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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 we can use to achieve a goal.

COMPONENTS OF PROBLEM SOLVING Problem solving has intrigued psychologists for generations. Newell, Shaw, and Simon (1958) developed an information-processing 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, 2013). 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, 2013). 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.

STEPS TO SOLVING PROBLEMS The first step in problem solving is understanding the problem (see Infographic 7.2, below). 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 you spend assessing the problem (Ericsson, 2003; Goldstein, 2011).

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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.

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

TRIAL AND ERROR 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. If one key doesn’t work, then you move on to another, and if that key doesn’t work, you try yet another key, and so on.

Trial and error is only useful in certain circumstances. It should not be used if the stakes are extremely high, particularly in situations where a wrong selection could 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.

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, March 31). Ha ha, hacker!

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

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HEURISTICS If using an algorithm is not an option, which is often the case with everyday problems, we can turn to heuristics (hyu̇-ris-tiks). 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.

Heuristics provide shortcuts, allowing you to ignore the many approaches 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 breaking the effort of sitting up into the smaller steps of rocking and then rolling upward” (Taylor, 2006, p. 93). When writing your last term paper, did you break it into shorter, more achievable parts? If so, you were using this type of heuristic, which instructors often recommend to students.

Another frequently used heuristic is means–ends analysis. Here, 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 also involve breaking your problem into subproblems that can be solved independently, incorporating the heuristic described in the last paragraph. 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 manner of reaching a solution is through insight, 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” we did to achieve it.

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). There is evidence that activity in the frontal and temporal lobes immediately precedes the “aha!” moment (Kounios & Beeman, 2009).

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Wolfgang Köhler, a Gestalt psychologist, made some remarkable discoveries on insight in chimpanzees. As early as 1913, he created various problems for 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).

The Gestalt psychologists believed that humans and animals solve problems through perception and cognition—by creating mental representations of objects and their relationships (Whitman, 2011). To solve the banana problem, the chimp’s mind reorganizes the relative positions of the banana-getting objects. We humans manipulate pictures in our minds in a similar fashion, and it requires no conscious effort. Ah, the beauty of insight.

With the capacity for insight, we can be masterful problem solvers. But as you probably know from personal experience, great ideas do not always materialize when we need them; there are many barriers to problem solving (Infographic 7.2). One such barrier is functional fixedness, which occurs when we can only imagine using familiar objects in their 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 a 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.

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.

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LO 7 Define decision making and explain how heuristics can lead us astray.

You may be wondering how decision making differs from problem solving. As you now know, problem solving refers to the variety of approaches we can use to achieve a goal. Decision making is the cognitive process of choosing from those alternative approaches. Thus, problem solving and decision making can occur at the same time.

PREDICTING THE FUTURE Decision making often involves predicting the future: What is the likelihood that Event A will occur under these circumstances? How about Event B? In cases like these, we can make an educated guess, but some situations lend themselves to more accurate guesses than others. If the weather channel predicts there is a 99% chance of thunderstorms today, it’s fairly safe to assume it’s going to rain. Better bring your umbrella.

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But there are many times when predicting the future is like rolling dice—you have almost no way of knowing the outcome. Suppose you are searching for a used car on craigslist. How do you choose a “gently used” car from among the hundreds listed in your locality? With no prior knowledge of the cars or their owners (apart from whatever information they decide to post on craigslist), all you can do is hope the car you choose is not a lemon. But who knows if your gamble is going to work? Choices that hinge on predictions can be very risky, and we sometimes make the wrong decision.

SINGLE FEATURE There are many ways to go about making decisions. One way is to focus on a single aspect, or feature, of the situation. Let’s say you are trying to decide where to stop for gas. If your only criterion is cost, you will seek out the gas station with the cheapest gasoline, paying no attention to what kind of donuts they sell inside or how clean their bathroom may be. The single feature on which you are basing your decision (where to stop for gas) is the price of the fuel (not tasty donuts or a clean bathroom).

ADDITIVE MODEL The single-feature approach may not be effective for making complex decisions, in which there are many features to consider. With a more complex decision, such as which car to purchase, you might create a list of the primary features you consider important (gas mileage, safety ratings, sound system, and so on). Using this list, you could rate each of the possible choices (for example, Ford Focus versus Toyota Prius) according to their features, and then tally these ratings to see which car comes out on top. This method of calculating the highest rating is often referred to as an additive model of decision making.

At the start of the section, we mentioned that decision making often involves making predictions, and different scenarios afford different levels of certainty about the future. Heuristics, which involve a rule of thumb or a broad application of a strategy, can help predict the probability of an event occurring. Unfortunately, heuristics can also lead us astray in our assessment of situations and prediction of outcomes. Daniel Kahneman and Amos Tversky (1973) were among the first to systematically research the ways in which heuristics can be ineffective. They found that people are prone to ignore important information while using heuristics (Kahneman & Tversky, 1996). This is particularly true for the availability heuristic and the representativeness heuristic.

THE AVAILABILITY HEURISTIC Using the availability heuristic, we predict the probability of something happening in the future based on how easily we can recall a similar type of event from the past. The availability heuristic is essentially a decision-making strategy that relies on memory. If we can easily recall a certain event, then we tend to base our decisions on the assumption that it can happen again. Many factors make an event more available, including its recency, frequency, familiarity, and vividness. Let’s look at each of these categories.

Imagine the year is 2010 and you have just learned about the mine collapse that left 33 Chilean workers trapped underground. If asked to predict the likelihood of a similar mining collapse occurring in the near future, your estimation would likely be higher than normal because you just heard about the Chilean incident. Our predictions using the availability heuristic are based on how easily we can recall similar events from the past, and the more recently a similar situation has occurred, the more easily it will be recalled. With an event still fresh in our minds, we are more likely to overestimate the odds of a similar event occurring in the future.

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Now imagine that you were asked to decide the following: Do more students at your college use Macs or PCs? Before deciding how to answer, you would probably think about the number of students you have seen using these types of computers and make an estimation based on that tally. In this case, the frequency of occurrence influences your decision. You rely on your recall of seeing students using computers in the halls, classrooms, and library. If you are in the graphic design department, for example, chances are you’ll see more Macs than PCs. Based strictly on your observations from a single department, your sample would not be representative of the entire college, and the availability heuristic would lead you to the wrong answer. The availability heuristic can be accurate, but only when based on appropriate information.

The familiarity of an event might also lead to inaccurate estimates. If you and your friends are all avid PC users, you may overestimate the extent to which others are using PCs. The more familiar you are with a situation, the more likely you are to predict a similar occurrence in the future.

Finally, the vividness of an event can influence our recall. Try to conjure up an image of someone winning the “big one” at a casino. There are lights, sounds, and a lot of hubbub. The prizewinner jumps joyfully in the air, hollering and crying at the top of his lungs, with onlookers clapping and shouting in approval. This type of dramatic display never occurs when some poor guy loses his last $100; the details of a losing bet would consequently be far more difficult to recall. Because the winning image is more vivid, we are more likely to recall it and thus to overestimate the likelihood it will occur in our own lives. Memorable imagery leads us to believe that these types of wins happen all the time, when in fact they are very rare. If an event has made a striking impression on you, even a rare occurrence such as an airplane crash, you will be more likely to overestimate the probability of it happening again (Tversky & Kahneman, 1982).

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THE REPRESENTATIVENESS HEURISTIC Sometimes we have to make decisions based on our judgment of a situation or person. The representativeness heuristic evaluates the degree to which their primary characteristics are similar to our prototypes. With the representativeness heuristic, we make quick, effortless judgments about how closely a person or situation fits our preconceived prototype (Shah & Oppenheimer, 2008). In contrast, the availability heuristic requires us to access information from long-term memory and use it to make predictions about events.

Let’s examine how the representativeness heuristic works in practice. Peter is a middle-aged man. He is conservative, a lovely speaker, thoughtful, and well read. He lives alone in an apartment in the city. Is Peter a truck driver or a poet? Forced to choose between these two occupations and using the representativeness heuristic, the majority of people would likely guess that Peter is a poet because his description better matches their prototype of a poet than their prototype of a truck driver. But this approach fails to consider the base rate (the prevalence of features or events in the population) of these occupations. There are far more truck drivers than poets, suggesting the better guess would be that Peter is a truck driver. The representativeness heuristic can be useful, but the accuracy of our information must also be taken into account; our conclusions should be drawn from base rates, not stereotypes. The other limitation of the representativeness heuristic is that prototypes are based on exposure to limited samples, which may not provide a good representation of the population.

THE CONFIRMATION BIAS We can also miss important information through the confirmation bias, when we unintentionally look for evidence that upholds our beliefs. People tend to overlook or discount evidence that runs counter to their original beliefs or positions. For example, you decide to go on a date with someone you are really interested in, even though you don’t know him very well. You Google stalk him and look on his Facebook page, and immediately connect with one of the “likes” he has. With this information in hand, you stop your search, convinced you now have evidence to support your decision to go out with him. We tend to focus on information that supports favorable outcomes (Krizan & Windschitl, 2007; Scherer, Windschitl, O’Rourke, & Smith, 2012), but what other sources of information could you use to avoid the confirmation bias in this case? The danger of the confirmation bias is that we miss or ignore relevant (and possibly contradictory) information without conscious intent; we don’t deliberately set out looking for information to support what we already think.

We have spent a great deal of time discussing factors that impede the decision maker. But in many situations, the characteristics of the problem itself, or the presentation of the problem, are to blame.

WHAT’S IN A FRAME? The framing effect demonstrates how the presentation or context of a problem can influence the outcome of a decision. To look at this effect, researchers conducted a study in which they instructed participants to imagine that they had purchased a $10 ticket to attend a show, but lost their ticket on the way to the theater. Each participant was then asked whether he or she would be willing to pay $10 for another ticket. Only 46% of participants indicated that they would spend another $10 for a new ticket. Participants were next instructed to imagine another situation: In it, they planned to buy a $10 ticket to attend a show, but once they got in the ticket line, they suddenly realized that they had lost one of their $10 bills. Faced with this second scenario, 88% of the participants were willing to fork over the $10. In each case, the participants were faced with the proposition of spending an additional and unexpected $10, but they tended to make different decisions in response to the different circumstances. The background information framing these hypothetical scenarios influenced the decisions made, even though the outcomes would have been identical—a net loss of $10 (Kahneman & Tversky, 1984; Tversky & Kahneman, 1981).

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WHAT’S IN A QUESTION? The specific wording of questions should also be considered. One study found that people are more likely to prefer ground beef if it is described as “80% lean,” as opposed to “20% fat.” Although 80% lean and 20% fat describe exactly the same product, these phrases evoke very different responses (Johnson, 1987). Another study investigated the effects of question framing on women using a telephone-based counseling service to inquire about the side effects of drugs taken during pregnancy (Jasper, Goel, Einarson, Gallo, & Koren, 2001). The women calling in were assigned to one of two groups. Members of the first group were told that “in every pregnancy there is a 1% to 3% chance that a woman will give birth to a child who has a major birth defect. This drug has not been shown to change that” (p. 1237). Women in the second group were told that “in every pregnancy, there is a 97–99% chance that a woman will give birth to a child who does not have a major birth defect. This drug has not been shown to change that” (p. 1237). The researchers then followed up with a series of questions. Participants in the first group believed that they faced a greater risk of bearing a child with a birth defect if they had taken the drug than those in the second group. Decision making is often influenced by whether a question is worded in a positive way (the glass is half full) or in a negative way (the glass is half empty) (Huber, Neale, & Northcraft, 1987).

Question 1

1. means–ends analysis.

2. an algorithm.

3. trial and error.

4. heuristics.

Question 2

Question 3

Question 4

1. framing effect.

2. confirmation bias.

3. representativeness heuristic.

4. availability heuristic.

Question 5