Problem Solving Techniques

Bill W. Tillery
Arizona State University - Department of Physics and Astronomy


 Problem Solving

The activity we call "problem solving" is an attempt to find a solution to an uncertain or difficult situation. In academic settings, the problem-solving activity usually involves logic or science problems, and tests to enter graduate college, medical school, or law school tend to be made up of these kinds of problems. You need to have both sharp reading and reasoning skills in interpreting such questions and answering them, and the purpose of this link is to provide some help with these skills.

Before starting, you should understand there is no "magic bullet" for learning good thinking skills in reading and problem solving. You will need to work hard to develop these skills, and reading about problem solving is not enough. Learning to swim requires you to do more than just read about swimming; you must get in the water and practice the fundamentals of swimming. Likewise, learning to solve problems requires practice with the basics of analysis and comprehension, and you must accept the responsibility for focusing on problems and practicing the skills. For example, did you focus on the previous paragraph to learn that reading skills are very important in successful problem solving? Or were you thinking about something else as your eyes "read the words"? If so, you might consider sharpening your reading skills by paying attention to what you are reading. Learn to catch yourself if your mind wanders and force yourself to reread the "missed" material. Before long, you will find you wander less and less as you develop habits of careful reading and patient thinking.

Sharp reading skills help you to comprehend a problem-solving situation, and sharp thinking skills help you to develop some problem-solving strategies. One way to introduce some thinking skills is to try some sample problems, such as those found in the following Creature Cards* links.


 Sample Problem Solving Questions

Click on the following link and then look at the information provided in the first two rows. After you do this, answer the problem-solving question in the third row of the card.

Click here to link to the Gligs problem-solving card.

What is a Glig? As you probably were able to identify, a Glig is an open figure. All the figures in the last line are Gligs except the second and third one from the left. If you were successful in solving this problem, how did you arrive at your answer? Was it a hunch? Did you answer "Yes" or "No" if each figure was a Glig, or did you just identify those you believe to be Gligs without thinking about it? The point of these questions is to get you to think about your style of thinking. We will return to the subject of your thinking after a few more Creature Puzzles, so try to review and then remember how you arrived at each solution.

Click on the following links to see other problem-solving cards.

Wibbles

Snorps

Mellinarks


 Learning to Problem Solve

 What did you learn about your thinking so far? The difficulty of the above three problems seems to depend not only on the number of defining attributes, but on the amount of irrelevant information as well. A Wibble, for example, has but one identifying attribute – a tail. A Snorp, on the other hand, must have spots as well as a tail. A Mellinark must have a tail, a black dot, and spots. More attributes alone do not make the problem more difficult, as you will see in the following Mokes link.

Mokes


 Developing Your Reasoning Ability and Problem Solving Skills

Reasoning ability seems to be more important than memory in most problem-solving activities. Often in academic settings memory is very important and the student with a good memory may be able to succeed with little thinking. In a problem-solving situation, however, the student who has grown accustomed to using memory only will probably become frustrated because the steps in his or her thinking have no relationship to one another.

It might be helpful to realize there are at least two ways of thinking. One way involves dealing with information without conscious, analytic thought. When you are performing the physical act of swimming, for example, you do not consider all the separate things you must do in order to swim. You may have solved some of the "Creature" puzzles above in the same way, by recognizing the important attribute without having to consider all the individual ones. This thinking may happen so fast that you were completely unaware of it happening. Most of the time this is the natural way to proceed and it is not necessary to analyze thinking. However, if you wish to improve your thinking skills, it becomes necessary to isolate the steps in your thinking and to deal with them one at a time. Try to analyze your thinking as you reason why only the first and third drawings above are Mokes.

Thinking can involve dealing with many components at the same time, or dealing with the components of thinking one at a time in a sequence. Both ways of thinking are probably not possible to do at the same time, but it is possible to switch back and forth between the two. It is important to realize these two ways of thinking do exist, and to use the sequential mode to your advantage. You should employ both modes of thought in problem-solving situations. One way to make sure you are using the sequence mode is to "talk to yourself" or "think aloud" as you analyze the situation of a difficult problem.


 Some Final Observations

Finally, observations of the actions and characteristics of good problem solvers lead to some generalizations that may be helpful. Here are some of those generalizations:

  1. One characteristic of good problem solvers is the tendency to fully understand a problem before doing anything else. This may mean reading parts or the entire problem several times, then reading it again to be completely sure they understand all of the parts and relationships of the problem. Yes, the use of good reading skills is very much a part of successful problem solving. A lack of success in problem solving is often a result of not understanding exactly what the problem is stating.

  2. In attempting to understand a problem, good problem solvers tend to be physically active rather than silently reading to themselves. For example, the good problem solvers might make a sketch as they read the problem in an attempt to better understand the situation being described. Other active actions include circling parts of the problem, making diagrams, and talking to themselves about their understanding of the problem. Talking to themselves or thinking aloud tends to cause problem solvers to be more careful as they analyze the problem.

  3. Once a problem is understood, part of the physical activity of good problem solvers involves the breaking of a complex problem into a series of subproblems—smaller steps that can be dealt with one after another. This is sometimes done by circling parts of the problem, drawing question marks, and thinking out loud. When possible, good problem solvers deal with problem situations by breaking the problem into parts and finding the solution in small, careful steps.

  4. While breaking a problem into smaller parts, the good problem solvers are continuously checking and rechecking the accuracy of each step. The poor problem solvers, on the other hand, tend to jump to conclusions, guessing the answer to one or more of the substeps, sometimes with hasty and illogical reasoning. They have not recognized the need to work each step precisely and accurately from the beginning to the end.

  5. The breaking of a complex problem into smaller steps and the checking and rechecking of the accuracy of each step require an understanding that the steps can be done, and that careful analysis will result in the correct answer. This is a matter of experience, but also requires confidence and an attitude that all problems can be solved by analysis. Confidence and attitude are critically important, and problem solving should be approached with a spirit of adventure rather than something to be dutifully and methodically done.

  6. Just like the acquisition and sharpening of any other skill, practice makes perfect. The more problems you solve, the better you will become at problem solving. All of this involves self-discipline, personal involvement, exploring your own thinking, and taking responsibility for your own learning.

*Creature Cards, Webster Division, McGraw-Hill Book Company, 1974.  
 
Return to the top of this page