Problem Solving – Overview of Polya’s Strategy

Problem solving is a skill everyone wants and which is needed in every aspect of your life, from work to hobby to family life. However, most people study problem solving in a very limited environment: high school mathematics (if at all). What we need is a plan of development for our problem solving skills. Fortunately, there has been some significant work in this area; one person who has worked in this area is George Polya.

Polya created a general algorithm for problem solving which can be used in many different areas. His strategy consists of four phases. Each phase has a particular purpose and goal. His structure is clear enough that it can be adapted and used almost immediately.

Phase I: Define the problem

Defining the problem has the goal of understanding. To understand the problem, there are two activities you go through. Defining the problem is significantly helped by writing your results down, such as in a journal.

The first activity of defining the problem is gathering data. You need to observe the situation. What are the circumstances? What facts do you know? What areas have unknown information? Is there a pattern of events? The more you know about the problem and the circumstances of the problem, the more likely you will be able to solve it.

The second activity is stating the problem. You can go about this several ways. You could state the desired result. You could state what is not part of the desired result. You could state how you want things to change. Regardless of how you state the problem, your statement should be as specific as possible. Details make or break a problem statement. Again, as with gathering data, you should spend time writing down the problem statement so it is as clear as possible.

Phase II: Create a Plan

Understanding the problem is a good start, but our desire is to solve the problem. Now that we know the current situation and the desired result (from our problem statement), we need to create a plan to move from where we are to where we want to be. There are many ways to create a plan, each with their strengths and weaknesses. Two techniques are working backwards and trial and error.

Working backwards is where you start with your goal and ask yourself what you need to directly accomplish your goal. What must you have in order to reach the desired result? Then you take each of those needs and determine what you must have in place to get them. For example, say you want a storage shed in your back yard. In order to have a storage shed, you need the money to buy the shed and a space to put the shed. Now, what must you do to get the money needed? What must you do to get the space ready? Then you ask yourself the same questions about whatever you came up with the previous time. Eventually, you will get a set of actions you can do right now. Working backwards to solve the problem is good when the needs are few in number but difficult to get immediately.

Trial and error is where you start with the current situation. You make a list of actions that you can do right now, and then you pick one action and do it. Maybe it works, maybe it doesn’t. If it doesn’t work, then try something else. Trial and error is very good when you are doing something totally new, where you have little expertise. As long as you can keep trying, this technique will almost always find a solution, eventually.

Phase III: Execute

The greatest plan in the world will accomplish nothing until you act. Action is the way you transition from your current situation to your desired situation. I know any number of people who can tell you what must be done to accomplish something, but they never accomplish anything because they never act. The reasons for not acting are many: procrastination, fear, lack of preparation, desire for security, and others. Whatever is preventing your action, you need to find a way to overcome.

While you are acting, you need to monitor your progress. You must keep in mind where you were and where you want to go. Is this action moving me in the desired direction? Am I making progress? What new information or conditions have become known, and how will that modify my plans? Tracking your results is essential to make sure you reach the desired state.

Phase IV: Reflect

In my opinion, this phase is the most important phase, and it is the one most people skip. Yes, the desired state has value. Otherwise, we would not have desired that result. However, it is in the reflection phase that we perform the uniquely human activity of learning and improving ourselves.

You need to look back on the process you used to solve the problem and ask yourself some questions. From the first phase, ask yourself did you understand the situation correctly? Did you state the problem clearly? Did you specify the results in such a way that you could evaluate your progress? The questions of the second phase are about your planning efforts. Where those efforts successful? Did you plan effectively? Were your estimates valid? When looking at the action phase, did you track your progress effectively? Did you adapt well to changes in the situation? What worked? What did not work? Why?

Wrapping Up

Problem solving is a very valuable skill. If you approach problem solving not just as a way of reaching a goal but also as a tool for self-improvement, you can become a much more valuable member of your world. And you will be more likely to reach your goals as well.