Steps same period of time at 60 mph.
Steps in Problem Solving:
In accomplishing their astonishing feat, the pilot and copilot had to rapidly gain an understanding of the problem they were facing, generate a solution, test that solution, and then evaluate the results. Problem solving typically proceeds through four stages. How well we carry out each of these stages determines our success in solving the problem.
1. Understanding, or Framing, the Problem:
Most of us have had the experience of feeling totally frustrated in our attempts to solve a problem. We may even think that the problem is unsolvable.
Then someone suggests a new way of looking at the problem, and the solution suddenly becomes obvious. How we mentally represent, or frame, a problem can make a huge difference. Many people approach the problem as a distance problem, which is quite natural because the question is stated in terms of distance. They try to compute how far the bird will fly during each segment of its flight between trains A and B, sometimes filling up several pages with increasingly frenzied computations in the process. But suppose you approach the problem by asking not how far the bird will fly but how long it will take the trains to meet.
The crow will have flown the same period of time at 60 mph. Now that you have reframed it as a time problem, the problem becomes much easier to solve. As you can see, our initial understanding of a problem is a key step toward a successful solution. If we frame a problem poorly, we can easily be led into a maze of blind alleys and ineffective solutions. If we frame it optimally, we at least have a chance to generate an effective solution. A knack for framing problems in effective ways that differ from conventional expectations has been called outside-the-box thinking; it is a prized ability in many academic and work environments.
Generating Potential Solutions:
Once we have interpreted the problem, we can begin to formulate potential solutions or explanations. Ideally, we might proceed in the following fashion: 1. Determine which procedures and explanations will be considered. 2. Determine which solutions are consistent with the evidence that has so far been observed. Rule out any solutions that do not fit the evidence.
3. Testing the Solutions:
Consider the possible solutions that remain.
If a solution requires you to choose between specific explanations, ask if there is any test that should give one result if a different explanation is true. If so, evaluate the explanations again in light of the evidence from that test. In essence, this is what scientists do when they design experiments. Let us consider a common difficulty in the process of discovering and applying solutions to problems. You have a 21-cup jug, a 127-cup jug, and a 3- cup jug. Drawing and discarding as much water as you like, how will you measure out exactly 100 cups of water? Try to solve all seven problems in order, and write down your calculations for each one before reading on. Does a common solution emerge? If so, can you specify what it is? Abraham Luchins developed the water jugs problems to demonstrate the manner in which a mental set—the tendency to stick to solutions that have worked in the past—can result in less- effective problem solving.
Luchins found that most people who worked on problems 6 and 7 were blinded by the mental set they had developed by working the first five problems. In contrast, people who had not worked on problems 1 through 5 almost always applied the simple solutions to problems 6 and 7. Studies of mental set show how easy it is to become rigidly fixated on one particular approach that has been successful in the past.
4. Evaluating Results:
The final stage of problem solving is to evaluate the solutions. As we saw in the water jugs problems, even solutions that prove successful may not be the easiest or the best.
Thus, after solving a problem, we should ask ourselves, “Would there have been an easier or more effective way to accomplish the same objective?” This can lead to the development of additional problem-solving principles that may be applicable to future problems.