Problem-solving stages

Problem-solving stages are the steps through which successful solutions to problems are obtained. Since problems are an inevitable and pervasive part of life, being successful at problem-solving is an important asset. Psychologists have examined the steps involved in various forms of problem-solving from multiple perspectives.

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 experts 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 their 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 . 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, andi 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.

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.

Another important area of research into problem-solving stages involves efforts to use computers to solve problems. One notable early example was the general problem solver (GPS) program devised by Allen Newell, J. C. Shaw, and Herbert Simon in 1957. While early problem-solving programs tended to quite limited in practice, the theory behind them proved influential in computer science and other fields. Conceptual models of problem-solving stages became particularly important in artificial intelligence (AI) research, laying a foundation for many of the breakthroughs of the AI boom of the late 2010s and early 2020s.

Bibliography

Andriole, Stephen J. Handbook of Problem Solving. Petrocelli, 1983.

Benjamin, Ludy T., J. Roy Hopkins, and Jack R. Nation. Psychology. 3rd ed., Macmillan, 1994.

Bransford, John, and Barry S. Stein. The IDEAL Problem Solver. 2nd ed., Freeman, 2002.

Cherry, Kendra. "Overview of the Problem-Solving Mental Process." Verywell Mind, 18 Apr. 2022, www.verywellmind.com/what-is-problem-solving-2795485. Accessed 12 Dec. 2024.

Coon, Dennis, and John O. Mitterer. Psychology: A Journey. Wadsworth, 2014.

Gerrig, Richard J. Psychology and Life. Pearson, 2013.

Hayes, John R. The Complete Problem Solver. 2nd ed., Lawrence Erlbaum, 1989.

Huffman, Karen, et al. Psychology in Action. 10th ed., Wiley, 2012.

Kahane, Adam. Solving Tough Problems: An Open Way of Talking, Listening, and Creating New Realities. Berrett-Koehler, 2007.

Puccio, Gerard J. Creativity Rising: Creative Thinking and Creative Problem Solving in the Twenty-First Century. ICSC, 2012.

Robinson-Riegler, Gregory, and Bridget Robinson-Riegler. Cognitive Psychology: Applying the Science of the Mind. Allyn, 2012.