About the Author: Dr. John Woodward currently serves as the Director of Research and Development for the North Central Association Commission on Schools. He has responsibilities for the Transitions pilot, software development and the graduate credit program for School Improvement Specialist at the University of Nebraska—Lincoln.  He can be contacted by email at 76vette@compuserve.com.

Critical Thinking

Critical thinking occurs when one uses a set of criteria to evaluate a set of things.  For example when people critique something, they are thinking critically about whatever they are evaluating.  They are using a specific set of criteria to evaluate or judge something, whether that something is a performance or an object.  The act of identifying the criteria and using those criteria to evaluate something is the act of thinking critically.  The more sophisticated the critical thinker, the clearer and more specific they will be about the criteria and the rationale for using those criteria.  In the case of problem solving, one must identify the criteria that will be used to determine the quality of a solution.  This can range from "it isn't a solution," to "it solves the problem but not very efficiently," to "it is a very high quality solution."  In short, problem solving cannot occur without critical thinking.  On the other hand, one can think critically when one does a critique, even though there is no problem to solve.

Decision-making occurs when one is making a choice from more than one option.  Decision making usually involves a standard of performance so that a person can determine which is the better or best choice.  To the extent that a problem solver is making a choice from among various solutions, he or she is using the cognitive process of “decision-making” as part of the process of “problem solving.”  However, as we will see below, the problem solving process contains cognition not required in “decision-making.”

Problem Solving

Problem solving begins with someone having a problem, so the first step in problem solving is to define the problem.  (This is not required in decision-making.)  A problem occurs when the existing situation is not what is desired.  For example, if a person had no means of transportation other than walking to work and the distance required is too great, the person has a problem with transportation to work.  (If the person doesn't care about the job, the problem may not be a very important; however, if the person cares about the job a great deal, the problem may be quite important.)  A teenager may state that a car is needed to get to work.  Although that may be true, the teenager has proposed a solution rather than a statement of the problem.

The first step in problem solving is to identify the perceived problem.  The perceived problem may not be the actual problem at all, so the person solving the problem needs to clarify the problem and be able to articulate it to others.

In school, students can have problems at multiple levels at the same time.  For example, if a student is given a task to do and he or she does not know how to do it, the student has a problem.  The solution to the problem lies in finding a way to do the task.  In math class, if the student already knows how to do the assignment, the student has exercises to do, not problems to solve.

The issue is the same if people confront a “real-world” task they don't know how to do.  For example, acquiring food is usually not a problem for most Americans.  However, the task of acquiring food in a strange town can be more of a problem if one is without money.  If the desire to accomplish a task immediately brings to mind an action to accomplish the task, there is no problem.  Thus, to solve a problem means “to search consciously for some action that is appropriate to attain a clearly conceived, but not immediately attainable, aim” (Polya, vol. 1, p. 118).

Further, there are big and small problems.  A problem appears much greater if it is very difficult to find a solution.  Ultimately, no solutions can be found until the problem is identified.  The more clearly a problem can be identified, the easier it is to know what a viable solution might look like.

Step 2:  Generate Possible Solutions

The second step in problem solving involves generating possible solutions based upon changing the existing situation.  Stated differently, people must develop the ability to perform the desired task.

Generally, there are several approaches to problem solving when the person does not know how to do the task.  The person can acquire help from someone else, the person can look at how others have accomplished the task or a similar task, and/or the person can use the information provided in the delineation of the task to determine how to complete the task.  In the first case, it should be noted that a problem solver who gets solutions from other people often does not develop the skills of solving the problem.

Polya (1966) identifies two basic kinds of problems and suggests that the type of problem may suggest the type of solution

Type 1 Problems—Problems to Find. 

Solutions to Type 1 problems typically take the form of constructing, producing, obtaining, or identifying.  For example, consider the task of getting somewhere when the car tire becomes flat.  Solutions might include:

1. Find someone to change and/or repair the flat tire.
2. Find another ride.
3. Find a way to change and/or repair the flat tire yourself.

Solutions to Type 2 problems typically take the form of deciding whether something is true or false and presenting a valid argument that proves the statement is either true or false.  For example, consider the task of proving that you are the best choice of the candidates for a specific job.  Solutions might include that you:

1. Provide evidence that you successfully have done all of the tasks required by the job and that you can do some things that few, if any, other candidates can do.
2. Provide evidence that you can do some of the tasks required by the job at a very high level.
3. Provide evidence that your previous experiences, combined with your ability to transfer learning, have prepared you to do the most important tasks required by the job and some tasks that may not yet be a part of the job.

Step 3:  Evaluate the Possible Solutions

The third step in problem solving is to evaluate each of the possible solutions and select the best solution based upon the task presented.  This means that the criteria for acceptable solutions need to be specified and those criteria need to be applied to each of the alternative solutions.  (Note: Adults are inclined to evaluate a student's solutions based upon adult criteria.  The student's ability to apply a specific set of criteria to the solutions is what should be evaluated.  This is an ideal opportunity to allow a student to rate solutions using multiple sets of criteria and to rank the solutions.)

Step 4:  Implement the Preferred Solution

The fourth step in problem solving is implementing one or more preferred solutions.  If the problem is satisfactorily addressed, a solution has been found and the criteria were effective discriminators of solutions.  In real-world problems, the individual may accept that a solution was found but at the same time not like the solution.  This may happen because important criteria were omitted from the criteria list or because the standard for selecting the best solution gave too much or too little weight to one or more criteria.  This is where emotions and logic collide in human problem-solving activities.  This is where the “soft logic” of problem solving becomes critical.  The goal is to modify the criteria or adjust the standard without rationalizing a predetermined solution.

Keys to Teaching Problem Solving

The following observations and tips provide guidance in how to teach students to be better problem solvers.

1. Students must be provided with opportunities to solve problems, but practice is not enough.  In addition to practice, students must be taught the four steps of problem solving.  More importantly, they must be taught how to do each step in a variety of contexts.
2. When students are provided practice, they must be provided feedback and they must be taught how to evaluate their own problem solving skills.
3. Remember that if the teacher solves the problems and shows the students how to do the problem, the students did not solve the problem.
4. Have students identify the problem steps they do well, the problem steps they don't do well, and their plans for improvement.
5. Homework assignments, projects, and tests must require students to problem solve.  Therefore, teacher lesson plans should address problem solving specifically every day. Problem solving needs to be a frequent focal activity in every subject area.  Students do not have to have massive content knowledge before they can engage in problem solving. For problem solving to be important to students, they must be evaluated on their ability to solve problems.

Better problem solvers tend to do a better job of defining and articulating the problem.  They can articulate for others how the existing state and the desired state differ.  They are willing to spend more time generating solutions, and they tend to generate a greater variety of possible solutions.  (American students tend to seek fast gratification; they pursue what the teacher will find acceptable rather than considering a greater variety of possible solutions.  Therefore, teachers must be careful to direct students away from teacher pleasing and toward the steps of problem solving.)  Better problem solvers learn how to revise the criteria and the standards they use to get better solutions.  Better problem solvers are able to remain objective in evaluating solutions while being realistic about the relative importance of the criteria they use.

The information we teach to students often remains true only for a period of time. The problems we solve for students benefit them only if they face the same problem at some point in the future and they can remember our solution.  When the problem or the context changes, only the generic process of problem solving will be of benefit to students.  We all have many opportunities to solve problems, but we do not get better through practice alone.  Remember that practice does NOT make perfect!  Practice makes permanent.

References

Polya, G.  (1966). Mathematical discovery: On understanding, learning, and teaching problem solving. (2 vols). New York: John Wiley & Sons.