Problem Solving Heuristic

A Problem Solving Heuristic is a cognitive heuristic that can support a problem solving process through simplified decision rules and cognitive shortcuts.

• AKA: Problem Solving Rule of Thumb, Solution Finding Shortcut, Problem Resolution Guideline.
• Context:
  • It can typically simplify Problem Analysis through mental model application.
  • It can typically accelerate Solution Discovery through cognitive shortcut application.
  • It can typically guide Solution Strategy through experience-based pattern recognition.
  • It can typically reduce Cognitive Load through mental effort optimization.
  • It can typically facilitate Complex Problem Navigation through simplified approach paths.
  • ...
  • It can often overcome Problem Solving Barriers through alternative perspective adoption.
  • It can often complement Analytical Methods during initial solution exploration.
  • It can often organize Solution Approach during early problem engagement.
  • It can often transfer Solution Patterns across related problem domains.
  • It can often leverage Past Experience during unfamiliar problem context.
  • ...
  • It can range from being a Simple Problem Solving Heuristic to being a Complex Problem Solving Heuristic, depending on its rule complexity.
  • It can range from being a Domain-Specific Problem Solving Heuristic to being a General Problem Solving Heuristic, depending on its application scope.
  • It can range from being a Sequential Problem Solving Heuristic to being a Parallel Problem Solving Heuristic, depending on its cognitive processing approach.
  • It can range from being a Conscious Problem Solving Heuristic to being an Unconscious Problem Solving Heuristic, depending on its awareness level.
  • It can range from being a Algorithmic Problem Solving Heuristic to being an Intuitive Problem Solving Heuristic, depending on its formalization degree.
  • ...
  • It can provide Problem Decomposition Techniques for complex problem simplification.
  • It can employ Pattern Recognition Strategy for solution pattern identification.
  • It can utilize Analogical Reasoning Approach for cross-domain knowledge transfer.
  • It can implement Constraint Relaxation Technique for solution space expansion.
  • It can apply Goal Reduction Strategy for manageable subgoal creation.
  • ...
• Examples:
  • Educational Problem Solving Heuristic Categories, such as:
    • Pólya's Problem Solving Heuristics, such as:
      • Problem Understanding Heuristic for problem clarification process.
      • Plan Devising Heuristic for solution strategy development.
      • Plan Execution Heuristic for solution implementation guidance.
      • Solution Review Heuristic for effectiveness evaluation.
    • Schoenfeld's Problem Solving Heuristics, such as:
      • Resource Identification Heuristic for available knowledge assessment.
      • Control Process Heuristic for solution progress monitoring.
      • Belief System Analysis Heuristic for solving approach evaluation.
  • Cognitive Problem Solving Heuristic Categories, such as:
    • Means-Ends Analysis Heuristics, such as:
      • Goal-State Difference Heuristic for gap reduction planning.
      • Subgoal Formation Heuristic for incremental progress management.
    • Working Backward Heuristics, such as:
      • Reverse Engineering Heuristic for solution path reconstruction.
      • Goal-to-Start Mapping Heuristic for inverse problem solving.
    • Analogy-Based Heuristics, such as:
      • Similar Problem Mapping Heuristic for solution pattern transfer.
      • Cross-Domain Application Heuristic for insight generation.
  • Domain-Specific Problem Solving Heuristic Categories, such as:
    • Scientific Problem Solving Heuristics, such as:
      • Parsimony Heuristic for simplest explanation selection.
      • Falsifiability Heuristic for hypothesis testing approach.
    • Mathematical Problem Solving Heuristics, such as:
      • Pattern Recognition Heuristic for mathematical structure identification.
      • Special Case Analysis Heuristic for general solution discovery.
    • Engineering Problem Solving Heuristics, such as:
      • Functional Decomposition Heuristic for system breakdown analysis.
      • Trade-Off Analysis Heuristic for constraint balancing.
  • ...
• Counter-Examples:
  • Algorithmic Solution Methods, which follow precise step-by-step instructions rather than simplified guidelines.
  • Trial and Error Approaches, which use random attempts rather than guided exploration.
  • Exhaustive Search Techniques, which examine all possible solutions rather than promising subsets.
  • Formal Logic Systems, which apply rigorous deduction rules rather than cognitive shortcuts.
  • Procedural Workflow, which executes predetermined sequences rather than adaptive guidelines.
• See: George Pólya, Problem Solving Method, Cognitive Shortcut, Decision Heuristic, Mental Model, Solution Strategy, Algorithmic Problem Solving.

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References

2009

• http://en.wikipedia.org/wiki/George_P%C3%B3lya#First_principle:_Understand_the_problem
  • Do you understand all the words used in stating the problem?
  • What are you asked to find or show?
  • It can you restate the problem in your own words?
  • It can you think of a picture or a diagram that might help you understand the problem?
  • Is there enough information to enable you to find a solution?
  • Do you need to ask a question to get the answer?
• http://en.wikipedia.org/wiki/George_P%C3%B3lya#Second_principle:_Devise_a_plan
  • Guess and check
  • Make an orderly list
  • Eliminate possibilities
  • Use symmetry
  • Consider special cases
  • Use direct reasoning
  • Solve an equation
  • …
  • Look for a pattern
  • Draw a picture
  • Solve a simpler problem
  • Use a model
  • Work backward
  • Use a formula
  • Be creative
  • Use your head/noggen
• http://en.wikipedia.org/wiki/George_P%C3%B3lya#Third_principle:_Carry_out_the_plan
  • This step is usually easier than devising the plan. In general (1957), all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work discard it and choose another. Don't be misled, this is how mathematics is done, even by professionals.
• http://en.wikipedia.org/wiki/George_P%C3%B3lya#Fourth_principle:_Review.2Fextend
  • Pólya mentions (1957) that much can be gained by taking the time to reflect and look back at what you have done, what worked and what didn't. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem.

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