Defined Problems can include social challenges and personal decisions, requiring more complex cognitive strategies than scripts or algorithms.

  • Cognitive Processes in Problem Solving

  • Different neurocognitive processes are activated for well-defined versus ill-defined problems.

  • Research identifies episodic memory as crucial for constructing scenarios in ill-defined problem-solving (observed through studies on those with memory impairments).

  • Artificial Intelligence and Problem Solving

  • AI excels at well-defined problems due to its reliance on known algorithms, but struggles with ill-defined ones.

  • Paradox in AI functionality: Easy problems for humans may be hard for AI, and vice versa.

  • Navigating Problem Spaces

  • A problem space comprises initial state, goal state, and possible intermediate states.

  • Tower of Hanoi is a classic example of a well-defined problem illustrating how to represent these spaces with operators and constraints guiding the paths to solutions.

  • Methods of Problem-Solving

  • Brute Force Approach:

    • Considers the entire problem space blindly.
    • Can lead to decision fatigue due to combinatorial explosion of options.

  • Heuristics:

    • A strategy to effectively navigate problem spaces through trial and error, hill climbing, and means-end analysis.
    • Trial and Error: Simple but inefficient for complex problems.
    • Hill Climbing: Emphasizes close proximity to the goal but may lead to local maxima or dead ends.
      • Classic example: Hobbit and Orcs problem that necessitates backward steps.
    • Means-End Analysis: Dynamic movement through problem spaces; evaluates overall progress towards the goal considering multiple sub-goals.

  • The Role of Expertise in Problem-Solving

  • Experts approach problems differently than novices, spending more time defining problems initially and understanding the holistic view of situations.

  • Expert problem-solving involves less cognitive load due to efficient information processing and holistic view.

  • Distinction in brain activity: Experts engage both hemispheres for complex problem-solving, while novices tend to rely on more concrete, left-hemisphere reasoning.

  • Learning and Application of Problem-Solving Skills

  • Transfer of skills may be limited; expertise does not necessarily translate across different domains.

  • Practicing defined strategies can enhance problem-solving effectiveness and cognitive resource management.

  • Exam Preparation Tips:

  • Focus on understanding problem definitions and what is being asked, process relevant information effectively, and check understanding against learned concepts.