What’s the Problem?

By admin • on November 11, 2009

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solution 300x200I often see posts on problem solving but do we actually know what problem soving actually is and the main techniques to help solve the problems themselves?

There are many approaches to problem solving, depending on the nature of the problem and the people involved in the problem. The more traditional, rational approach is typically used and involves, eg, clarifying description of the problem, analyzing causes, identifying alternatives, assessing each alternative, choosing one, implementing it, and evaluating whether the problem was solved or not.

Problem solving is a mental process and is part of the larger problem process that includes problem finding and problem shaping. Considered the most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of more routine or fundamental skills.

Problem solving occurs when an organism or an artificial intelligence system needs to move from a given state to a desired goal state.

Whats the Problem? Characteristics of difficult problems

As elucidated by Dietrich Dörner and later expanded upon by Joachim Funke, difficult problems have some typical characteristics that can be summarized as follows:

  • Intransparency (lack of clarity of the situation)
    • commencement opacity
    • continuation opacity
  • Polytely (multiple goals)
    • inexpressiveness
    • opposition
    • transience
  • Complexity (large numbers of items, interrelations and decisions)
  • Dynamics (time considerations)
    • temporal constraints
    • temporal sensitivity
    • phase effects
    • dynamic unpredictability

The resolution of difficult problems requires a direct attack on each of these characteristics that are encountered.In reform mathematics, greater emphasis is placed on problem solving relative to basic skills, where basic operations can be done with calculators. However some “problems” may actually have standard solutions taught in higher grades. For example, kindergarteners could be asked how many fingers are there on all the gloves of 3 children, which can be solved with multiplication.

Some problem-solving techniques

  1. Divide and conquer: break down a large, complex problem into smaller, solvable problems.
  2. Hill-climbing strategy, (also called gradient descent/ascent, difference reduction, greedy algorithm) – attempting at every step to move closer to the goal situation. The problem with this approach is that many challenges require temporarily moving farther away from the goal state. For example, traveling 1,000 miles to the west might require driving a few miles east to an airport. (see river crossing puzzle).
  3. Means-ends analysis, more effective than hill-climbing, requires the setting of subgoals based on the process of getting from the initial state to the goal state when solving a problem.
  4. Trial-and-error (also called guess and check)
  5. Brainstorming
  6. Morphological analysis
  7. Method of focal objects
  8. Lateral thinking
  9. George Pólya’s techniques in How to Solve It
    George Pólya ca 1973 at the Stanford Universit...
    Image via Wikipedia
  10. Research: study what others have written about the problem (and related problems). Maybe there’s already a solution?
  11. Assumption reversal (write down any assumptions about the problem, and then reverse them all)
  12. Analogy: has a similar problem (possibly in a different field) been solved before?
  13. Reduction (complexity): transforming the problem into another problem for which solutions exist.
  14. Hypothesis testing: assuming a possible explanation to the problem and trying to prove the assumption.
  15. Constraint examination: are you assuming a constraint which does not really exist?
  16. Incubation: input the details of a problem into the mind, then stop focusing on it. The subconscious mind will continue to work on the problem, and the solution might just “pop up” while are doing something else
  17. Build (or write) one or more abstract models of the problem
  18. Try to prove that the problem cannot be solved. Where the proof breaks down can be the starting point for resolving it
  19. Get help from friends or online problem solving community (e.g. 3form, InnoCentive)
  20. delegation: delegating the problem to others.
  21. Root Cause Analysis
  22. Working Backwards
  23. Forward-Looking Strategy
  24. Simplification
  25. Generalization
  26. Specialization
  27. Random Search
  28. Split-Half Method
  29. The GROW model
  30. TRIZ 40 Principles: Segmentation, Extraction, Local Quality, Asymmetry, Consolidation, Universality, Nesting, Counterbalance, Prior Conteraction, Prior Action, Cushion in Advance, Equipoteniality, Do It in Reverse, Spheroidality, Dynamicity, Partial or Excessive Action, Transition to a New Dimension, Mechanical Vibration, Periodic Action, Continuity of Useful Action, Rushing Through, Convert Harm to Benefit, Feedback, Mediator, Self Service, Copying, Disposable, Replacement ofMechanical system, Pneumatic or Hydraulic construction, Flexible Membranes or Thin Films, Porous Material, Changing the Color, Homogeneity, Rejecting and Regenerating Parts, Transformation of Properties, Phase Transition, Thermal Expansion, Accelerated Oxidation, Inert Environment, Composite Materials
  31. Eight Disciplines Problem Solving
  32. Southbeach Notation
  33. The WWXXD Method: This method requires you to ask yourself What Would XX Do, where XX is the person in question. Such variations of this method are the WWJD, What Would Jesus Do, WWUJD, What Would Uncle Jesse Do, WWCND, What would Chuck Norris Do, and WWJBD, What Would Jack Bauer Do. This method allows you to frame the question, resolve the question and act upon it in a similar way to the person in question.

Have I missed a technique out? If so please leave a comment below.

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By robthompson on November 11th, 2009 at 9:16 am

Just published: What’s the Problem?: I often see posts on problem solving but do we actually know what problem sov… http://bit.ly/2xmF5j

This comment was originally posted on Twitter

By Hire php developer on November 11th, 2009 at 12:12 pm

Awesome tips on problem solving approach, what i believe that root core analysis and divide and solve are the best defeat against problem, if you are in big trouble then positive thinking is boost your confidence. thanks for sharing it.

By shaun sayers on November 13th, 2009 at 12:28 pm

Yes, and then there's proportionality …

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