Problem Solving

Understanding problems: The process of representation
  1. Finding the problem- recognizing that there is a problem to be solved.
  2. Representing the problem- understanding the nature of the gap to be crossed.
    1. Internal representation.
      1. The goal.
      2. The initial state.
      3. The operators- the actions that change one problem state into another.
      4. The restrictions on the operators.
    2. External representation- sketches, lists, equations, diagrams, etc.
  3. Planning the solution- understanding the nature of the to be crossed.
    1. Planning allows us to avoid irreversable errors.
    2. It allows us an inexpensive way to explore alternate methods for performing a task.
    3. It allows us to employ a range of powerful problem solving procedures which are not available in the task environment, e. g. working backward, hypothetical reasoning, abstraction, etc.
  4. Carrying out the plan.
  5. Evaluating the solution- asking "How good is the result?" once the plan is carried out.
  6. Consolidating gains- learning from the experience of solving.
    1. Why was this problem difficult?
    2. Why was it hard to find an appropriate representation?
    3. Was it difficult for me to keep my place in the problem?
    4. Was it hard to find a solution method?
    5. Was there a detour?
    6. Why did I miss critical clues?
    7. Did I make false assumptions?
    8. Should I have used a different representation?
    9. What mistakes did I make?
    10. Did I make important discoveries about representations, methods, detours?
    11. If so, how did I make them"
    12. Are there other problems similiar to this one?
    13. Could they have been solved in the same way?
Search:
  1. Trial-and-error - blind and systematic.
  2. Proximity - solve problems by selecting a step at a time, each of which reduces the distance to the goal.
    1. The hill climbing method sees one kind of difference between the current state and the goal.
    2. Means-end analysis.
      1. Find a list of differences between the current state and the goal.
      2. Take the first difference in finding an operator for reducing it. If you can't find an appropriate operator, go to the next difference. If you run out of differences to find operators for, report that you can't solve their problem.
      3. Compare the conditions for applying the operator it with the current state to find a difference. If there is a difference, try to reduce it.
    3. Fractional methods- involve breaking the problem into a sequence of smaller parts, that is, by setting up some goal.
    4. Knowledge-based methods- use information stored in the problem and solver's memory to guide the search for a solution.
Using memory effectively:
Learning strategies:
  1. Basic learning strategies
    1. The structural strategy
    2. The context strategy
    3. Monitoring
    4. Inferencing
    5. Instantiation
    6. Multiple coding
  2. Study systems
    1. Survey Q3R (Survey, Question, Read, Recite, and Review)
    2. Dansereu's MURDER system.
      1. Mood. Creating a positive attitude, and coping with distractions.
      2. Understand. When first reading a text to mark any parts of the text you don't understand.
      3. Recall. Recall the information you have been reading about and to transform it.
      4. Digest. Attend to the marked parts which are still unclear to you after further reading.
      5. Expand. 
        1. If you could talk to the author, what sorts of questions or criticisms would you raise?
        2. How can the material be applied?
        3. How could you make the material more understandable and interesting to others?
      6. Review. Review your errors with the intent of finding their causes and making appropriate changes in your study habits.
Source: The Complete Problem Solver (1981) by John R. Hayes.