What are problem-solving stages? |

Introduction

Every person must solve problems every day. They solve problems as simple as deciding which television show to watch and as complex as deciding on a marriage partner. In either case, through effective thinking, a satisfactory answer can usually be found. Psychologists believe that there are a number of discrete stages in problem solving. Although they disagree over the exact number of stages required, as well as their exact descriptions and names, the following four stages are often described.

The first stage in problem solving is often called the information-gathering stage. During this stage, considerable information is collected, including the facts surrounding the problem, the goal or outcome desired, the major obstacles preventing a solution, and what information (knowledge) is needed to move toward the solution stage. One key factor in the information-gathering stage is the ability to separate relevant from irrelevant facts. Another key factor is assessing the problem accurately. A clear understanding of the problem is essential to problem solving.

In the second stage of problem solving, potential solutions are generated. Under normal situations, the more solutions generated, the better the chance of solving the problem, since a large number of potential solutions provide a wide choice of alternatives from which to draw. One method used in generating solutions is called trial and error. Here the would-be problem solver tries one approach and then another and perhaps arrives, by chance, at a solution. Although time consuming, exhaustive procedures such as trial and error do eventually result in a solution. Psychologists call any method that guarantees a solution to a problem an algorithm.

Once one or more possible solutions have been generated, it is necessary to choose a specific course of action. The third stage of problem solving, the implementation stage, begins with making a decision. In some problem-solving situations, a number of solutions may be appropriate or suitable. Yet, in comparison, some solutions may be better than others. Some solutions may involve less time and may be easier or more efficient to implement.

The implementation stage involves carrying out the specific plan of action. For many people, this stage of problem solving is difficult. Especially with difficult or complex problems, people are often reluctant to follow through on courses of action. Commitment to follow through is, in many ways, the turning point of problem solving. Intentions and plans of action become meaningless unless there is the commitment to carry them out.

The fourth and final stage of problem solving, in this model, is the evaluation stage. Once the solution or plan of action has been implemented, the person needs to consider whether it has met the original goal (the intended outcome). If not, the person needs to consider other plans of action. In some situations the person may need to retrace his or her steps—beginning again with stage two, the potential solutions stage. Eventually, with perseverance and commitment, workable solutions are usually found.

Another stage worth consideration is incubation. Even though it is considered optional (occurring at some times and not others), incubation can be an important part of problem solving. Incubation refers to a period of time when the person stops thinking about the problem and focuses his or her attention on some other activity. During this time the solution may suddenly appear; it is often said to come “out of the blue.”

Many people have experienced this sudden insight, and history is filled with reports of people who have made remarkable discoveries this way. Such reports point to the fact that it may be advisable to take time off from an unsolved problem. To continue to work ceaselessly on an unsolved problem may only create frustration.

Techniques for Problem Solving

Heuristics
are general strategies for problem solving that lessen the time and mental strain necessary for solving problems. Although much faster than algorithms—problem-solving methods that guarantee a solution—heuristics do not guarantee solutions. They work most of the time, but not always. A number of heuristic approaches exist. In hill climbing, the person moves continually closer to the final goal without ever going backward. In subgoal analysis, a problem is broken down into smaller, more manageable steps.

One often-used heuristic technique combines hill climbing and subgoals. Means-end analysis compares a person’s current position with the desired end (the goal). The idea is to reduce the distance to the goal. By dividing the problem into a number of smaller, more manageable subproblems, a solution may be reached. Another heuristic strategy is called working backward. With this strategy, the search for a solution begins at the goal, or end point, and moves backward to the person’s current position.

Brainstorming is another popular problem-solving technique. Here people are asked to consider all possible solutions while, at the same time, not considering (judging) their immediate value or worth. The advantage of brainstorming is that it increases the diversity of solutions and promotes creative problem solving. So far, in stage two, various methods have been mentioned to generate potential solutions. Yet in real life, problem solving often bogs down, and solutions to problems (especially difficult or complex problems) are hard to find. The importance of perseverance in problem solving cannot be overemphasized.

Another method used in problem solving is called information retrieval. Here the would-be problem solver simply retrieves information from memory that appears to have solved similar problems in the past; however, information retrieval is limited. Many problems do not fit neatly into patterns of the past. Moreover, memory is not always reliable or accurate.

Types of Problems

In a review of problem-solving research published in 1978, J. G. Greeno classified problems into three basic types: problems that involve arrangement, problems that involve inducing structure, and problems that involve transformation.

Arrangement problems require the problem solver to arrange objects in a way that solves the problem. An example is arranging the letters t, g, l, h, and i to spell “light.” Solving such problems often involves much trial and error.

The second type of problem requires a person to discover a pattern or structure that will relate elements of the problems to one another. For example, in solving the problem, “2 is to 4 as 5 is to _____,” the problem solver discovers that 4 is twice as large as 2. Thus, the number needed to solve the problem may be twice as large as 5; that number is 10. Another possible solution is 7, because both the difference between 2 and 4 and that between 5 and 7 is 2.

The third type of problem is one of transformation. Transformation problems differ from the other two types by providing the goal rather than requiring solvers to produce it. Word problems that give the answer and require a person to find the means to the solution are one example.

Examples of Problem Solving

Typically, progress through problem-solving stages is done in a relatively short time. Other situations require more time. Days, weeks, or months may be needed. The following hypothetical examples show how the stages of problem solving can be applied to real-life situations.

Jim has a problem. A friend of his, Bob, recently returned from a year of studying in France. On meeting Jim, Bob was cold and distant; he was not like the person Jim once knew, who was jovial, warm, and happy. Moreover, Bob did not want to associate with Jim. Jim is surprised, hurt, and confused; he does not know what he should do.

First, Jim needs to gather all the information he can. This represents the first stage of problem solving. Jim talks with Bob’s parents, other family members, and students who were with him in France. After collecting this information and separating the relevant facts from the irrelevant ones, Jim notes that his friend’s disposition changed dramatically after his breakup with a girlfriend after a six-month relationship. Jim notes that the presenting problem (Bob being cold and distant) is, under close scrutiny, not the “real” problem. Bob’s present behavior is only a symptom (a consequence) of the real problem, which centers on the breakup of the relationship.

Jim wishes to help his friend. He talks with Bob’s family about what can be done. Together they produce three possible solutions. After comparing the solutions, they decide that the best solution would be for Bob to seek personal counseling. Together they encourage Bob to make an appointment at the local mental health center. If Bob implements this plan of action, he may get the help he needs. If this does not work, the family and Jim will need to reevaluate the situation and try another plan of action.

Susan’s assignment is to write a history paper; however, history has been a difficult subject for her in the past. She needs to do well on this paper to keep her grade-point average high. Susan needs to gather as much information as she can on her topic. She then needs to separate the relevant information from the more trivial or irrelevant. Next she needs to consider potential solutions to ensure a quality paper. She breaks down the paper-writing process into separate tasks (subgoals): preparing an outline, writing the first draft, editing, and rewriting. She executes the plan, doing one task at a time. After the final draft, she asks a classmate to read her paper and to make comments and suggestions. Finally, with a few modifications (revisions), Susan’s paper is ready to be submitted.

Ellen is a high school senior. Her goal is to become a lawyer, but she is unsure of what steps she must take to accomplish this goal. Her first step is to gather all the information she can on how to become a lawyer. She begins by surveying the literature on lawyers in her public library. She also checks with her high school counselor. The counselor gives her some of the specifics: the number of years required for college and law school; the best courses to take as an undergraduate student; the admissions tests necessary for college and law school; the cost of college and law school (including sources of financial aid).

Her next two steps are to devise a plan of action and to implement this plan. She begins by taking a college entrance examination and applying to the college of her choice. After being accepted, she plans her course of studies, keeping in mind the educational requirements of law school. Early in the fall semester of her senior year, she takes the law school admission test and then applies to law school. If she is accepted to law school, her goal of becoming a lawyer is within reach. If she is not accepted, she needs to revise her plan of action or even her goal. She may need to apply to another law school, retake the law school admission test if her score was low, or consider other options: perhaps becoming a paralegal or law assistant or changing fields entirely.

Steve’s car breaks down, and he has it towed to the garage. The mechanic on duty, whether he realizes it or not, applies various stages of problem solving. First of all, he gathers information by asking Steve what happened. Steve states that he was driving down Main Street and suddenly the motor stopped. The mechanic thus focuses on things that can cause the motor to stop suddenly (the potential solutions stage). The most obvious is a problem with the electrical system. After checking various electrical components (the implementation stage), the mechanic notes that the ignition coil is dead. After replacing the coil, the mechanic attempts to start the car (the evaluation stage). The car starts.

Evolution of Problem-Solving Research

Various writers have attempted to analyze the stages in problem solving. One of the first attempts was that of John Dewey
in 1910. Dewey’s five stages utilized the “scientific method” to solve problems systematically through the reasoning process. The five stages are becoming aware of the difficulty; identifying the problem; assembling and classifying data and formulating hypotheses; accepting or rejecting the tentative hypotheses; and formulating conclusions and evaluating them.

Another attempt to analyze the stages of problem solving was that of Graham Wallas in 1926. He proposed that problem solving consisted of the following four steps: preparation, incubation, illumination, and verification. Gyrgy Plya, in 1957, also considered problem solving as involving four stages: understanding the problem, devising a plan, carrying out the plan, and checking the results. In The IDEAL Problem Solver (1984), John Bransford and Barry Stein outline a method of problem solving based on the letters IDEAL: Identify the problem, define the problem, explore possible strategies, act on the strategies, and look at the effects of one’s efforts.

One of the most famous scientific studies of the stages in problem solving was that of Karl Duncker in 1945. In his study, subjects were given a problem and asked to report aloud how their thinking processes were working. After examining the subjects’ responses, Duncker found that problem solving did indeed involve a sequence of stages. Presently, computers are used to solve problems. One of the early attempts to use computers in this way was called the general problem solver (GPS), devised by Allen Newell, J. C. Shaw, and Herbert Simon. Historically, problem solving has not been an area of wide research or interest; however, with increasing interest in cognitive psychology and its emphasis on thinking processes, the study of problem solving seems to have a secure future. Considering the number and scope of the problems that face people from day to day, it seems reasonable to continue—and even expand—the study of problem solving.

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