Thinking and problem solving

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From organizing your movie collection to deciding to buy a house, problem-solving makes up a large part of daily life. Problems can range from small (solving a single math equation on your homework assignment) to very large (planning your future career).

In cognitive psychology, the term problem-solving refers to the mental process that people go through to discover, analyze, and solve problems.1 The steps in the problem process include:

• The discovery of the problem
• The decision to tackle the issue
• Understanding the problem
• Researching the available options
• Taking actions to achieve your goals

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

There are a number of mental processes at work during problem-solving. These include:

• Perceptually recognizing a problem
• Representing the problem in memory
• Considering relevant information that applies to the current problem
• Identify different aspects of the problem
• Labeling and describing the problem

Problem-Solving Strategies

There are a number of different ways that people go about solving a problem. Some of these strategies might be used on their own, but people may also employ a range of approaches to figuring out and fixing a problem.

Algorithms

An algorithm is a step-by-step procedure that will always produce the correct solution. A mathematical formula is a good example of a problem-solving algorithm.

While an algorithm guarantees an accurate answer, it is not always the best approach to problem-solving.

This strategy is not practical for many situations because it can be so time-consuming. For example, if you were trying to figure out all of the possible number combinations to a lock using an algorithm, it would take a very long time.

Heuristics

A heuristic is a mental rule-of-thumb strategy that may or may not work in certain situations. Unlike algorithms, heuristics do not always guarantee a correct solution.

However, using this problem-solving strategy does allow people to simplify complex problems and reduce the total number of possible solutions to a more manageable set.2

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of different solutions and ruling out those that do not work. This approach can be a good option if you have a very limited number of options available.

If there are many different choices, you are better off narrowing down the possible options using another problem-solving technique before attempting trial-and-error.

Insight

In some cases, the solution to a problem can appear as a sudden insight. This can occur because you realize that the problem is actually similar to something that you have dealt with in the past. However, the underlying mental processes that lead to insight happen outside of awareness.

Obstacles in Problem-Solving

Of course, problem-solving is not a flawless process. There are a number of different obstacles that can interfere with our ability to solve a problem quickly and efficiently. Researchers have described a number of these mental obstacles, which include functional fixedness, irrelevant information, and assumptions.

• Assumptions: When dealing with a problem, people often make assumptions about the constraints and obstacles that prevent certain solutions.
• Functional fixedness: This term refers to the tendency to view problems only in their customary manner.3 Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
• Irrelevant or misleading information: When you are trying to solve a problem, it is important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. When a problem is very complex, the easier it is to focus on misleading or irrelevant information.
• Mental set: A mental set is the tendency people have to only use solutions that have worked in the past rather than looking for alternative ideas.4 A mental set can often work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

Define the Problem

The first step on problem solving is to define the problem- don’t skimp here because the problem may NOT be what you think it is! People often define problems in self-centered ways (“It’s about me!”) when the actual problem has little to do with them. For instance, if your partner forgets your birthday, you might think they don’t care as much for you as they once did, when it might really be about the partner being exhausted after working double shifts several days in a row. So, spend some time thinking about the circumstances of the problem before defining it. Also, be willing to re-define the problem as needed! Problems can be slippery things.  A car mechanic has to take information from a customer as well as examining the car, both of which can give erroneous information! So she needs to adapt to new information. If the problem is with another person, that flexibility needs to be double. You’ll find a problem you thought you’d defined is really something else entirely.

One case study: June forgot Henry’s birthday. Henry initially thinks the issue relates to frustration with June’s  unreliability, but if he thinks further, he might decide it is about how birthdays were the one place he felt special while growing up. The missed birthday brought back those feelings, and so he was upset at not at June, but at not feeling special. June’s actions were just a catalyst; it was really about the person’s feelings. Henry can’t expect June to know why birthdays mattered so much to him, unless  he told her the story. And he might not even realize it himself until this situation happens, and he has to think about it!

Any sort of problem becomes easier once it is specified. Once you understand the kinds of math a word problem requires, it is just a matter of going through the steps!

2) Create your Solution, and Apply

Once the problem is specified, then a solution often becomes easier to find. In the Missed Birthday case, once Henry understands that the issue is about him feeling special, then he can talk to June about why events like birthdays matter. He may realize that talking about it makes it less important, and she does not need to change. He might say, “This is silly. I’m not twelve anymore, and I don’t need to be stuck on this anymore.” He might also decide it still matters, and they can then work on  ways for her to do things that say to him, “You are special.” Knowing his feelings, she’s probably motivated to do more than just the birthday too. It might be telling him she appreciates how he contributes to their lives, for instance.  

3) Review

A solution is only step 2. The last step is to check and see how the solution worked. In a math problem, you might check your work. In a problem that involves people, it would involve the person checking in with the other. So to go back to the Missing Birthday case, after a while Henry and June should check back in to see how they each feel about their solution.

Problems in Problem Solving

Most of the time, people solve problems fairly well. They get their needs met, they achieve their goals, and life is good. But there are the times when people don’t solve problems in good or accurate ways. They are not able to achieve their goals. Psychologists have found that there are typical patterns in the way people fail to solve problems correctly or accurately. There are two broad categories of these patterns. They are called Heuristics and Cognitive Biases.

 Heuristics are estimates or educated guesses we use to solve a problem. At the grocery store, for example, you probably estimate how much you’ll spend to buy the items in your buggy. That estimate is a heuristic. When you see two people walking hand in hand and assume they are a couple, you’re using a heuristic. This method works “well enough” much of the time, and it saves a lot of time and energy. But there’s a problem when the heuristic doesn’t work, because then the person doesn’t meet their goals.

Cognitive Biases are tendencies or habits of mind that prevent people from solving a problem correctly. These biases can result in the person misrepresenting or even distorting their own experience or memory! A bias can be seen as like trying to roll a ball on a tilted floor. The ball will always tend to go “down” the tilt. Similarly, a cognitive bias tends to push thinking toward particular conclusions. For instance, a person who is a Democrat will tend to accept democratic ideas, candidates, etc, with less thinking and analysis than if looking at a Republican idea. The Democrat’s thinking is “tilted” toward Democratic ideas. This kind of bias is normal, and is fine as long as it is not so deeply rooted that it prevents the person from meeting their needs or goals.

Problem- a problem is anything that a person sets out to solve. It could involve figuring out the best choice for dinner, or troubleshooting a computer, or a disagreement between people.  A “problem” can be a lot of things!

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Cognitive Biases

• Confirmation bias-is a tendency for people to favor information that accords with their preconceptions regardless of the truth or strength of those claims. As a result, people gather evidence and recall information from memory selectively (Text). So someone who believes that their car is NOT reliable will tend to think about how often it has broken down, how much the breakdowns have cost, and so on, while minimizing or ignoring evidence to the contrary. They will actually be more likely to remember events, like the breakdowns, that confirm their belief and not recall all the times the car started and ran fine. As will all biases, this bias can mean that someone remembers one event over many, perhaps even dozens or hundreds of other events.

• Attitude Polarization- This one describes a process where two people arguing take more extreme positions after the argument than before it. So their positions move apart instead of together.

• Illusory Correlation- this bias refers to seeing relationships between events that don’t exist. One example is the relationship between cold weather and getting sick. Parents for generations have told children to wear their coats in the cold or they would get sick, but that is an illusion. Bacteria and viruses make people sick, not cold weather.

• Overconfidence- the tendency to think we are better than we really are. This bias is good in that it gets us to try new things and attempt challenges. But it can be bad because it can lead to failure too. It is not well known, but the United States had a radar station in Hawaii on December 7, 1941, and that station picked up the Japanese aircraft as they approached Pearl Harbor to begin the surprise attack (MacDonald, n.d., Morgan, 1991). But the warning was ignored when they notified higher command. US commanders did not believe (overconfidence) that the Japanese could mount such an attack. Instead the officer concluded that the aircraft they saw had to be a flight of American planes coming in from the US mainland, even though they detected far more Japanese aircraft than the flight of six American planes they expected (MacDonald, n.d.; Morgan, 1991). Daniel Kahneman, one of the pioneers of this kind of research, has said that overconfidence is one of the most problematic of the biases, probably because it is so common.
  • Students sometimes confuse Overconfidence and Belief Perseveration. One difference is that Overconfidence is about the future; the overconfident person is overly optimistic about their ability to do something in the future. Someone showing Belief Perseveration is just about the belief continuing even in the face of evidence to disprove it.

• Planning Fallacy- a special case of overconfidence, referring to people’s tendency to overestimate how much they can accomplish in a given time.

• Framing- this is a bias in which the context, or lack of context, influences thinking. So a person who hears only that person A broke up with person B may think badly about person A. But with more context, it may be that person A really acted appropriately, such as if person B was abusive. What details and information are included about a situation have significant effects on a person’s thinking about that situation!

• Belief Perseverance- this bias involves a person keeping to a belief even in the face of evidence to the contrary. Sometimes the evidence is overwhelming, but the person still holds to their belief. One example would be the “Flat Earth society” which still believes, based on a literal interpretation of the Bible, that the Earth is flat, despite all the evidence to the contrary.

• Functional Fixedness- a special case of fixation, in which a person is unable to use an object for a purpose other than its “usual” purpose. For example a person needs a pointer, and has a pen. But they don’t use the pen because they can only see using the pen for writing.

• Set Effect- a “Mental Set” is a subconsciously learned set of problem-solving techniques. Set effect is the tendency to use a mental set in solving new problems, and fail to solve the new problems correctly. The phrase, “If all you have is a hammer, everything starts to look like a nail” is an example. Another example- math problems  can look similar, but require different techniques for solution. A person showing the Set Effect would try to solve new problems with the solutions they had learned for previous problems.

Heuristics

• Representativeness- This heuristic involves making judgments about how likely something is to occur. When we encounter something new we tend to rely on what we’ve experienced before to make judgments about the new thing (Clause, 2015). The problem is that while the new thing might be like the previous, it might also be very different, and that can lead to errors in judgment, and bad decisions. Stereotyping can come from representativeness. If someone has an experience with a person of a group, and that person has little experience with that group, then they will tend to use the one experience to describe other members of that group. If that experience is bad, then this can create a negative stereotype.

• Availability- This heuristic is a little complex. It involves us believing that certain events or actions are more common or more likely to occur than they really are. So a person believes that shark attacks are common even though they really are very rare. The process is that a person hears a lot about an event, and because they hear a lot about it, they can more easily remember information about it. That “ease of recall” leads people to believe that the event is more likely or common. So our person might hear news reports about a shark attack and think they happen all the time, when in reality they happen very very rarely. News encourages this kind of thinking, since rare events are what gets the most attention and reporting. As an example, there are many more news reports on airplane crashes than car crashes. Due to availability, people tend to think airplanes are more dangerous, even though cars are far more dangerous. like shark attacks. essentially means making decisions based on what comes to mind first. 

• Gambler’s Fallacy- this heuristic has to do with probability. It is the belief that if a random event has been occurring in a certain way, future events must change.  So the gambler who has been losing at cards takes each loss as indication that the next time she’ll win. Of course, since the events are random, previous events have NO bearing on what happens in the future.

• Anchoring and Adjustment- This heuristic is complicated, but in essence it indicates that the first piece of information a person receives about an object can set a person’s view of that object. So a person who doesn’t know about college tuition is looking at college costs. If they start looking at Harvard, then ODU will look cheap. If they start by looking at TCC, however, then ODU will look expensive! The first piece of information (the “Anchor”) will set the sense of “normal” and people’s thinking will change as a result. After being “anchored” the person will use it as the point from which they consider other events. If the person exposed to Harvard tuition was asked about what was reasonable college tuition, they would “adjust” from Harvard tuition, and give a higher number than the person exposed to ODU tuition instead.

• Escalation of Commitment- involves a person, once making an initial effort or contribution to some effort, making more contributions because of the first one. This is often used to justify increased commitment in wars- a politician will say something about how our sacrifices would be in vain if we withdrew now, and that we should commit more to the war. This heuristic is separate from the validity of the effort in question; the problem comes out of using the initial investment as justification for more investment. The problem is that the new investment may turn out just as badly as the previous one. In those committing this fallacy, now the two commitments both “justify” another, and another, and so on. This can lead to far greater losses than had the person gotten out in the first place.

• Familiarity- this heuristic refers to a person examining a new problem, seeing it as like a previous problem, and using the solution from the previous problem for the new one. The person doesn’t notice the differences between the old and new problems, and it is easy for them to retrieve the old solution.  The new problem, however, may not be enough alike the old one for the solution to work.

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