Introduction
Problem solving is a complex process that involves the use of cognitive skill, prior experiences and their memories, and general knowledge about how the world works. In other words, people use logical thinking and reasoning, memory, and common sense when trying to solve any problem. When psychologists study problem solving, the process is typically divided into three steps: forming a representation of the problem, using a strategy to plan an approach to the problem, and executing the strategy and checking the results. This basic sequence is repeated each time one encounters a problem. First, one must understand the nature of the problem. Second, one thinks of different ways that the problem could be solved, relying on one’s reasoning skills, memory for similar problems, or common sense. Third, one attempts to solve the problem with whatever strategy was formed and, if unsuccessful, forms another strategy and tries again. For example, when a sports team plays a game, first the players study the other team, looking for strengths and weaknesses. Then a game plan is formed and executed. The process can fail at any step: The team members might not really understand their opponents, a bad game plan may be formed, or the implementation of the plan may fail. The inability to complete any step in the process results in an obstacle to solving the problem, whatever that may be.
An old story describes the problem-solving ability of a college student taking a physics examination. One question on the exam asked how a barometer could be used to measure the height of a building (a barometer is a device sensitive to changes in atmospheric pressure). The student responded that a string could be tied to the barometer, and, after the barometer was lowered from the roof of the building, the string could be measured. The professor found this solution unacceptable, since it did not rely on a principle from physics. The student’s second solution was to drop the barometer from the roof, measure the time it took to hit the ground, and then calculate the height of the building using a formula involving gravity. Since this was not the solution for which the professor was looking, the student next suggested that the barometer be placed near the building on a sunny day and the height of the barometer as well as the length of the shadows from the barometer and building be measured. Then the student could develop two ratios and solve for the unknown quantity. While the professor was impressed, the student had not provided the desired solution, and the professor gave the student one more chance. If the student could think of one more method of using the barometer to discover the height of the building, the professor would give full credit. The student finally suggested that they find the owner of the building and say, “If you tell me how tall the building is, I will give you this barometer.”
Three Types of Strategies
Three different types of problem-solving strategies emerge when the issue is studied systematically: means-ends analysis, working backward, and problem solving by analogy. In means-ends analysis, the person examines and compares the solutions desired (sometimes called the goal state) with the methods (the means) available. When making this comparison of where one is to where one wants to be, subgoals are usually generated in such a way that when all the subgoals are completed, the problem is solved. For example, while the ultimate goal in planning a wedding is for two people to be married, there are also several subgoals to be considered, such as a marriage license, a minister, a place to be married, and what to wear. A person using means-ends analysis might develop subgoals to accomplish over time, keeping the ultimate goal in mind. This procedure of identifying the difference between the current state and the ultimate goal state and working to reduce the differences by using subgoals is called difference reduction, a particular form of means-ends analysis.
A second problem-solving strategy is to work backward. When one knows what the solution should be, often one can then work backward from the solution to fill in the means to the end. In solving a maze, for example, one may start working on the maze by beginning at the end line and working backward to the start line. After misplacing something, one often retraces one’s steps, working backward to try to find the item. Another example is the person who wants to have a set amount of money left after paying all the bills. Working the problem in the forward direction (that is, paying the bills and seeing what is left over) may not result in the desired goal; starting with the goal first, however, can achieve the overall desired solution.
It should be noted that the working-backward strategy works only when the solution (or goal state) is known or believed to be known. When it is unknown, working backward cannot work. That is the case with a mechanic who is trying to fix a car when the exact cause of the malfunction is unknown. Although the desired solution is known (a working car), tracing the path backward does not work. In this type of situation, the mechanic is likely to try a means-ends strategy (for example, testing each major system of the car) or to use the next strategy, problem solving by analogy.
Solving problems by using analogies relies on the use of memories from prior problem-solving situations and the application of this information in solving a new problem. Often the initial representation of the problem may trigger memories for similar problems solved in the past. At other times, a person may actively search in memory for analogous or similar situations, then retrieve and apply such information.
The American educational system is largely based on the strategy of problem solving by analogy. Children are taught the facts, figures, and skills that are analogous to the facts, figures, and skills necessary in later life. Education is meant to be the prior experience, to be used in solving later problems. Homework is based on the idea of problem solving by analogy—providing early experiences that may be applicable to later problems (such as on a test).
Functional Fixedness
The three general steps in the problem-solving process are problem representation, strategy formation, and execution of the strategy. Many obstacles in solving everyday problems are particularly sensitive to the role of problem representation. Two examples of common obstacles in problem solving are functional fixedness and mental set effects.
Functional fixedness is the idea that people often focus on the given function of an object while neglecting other potentially novel uses. Norman R. F. Maier in 1931 demonstrated functional fixedness in his now-classic two-string problem. In this problem, two strings hang from the ceiling of a room, too far apart for a person to reach both at once. Yet the strings are long enough to reach one another and be tied. The problem is to tie the strings together. The only objects available to the person are a chair, some paper, and a pair of pliers. Maier found that most people he tested exhibited functional fixedness (that is, they did not use the items in the room in novel ways to solve the problem). Those that did solve the problem realized they needed to attach a weight (the pliers) to one string and swing the string like a pendulum to tie the strings together, thus avoiding functional fixedness.
Another classic example of functional fixedness can be found in Karl Duncker’s 1945 candle-and-box problem. In this problem, people are presented with a candle, a box of tacks, and a book of matches; the problem is to attach the candle to the wall so that the candle can burn in its upright, proper position. People who possess functional fixedness are unable to see the box holding the tacks as a candle holder, emptied and attached to the wall, with the candle attached to the top of the box. Whenever one uses a knife or a dime as a screwdriver, one is showing a lack of functional fixedness, that is, using an object in a manner for which it was not intended.
Mental Set Effects
A second general obstacle in problem solving is called a mental set. A mental set is a conceptual block that prevents the appearance of an appropriate problem solution. Set effects most often occur because of sheer repetition of information (therefore, one does not search for alternative solutions) or because of a preconceived notion about the problem. One example of the mental set effect comes from Abraham Luchins’s water-jug problem. In this problem, people were given three water jugs—A, B, and C—and the task was to manipulate the water in the jugs to obtain a desired quantity. For example, jug A holds 21 cups of water, jug B holds 127 cups, and jug C holds 3 cups; the desired amount is exactly 100 cups. The desired amount can be reached by filling B once, pouring once into jug A, then pouring twice into jug C. This answer can be expressed as “B − A − 2C” (or “127 − 21 − 3 − 3 = 100”). Luchins gave people a series of problems, all of which could be solved by this formula; however, he would occasionally include a problem that could also be solved by a simpler formula, such as A − C. People continued to use the more complex formula. Luchins thought that people get into a rut or mental set, and when the set yields positive results, they do not bother to exert effort to change (even when a simpler method exists).
Nine-Dot Problem
A different example of the importance of problem representation is found with the nine-dot problem. In the nine-dot problem, three rows of three dots each must be connected by four straight lines, with the restriction that the pen or pencil cannot be lifted from the page. The natural box shape that the dots form presents an obstacle similar to mental set: People cannot solve the problem until they realize that the lines must go outside the perceived square before the problem can be solved.
Implications for Psychological Study
The formal study of problem solving is almost as old as the field of psychology itself. As early as 1898, Edward L. Thorndike
studied the problem-solving ability of cats trying to escape from a puzzle box. This box was designed with levers, pulleys, and latches so that when the cat made a particular response inside, the door to the box would open and the cat could escape. Thorndike found that the cats could remember the escape sequence and that each time the cat was placed in the box, it escaped more quickly. He considered problem-solving ability as evidence of learning and called it the stamping in of behavior. Wolfgang Köhler
in 1925 studied chimpanzees and found that they could experience a flash of insight (sometimes called the “aha!” phenomenon) in solving a problem, just as humans do. In the 1930s and 1940s, Edward C. Tolman
studied the problem-solving abilities of rats in different types of mazes and found them to be very good at navigating a maze.
Problem solving is an exciting area in psychology because it is a basic, universal characteristic of all humans. Everyone faces a number of problems each day. To understand how people solve problems is, to a large degree, to understand basic human behavior, the goal of every psychologist. Problem-solving strategies and obstacles lie at the foundation of understanding humankind.
The future is bright for those interested in the study of problem solving. The increasing use of computer technology has advanced the field considerably. Computer simulations are used in an attempt to emulate (mimic) how humans solve problems. In this approach, the human is most important. In other words, computer simulations are valuable in helping to understand why people do the things they do. Artificial intelligence, on the other hand, uses computer technology to seek the best possible and most efficient solutions to problems—not necessarily mimicking the processes of humans. In the study of artificial intelligence, the problem is the most important aspect. Regardless of the specific area of study, the various strategies and obstacles observed by psychologists make intriguing work, and they lie at the very heart of what humans continually do: solve problems.
Bibliography
Anderson, John R. Cognitive Psychology and Its Implications. 7th ed. New York: Worth, 2010. Print.
Eysenck, Michael W., and Mark T. Keane. Cognitive Psychology: A Student’s Handbook. 6th ed. Hove: Psychology, 2010. Print.
Fogler, H. Scott, and Steven E. LeBlanc. Strategies for Creative Problem Solving. 3rd ed. Upper Saddle River: Prentice, 2014. Print.
Kalat, James W. Introduction to Psychology. 10th ed. Belmont: Wadsworth, 2013. Print.
Mayer, R. E. Thinking, Problem Solving, Cognition. 3rd ed. New York: Worth, 2007. Print.
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