7.2 Problem Solving

THE BIG DILEMMA

On Day 3 at the hospital, a team of doctors arrived at Dr. Jill’s bedside to discuss the possibility of performing surgery. One of the doctors, an expert in AVMs (the blood vessel abnormality responsible for her stroke), informed Dr. Jill that there was a blood clot as big as a “golf ball” on the left side of her brain. Both the clot and the remainder of the AVM needed to be extracted; otherwise, she risked suffering another stroke (Taylor, 2006).

Dr. Jill did not understand much of what she heard from the doctors because her language-processing neurons were, as she puts it, “swimming in a pool of blood” (Taylor, 2006, p. 91). But she did catch the part about slicing open her skull, a prospect that she found quite unappealing. “Any self-respecting neuroanatomist would never allow anyone to cut their head open!” she writes. Dr. Jill had good reason to worry, for brain surgery is not without risks. When surgeons go into the brain to fix one problem, there is always the possibility that they will unintentionally create a new one. Dr. Jill worried that she might emerge from the operating room unable to speak or see. And there were other potential complications of brain surgery, including infections, internal bleeding, and coma (Medline Plus, 2011). No one could be certain of the operation’s outcome.

Dr. Jill had a very big problem on her hands and a very important decision to make. The next two sections of this chapter are devoted to problem solving and decision making, two distinct yet tightly interwoven topics. We will explore many types of problems, from life-changing dilemmas to minor hassles, and how we arrive at decisions. Read carefully: The knowledge we are about to impart may be very useful to you. Understanding problems and how they are solved can make life’s difficulties a lot more manageable.

What’s the Problem?

Have you ever considered the multitude of problems you encounter and solve every day? Problems crop up when something gets in the way of a goal, like a computer crashing when you are racing to finish a project or a tricky scheduling situation at work. Problems range from the mundane (My profile picture on Facebook is old.) to the potentially overwhelming (I have a life-threatening brain bleed.). In psychology, problem solving refers to the variety of approaches that can be used to achieve a goal.

© Randy Glasbergen/glasbergen.com

Components of Problem Solving

Problem solving has intrigued psychologists for generations. Newell, Shaw, and Simon (1958) developed an information-processing approach to solving problems, a model suggesting that problem solving proceeds from an initial state (the situation at the start of a problem) to a goal state (the situation when the problem is solved; Matlin, 2009). Think about how this model applies to Dr. Jill. Her initial state included two very big problems: a massive blood clot and a troublesome clump of blood vessels in the left hemisphere of her brain. The goal state was maximizing her health, both physically and cognitively.

Another crucial component of problem solving is recognizing obstacles that block the path to a solution (Matlin, 2009). Think about a problem you want to solve and try to identify the initial state, the goal state, and the obstacles in your way. If your initial state is unfinished homework and your goal state is the completion of your homework in a timely manner, the obstacles might include the competing duties of household chores or something more internal, like sleepiness or lack of motivation.

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Steps to Solving Problems

The first step in problem solving is understanding the problem (see Infographic 7.2). If you can’t identify or label a problem, then solving it is going to be difficult. Once you grasp the problem, you must choose one of many available approaches or strategies to tackle it. Which one you settle on—and the speed, accuracy, and success of your solution—will depend on many factors, including your fund of knowledge, your organization of knowledge, and the amount of time spent assessing the problem (Ericsson, 2003; Goldstein, 2011).

Problems are a constant part of life, but they are much easier to manage if we understand the strategies available to solve them. The aim of the upcoming discussion is to provide you with several approaches for solving problems, while also examining the various factors that come into play during the process.

Approaches to Problem Solving

Trial and Error

LO 5     Explain how trial and error and algorithms can be used to solve problems.

One common approach to problem solving is trial and error, the process of finding a solution through a series of attempts. Mistakes will likely be made along the way, but attempts that don’t work are simply eliminated. Let’s say you have a HUGE set of keys and you have to unlock a door you don’t use very often. With the trial-and-error approach, you would insert keys, one by one, hoping the correct key is on the ring. By the process of elimination, you would rule out each key before you tried the next one on your key ring.

Trial and error is only useful in certain circumstances. This approach should not be used if the stakes are extremely high, particularly in situations where a potentially wrong selection would be harmful or life-threatening. Imagine, for example, if Dr. Jill’s physicians had used trial and error to figure out what procedure she needed. Let’s try this surgery first: If it doesn’t work, we’ll try a different one next week, and then another the following week. When people’s health and well-being are on the line, trial and error is clearly not the way to go.

64,000 Combos Forgot your lock combination? Trying to figure it out by trial and error is not an effective strategy, as there are 64,000 possible solutions. Better buy a new lock.
Pixel Embargo/shutterstock.com

Nor is this approach recommended for problems with too many possible solutions. If your keychain has 1,000 keys, you probably would not want to spend your time randomly selecting keys until one fits (potentially trying the same key more than once). Trial and error is somewhat of a gamble because there is no guarantee it will lead to a solution. By the way, computer hackers may use this approach to get your password and gain uninvited access to your digital world. More about this to come.

Algorithms

If you’re looking for a problem-solving approach that is more of a sure thing, an algorithm is probably your best bet. Algorithms (al-gə-ri-thəmz) use formulas or sets of rules that provide solutions to problems. Unlike trial and error, algorithms ensure a solution, as long as you follow all the steps. Suppose you are trying to figure out a 20% tip for a server at a restaurant. Here’s an easy algorithm to calculate your tip—take the total amount of your bill, move the decimal to the left one space, and multiply by 2. This will result in 20% of your bill. This simple algorithm provides a guaranteed “correct” solution to the problem.

As reliable as algorithms may be, they are not always practical. If you don’t know the algorithm’s formula, you obviously cannot use it, and sometimes the steps may require too much time. Let’s return to our example of computer hacking. After losing patience with trial and error, the hacker designs an algorithm that generates a series of possible passwords made up of letters, numbers, and symbols. Because algorithms guarantee solutions, the hacker eventually will generate your password. But the question is: Will it happen in this century? If you have chosen your password wisely, the algorithm may not work within a time frame that the hacker is willing—or able—to wait. For example, simply changing your eight-letter password by one character (lowercase to uppercase) and adding an * can increase a hacker’s processing time from 2.4 days to 2.1 centuries (Mahmood, 2010). “Ha ha, hacker!”

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Heuristics

LO 6     Identify different types of heuristics used to solve problems.

If using an algorithm is not an option, which is often the case with everyday problems, we can turn to heuristics ( ). A heuristic is a problem-solving approach that employs a “rule of thumb” or broad application of a strategy. Although heuristics are not always reliable in their results, they do help us identify and evaluate possible solutions to our problems. Let’s say you are cooking rice, but the instructions are unavailable. One good rule of thumb is to use 2 cups of water for every cup of rice. Another heuristic is to put the rice in the pot and add water until it is one thumb-knuckle above the rice. But unlike algorithms, which use formulas and sets of rules, there is no guarantee a heuristic will yield a correct solution. The advantage of heuristics is that they allow you to shrink the pool of possible solutions to a size that is manageable (given all the varieties of rice, there are many different ways to cook it). Heuristics provide shortcuts, allowing you to ignore the pool of solutions you know will not work and move on to solutions more likely to be successful. But you might need to use trial and error to choose the best solution from that smaller pool of possibilities. A hacker might use a heuristic that combines a commonly used password (123456, password, football) and then add something from the domain itself. For example, if the hacker is trying to break into a Sony PlayStation account, her heuristic might be to try a variety of commonly used passwords and add “PS” at the end (123456PS, passwordPS, footballPS). She would then use trial and error until she breaks into the account. Most problems in life do not come with ready-made algorithms for reaching a correct solution, so we tend to fall back on heuristics.

Heuristics come in a variety of forms. One commonly used heuristic involves creating subgoals or subproblems. In the days following her stroke, Dr. Jill had a great deal of trouble moving her body. One of her main challenges was sitting up, but she was able to solve this problem by parsing the laborious process into smaller, more manageable steps. “By breaking the effort of sitting up into the smaller steps of rocking and then rolling upward, I found regular success along the way” (Taylor, 2006, p. 93). When writing your last term paper, did you break it into shorter more achievable parts? If so, you were using a type of heuristic that instructors often recommend to students.

Another frequently used heuristic is means–ends analysis. With this heuristic, you try to figure out how to decrease the distance between your goal and your current point in the process. You determine how to reach your goal (the means), which allows you to solve the problem (the end). Using means–ends analysis may involve breaking a problem into subproblems that can be solved independently. The challenge is to decide which subproblem to address first. If you are struggling with your term paper, you must first identify the problem (finding appropriate support for your thesis) and then divide the problem into two subproblems: (1) identifying an appropriate database to search for articles in the field; and (2) finding a library where you can obtain and read the articles.

Insight

Another way of finding a solution insight, which represents an understanding that occurs in a sudden stroke of clarity (that oh-so-satisfying “aha!” moment). It can stem from experience solving previous problems, or it can be totally new. Insight often comes as a pleasant surprise because we are not aware of the mental “work” that occurs to achieve it.

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I Want Bananas In a classic study, Wolfgang Köhler provided chimpanzees with some out-of-reach bananas and materials that could potentially be used to fetch them. Resourceful chimps they were, building towers of crates and poking at the fruit with sticks. Rather than using trial and error to solve the problem, they seemed to rely on insight.
Wolfgang Köhler Papers/American Philosophical Society

Insight happens so suddenly that we sometimes say to ourselves: Why did it take me so long to figure that out? The answer seems so obvious now. Theories suggest that, without our conscious awareness, our minds are busy reorganizing the way the problem is represented, and this allows us suddenly and inexplicably to see things in a new light. Sometimes stepping away from a problem for a short time allows the solution to “suddenly appear” (Sio & Ormerod, 2009). Various areas of the brain seem to be involved in this cognitive work. Research suggests that activity in the frontal and temporal lobes immediately precedes the “aha!” moment (Kounios & Beeman, 2009).

Wolfgang Köhler, a Gestalt psychologist, made some remarkable discoveries on insight in chimpanzees. As early as 1913, he created various problems for the chimps to solve. For example, Köhler put bananas just out of the chimps’ reach, supplied them with various “tools” (crates, sticks, and so forth), and watched how they went about getting the bananas. The chimps were very clever; they stacked crates, used sticks, and managed to retrieve the bananas using what Köhler hypothesized was intelligence and insight (Köhler, 1925).

Gestalt psychologists believed that humans and animals solve problems through perception and cognition—by creating mental representations of objects and their relationships (Whitman, 2011). As the chimp faces the “how do I get that banana” problem, its mind is reorganizing the relative positions of the objects to reach a solution. We humans manipulate pictures in our minds in a similar fashion, and it requires no conscious effort. Ah, the beauty of insight.

As you probably know from personal experience, great ideas do not always materialize when we need them. How might we increase the chances of having bright insights? When struggling with a problem, sometimes the best thing to do is let loose and laugh.

from the pages of SCIENTIFIC AMERICAN

Laughter Leads to Insight

Happy moods facilitate aha! moments

Stumped by a crossword puzzle? Try taking a break to watch a funny TV show. Recent research shows that people in a lighthearted mood more often have eureka moments of sudden inspiration.

Karuna Subramaniam, then at Northwestern University, and her colleagues found that boosting the mood of volunteers increased their likelihood of having an aha! moment that helped solve a word association puzzle. Those who watched a Robin Williams comedy special did measurably better at the task using insight than those who watched a quantum electronics talk or a scary movie. The games, in which players must find a word that connects three seemingly unrelated words, have been used for decades to demonstrate creative problem solving.

In the brain, sudden insight is accompanied by increased activity in the brain’s anterior cingulate cortex (ACC) prior to solving each problem. The region is involved in regulating attention; in problem solving, it seems to work in conjunction with other brain areas either to stay focused on a particular strategy or to switch to a new one. Subramaniam found with functional MRI that people in a positive mood had more ACC activity going in to the task, which probably helped prepare the brain to find novel solutions. Participants who watched anxiety-producing movies such as The Shining, however, showed less activity in the ACC and less creativity in solving the puzzles. Elizabeth King Humphrey. Reproduced with permission. Copyright © 2011 Scientific American, a division of Nature America, Inc. All rights reserved.

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INFOGRAPHIC 7.2: Problem Solving

Problem solving involves figuring out how to achieve a goal. Once you understand a problem, you can identify an approach to solving it. A successful approach will help you manage obstacles that come from the problem itself, such as a rigid deadline for an essay you’re struggling to write. But sometimes the way we think about a problem can itself be a barrier, preventing us from identifying available approaches.

Credits: Ship ropes with knot, Shutterstock; Collection set of vertical ropes with knots, Shutterstock; Collection of various ropes, Shutterstock; Bushes, Shutterstock

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Barriers to Problem Solving

But problems are not always a laughing matter. As you may have noticed in your own life, there are many barriers to problem solving (Infographic 7.2). You might be trying to get your car out of the driveway, but the wheels keep slipping in the snow. Or perhaps you are trying to calculate a tip for your server, but you can’t concentrate because of the noise in the room. These types of problems are not always easily solved, sometimes due to common barriers.

One barrier is functional fixedness, which occurs when we can only imagine using familiar objects in their normal or usual way. This fixation can hinder problem solving, because it stops us from being able to find other creative uses for objects. Suppose the hem of your pants gets caught on something and the thread starts unraveling. A roll of tape and a stapler are on your desk, and both could be used to “fix” your wardrobe malfunction. But because of functional fixedness, you only view these items in their “usual” capacities. Children have less trouble with functional fixedness than adults because they have not become accustomed to using familiar objects in a fixed way (German & Defeyter, 2000).

Mental sets represent another barrier to problem solving. When faced with a problem, we tend to fall back on solution strategies we have always used—even if they don’t work so well. For example, when your hem comes out of your pants, you grab for the needle and thread because that is the solution you have always used. With mental sets, an approach that has worked in the past will often come immediately to mind and be reused, preventing us from seeing other solutions to a problem.

Emotional barriers can also get in the way of problem solving. If you are trying to figure out how to fix the dripping faucet and someone is peering over your shoulder saying, “Hurry up! What’s taking you so long?”, you may feel rushed, anxious, and annoyed. These negative emotions affect your ability to think clearly and creatively. Positive emotions, on the other hand, may set the stage for innovative thinking. Good feelings are thought to promote a “flexible” way of thinking, one that enables quick attention shifting and the ability to develop new strategies in response to a changing environment (Isen, 2008). Keep this in mind when you are trying to help someone solve a problem.

Think Outside the Box Who knew that a paint roller could be used for holding toilet paper and that car tires doubled as planters? Sometimes it’s hard to imagine using objects for unconventional purposes. Our resistance toward using familiar objects in new ways is known as functional fixedness, and it can get in the way of problem solving.
top: Andrea Jones/Garden World Images/age fotostock; right: Andreas Schlegel/age fotostock

across the WORLD

Problem Solving in Different Cultures

Another factor influencing problem solving is culture. People from highly individualistic or self-focused societies, such as the United States, tend to be action oriented in their problem solving, making a lot of decisions in a short amount of time. In contrast, those from more collectivist or community-focused countries, such as Brazil, tend to be more careful in their approach, making fewer decisions when faced with a problem (Güss, 2011; Ohbuchi, Fukushima, & Tedeschi, 1999).

Building on these and other findings, researcher Dominick Güss investigated how people from five countries—Germany, the United States, Brazil, India, and the Philippines—approached different problems. Güss hypothesized that participants who leaned toward individualism, particularly those who placed a high value on equality and uniqueness, would be more action oriented in solving problems. Collectivists who recognized inequalities and prioritized group needs would be more careful in generating solutions (Güss, 2011).

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Overall, the results of the study supported Güss’s hypothesis. There were notable exceptions, however. Participants from India and the Philippines (collectivist cultures) were expected to be hesitant problem solvers. Nevertheless, when it came to tackling a problem without a clear cause (trying to maintain the temperature of a supermarket freezer department when the thermostat appears to be failing), they seemed to have little trouble cranking out decisions. In fact, they were more action-oriented than their U.S. and German counterparts who were expected to be the enthusiastic decision makers. One possible explanation is that the Indian and Filipino participants were more comfortable with the ambiguity surrounding that particular problem, and thus had an easier time responding to it (Güss, 2011). As it turns out, different cultures have varying degrees of tolerance for unpredictability. This characteristic is known as uncertainty avoidance (Hofstede, 1993), and is one of several cultural forces shaping the problem-solving process.

CRANKING OUT DECISIONS ACROSS CULTURES

Untangling the cultural factors affecting problem solving and other cognitive functions is no easy task. Culture is complex. Cognition is complex. Add other characteristics to the mix, and you’ve got a lot of exciting research for the future!

The last few pages have been devoted to problem solving, the many approaches used to attain an out-of-reach goal. In the process, we have made various references to decision making. Next we will examine what decision making is, and how it relates to problem solving.

FIGURE 7.3Solution to the Dot Problem in Infographic 7.2Did your mental set cause you to assume the square implied boundaries? If so, it may not have occurred to you that you could draw lines extending outside the square.
FIGURE 7.4Solution to the Two-Rope Problem in Infographic 7.2Using a shovel to create a pendulum will allow you to swing the second rope. When it swings near you, you can grab it and hold both ropes at the same time.

show what you know

Question 7.5

1. Imagine it is the first day of classes, but you forgot to write down the number of the room where your psychology class is meeting. You decide you will try to find your classroom by sticking your head in a random number of rooms until you see the assigned psychology textbook on someone’s desk. This approach to finding your classroom uses:

  1. means–ends analysis.
  2. an algorithm.
  3. trial and error.
  4. heuristics.

Question 7.6

2. One common barrier to problem solving is _________, which occurs when we can only imagine using familiar objects in their usual way.

  1. functional fixedness
  2. uncertainty avoidance
  3. an algorithm
  4. a goal state

Question 7.7

3. One assignment in your psychology class is to design an experiment. Describe how you would use means–ends analysis to choose a topic for your experiment and write a review of the literature.

CHECK YOUR ANSWERS IN APPENDIX C.

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