Problem-solving is the active effort people make to achieve a goal that cannot be easily attained.
Three common categories of problems include inducing structure, arranging, and transformation.
Some problems involve finding relationships between elements.
Example: “Pineapple is to fruit as cabbage is to ___.” In this analogy problem, the answer, “vegetable,” requires people to figure out the relationship between “pineapple” and “fruit” and apply a similar relationship to “cabbage.”
Other problems involve arranging elements in a way that fulfills certain criteria.
Example: The answer to the problem “Arrange the letters in LEPAP to make the name of a fruit” is “APPLE.”
Other problems involve making a series of changes to achieve a specific goal, a process called transformation.
Example: A familiar riddle describes a situation in which a man has to take his fox, his chicken, and his tub of grain across a river in a boat. The boat will hold only him and two of his possessions at any one time. He can’t leave the fox and the chicken on the riverbank by themselves because the fox will eat the chicken, and he can’t leave the chicken with the grain because the chicken will eat the grain. He also can’t take the fox and the chicken in the boat together because the fox will eat the chicken when he’s occupied with rowing the boat. The same goes for the chicken and the grain. How will he get all three across? First he takes the fox and the grain across. He leaves the fox on the opposite bank and takes the grain back with him. He then leaves the grain on the bank and takes the chicken across. He leaves the chicken on the opposite bank and takes the fox back with him to retrieve the grain.
There are many strategies for solving problems, included trial and error, algorithms, deductive reasoning, inductive reasoning, heuristics, dialectical reasoning, forming subgoals, using similar problems, and changing the way the problem is represented.
Trial and error involves trying out different solutions until one works. This type of strategy is practical only when the number of possible solutions is relatively small.
Example: It’s dark, and a man is trying to figure out which button on the dashboard of his newly rented car switches on the headlights. He might press all the available buttons until he finds the right one.
Algorithms are step-by-step procedures that are guaranteed to achieve a particular goal.
Example: A chocolate chip cookie recipe is an algorithm for baking chocolate chip cookies.
Deductive reasoning is the process by which a particular conclusion is drawn from a set of general premises or statements. The conclusion has to be true if the premises are true.
Example: If the premises “All birds have wings” and “A penguin is a bird” are true, then the conclusion “A penguin has wings” must also be true.
Inductive reasoning is the process by which a general conclusion is drawn from examples. In this case, the conclusion is likely, but not guaranteed, to be true.
Example: Given the premise “All the butterflies Fred has ever seen have wingspans of less than two inches,” Fred might conclude, “All butterflies have wingspans of less than two inches.”
A heuristic is a general rule of thumb that may lead to a correct solution but doesn’t guarantee one.
Example: A useful heuristic for finishing a timed exam might be “Do the easy questions first.”
Dialectical reasoning is the process of going back and forth between opposing points of view in order to come up with a satisfactory solution.
Example: A student might use dialectical reasoning when she considers the pros and cons of choosing psychology as her college major.
Forming subgoals involves coming up with intermediate steps to solve a problem. This is a way of simplifying a problem.
Example: Susan is asked to solve the analogy problem “Prison is to inmate as hospital is to ____.” Susan’s subgoal could be to figure out the relationship between “prison” and “inmate.” Once she achieves this subgoal, she can easily find the answer, “patient.”
A problem is often easier to solve if it can be compared to a similar problem.
Example: Mike has to give his two-year-old daughter a bath, but she resists because she is afraid of the water. Mike remembers that he convinced her to get in the kiddie pool last week by letting her take her large plastic dinosaur toy with her for “protection.” He gives her the toy again, and she agrees to get in the tub.
A problem may be easier to solve if it is represented in a different form.
Example: If hundreds of guests at a banquet are trying to figure out where they are supposed to sit, written instructions might not be easy to follow. A seating chart, however, makes the seating arrangement easy to understand.
Researchers have described many obstacles that prevent people from solving problems effectively. These obstacles include irrelevant information, functional fixedness, mental set, and making assumptions.
Focusing on irrelevant information hinders problem-solving.
Example: A familiar children’s riddle goes like this: As I was going to St. Ives, I met a man with seven wives. Every wife had seven sacks, every sack had seven cats, every cat had seven kits. How many were going to St. Ives? People may think of this as a complicated math problem, but in reality, only one person, the “I,” is headed to St. Ives. The seven wives and their respective entourages are headed the other way.
Functional fixedness is the tendency to think only of an object’s most common use in solving a problem.
Example: Rachel’s car breaks down while she is driving through the desert. She is terribly thirsty. She finds several soda bottles in the trunk but no bottle opener. She doesn’t think of using the car key to open the bottles because of functional fixedness.
A mental set is a tendency to use only those solutions that have worked in the past.
Example: When Matt’s flashlight hasn’t worked in the past, he’s just shaken it to get it to work again. One day when it doesn’t come on, he shakes it, but it still doesn’t work. He would be subject to mental set if he keeps shaking it without checking whether it needs new batteries.
Making assumptions about constraints that don’t exist prevent people from solving problems effectively.
Example: Another familiar riddle goes as follows: A father and his son are driving on a highway and get into a terrible accident. The father dies, and the boy is rushed to the hospital with major injuries. When he gets to the hospital, a surgeon rushes in to help the boy but stops and exclaims, “I can’t operate on this boy—he’s my son!” How can this be? If people have a hard time answering, they may be making a false assumption. The surgeon is the boy’s mother.