You Have to Ask Questions to Get Answers

In high school, I wrote a column in the newspaper called “The Question Man.” I was never afraid to ask the hard questions. For instance, I dared to ask whether one of our valedictorians really was God. As I’ve gotten older, I’ve realized more and more the value of asking the right questions before attempting to come up with answers. In this post, I wanted to explore some, but not all of those questions.

George Polya, a mathematician, wrote a book called “How to Solve It” that provides great insights on questions to ask when attempting to solve problems. While I avoided math like the plague (unfortunately) in high school, college, and my choice of profession, Polya provides great insights on how to solve specific problems. (Since these steps involve math, they assume that you have defined the problem).

  1. Understand the Problem
    1. What is the unknown?
    2. What are the data?- What do we know?
    3. What are the conditions?- Conditions link the unknown to the data in a “problem to find” ( a problem in which you are asked to find a certain piece of data, i.e., value of x.
    4. Can you draw it out?
  2. Developing A Plan
    1. Do you know a related problem?- Try to solve it.
    2. Look at the unknown.
    3. Keep the unknown and change the rest.
    4. Keep the data and change the rest.
    5. Change the unknown and the data.
    6. Do you know a theorem that could be useful.
    7. Could you restate the problem.
    8. Add an auxiliary element.
    9. Can you solve part of the problem?
  3. Carrying Out the Plan
    1. Check each step.
    2. Can you see that each step is correct?
    3. Can you prove it is correct?
  4. Looking back
    1. Can you derive the result differently?
    2. Can you see it at a glance?
    3. Can you use the result with some other?
    4. Can you test the formula?

While Polya formulated these questions to help his students solve mathematical problems, when rephrased they can provide a useful set of questions for solving many different types of problems.

  • Have you defined what constitutes a successful solution?
  • Have you defined the measurements that you will use to judge success?
  • Have you set minimum parameters for a successful solution?
  • Have you determined what additional facts that you need to know?
  • Have you determined how you can find the information?
  • Has someone solved the same problem before?
  • Has someone solved a similar problem?
  • Can you solve the problem by changing some of the facts?
  • Can you solve the problem by changing some of the conditions?
  • Can you draw it out visually?
  • Have you tested the different alternatives?
  • After you have made a decision, have you set up a time in the future to judge how it fares against reality?
  • Is the solution the simplest possible solution?

Of course, all of these questions pale next to the really important question: Who is the greatest Rock ‘n Roll group of all time?

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