problem solving mental ability

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7 Module 7: Thinking, Reasoning, and Problem-Solving

This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure out the solution to many problems, because you feel capable of using logic to argue a point, because you can evaluate whether the things you read and hear make sense—you do not need any special training in thinking. But this, of course, is one of the key barriers to helping people think better. If you do not believe that there is anything wrong, why try to fix it?

The human brain is indeed a remarkable thinking machine, capable of amazing, complex, creative, logical thoughts. Why, then, are we telling you that you need to learn how to think? Mainly because one major lesson from cognitive psychology is that these capabilities of the human brain are relatively infrequently realized. Many psychologists believe that people are essentially “cognitive misers.” It is not that we are lazy, but that we have a tendency to expend the least amount of mental effort necessary. Although you may not realize it, it actually takes a great deal of energy to think. Careful, deliberative reasoning and critical thinking are very difficult. Because we seem to be successful without going to the trouble of using these skills well, it feels unnecessary to develop them. As you shall see, however, there are many pitfalls in the cognitive processes described in this module. When people do not devote extra effort to learning and improving reasoning, problem solving, and critical thinking skills, they make many errors.

As is true for memory, if you develop the cognitive skills presented in this module, you will be more successful in school. It is important that you realize, however, that these skills will help you far beyond school, even more so than a good memory will. Although it is somewhat useful to have a good memory, ten years from now no potential employer will care how many questions you got right on multiple choice exams during college. All of them will, however, recognize whether you are a logical, analytical, critical thinker. With these thinking skills, you will be an effective, persuasive communicator and an excellent problem solver.

The module begins by describing different kinds of thought and knowledge, especially conceptual knowledge and critical thinking. An understanding of these differences will be valuable as you progress through school and encounter different assignments that require you to tap into different kinds of knowledge. The second section covers deductive and inductive reasoning, which are processes we use to construct and evaluate strong arguments. They are essential skills to have whenever you are trying to persuade someone (including yourself) of some point, or to respond to someone’s efforts to persuade you. The module ends with a section about problem solving. A solid understanding of the key processes involved in problem solving will help you to handle many daily challenges.

7.1. Different kinds of thought

7.2. Reasoning and Judgment

7.3. Problem Solving

READING WITH PURPOSE

Remember and understand.

By reading and studying Module 7, you should be able to remember and describe:

• Concepts and inferences (7.1)
• Procedural knowledge (7.1)
• Metacognition (7.1)
• Characteristics of critical thinking:  skepticism; identify biases, distortions, omissions, and assumptions; reasoning and problem solving skills  (7.1)
• Reasoning:  deductive reasoning, deductively valid argument, inductive reasoning, inductively strong argument, availability heuristic, representativeness heuristic  (7.2)
• Fixation:  functional fixedness, mental set  (7.3)
• Algorithms, heuristics, and the role of confirmation bias (7.3)
• Effective problem solving sequence (7.3)

By reading and thinking about how the concepts in Module 6 apply to real life, you should be able to:

• Identify which type of knowledge a piece of information is (7.1)
• Recognize examples of deductive and inductive reasoning (7.2)
• Recognize judgments that have probably been influenced by the availability heuristic (7.2)
• Recognize examples of problem solving heuristics and algorithms (7.3)

Analyze, Evaluate, and Create

By reading and thinking about Module 6, participating in classroom activities, and completing out-of-class assignments, you should be able to:

• Use the principles of critical thinking to evaluate information (7.1)
• Explain whether examples of reasoning arguments are deductively valid or inductively strong (7.2)
• Outline how you could try to solve a problem from your life using the effective problem solving sequence (7.3)

7.1. Different kinds of thought and knowledge

• Take a few minutes to write down everything that you know about dogs.
• Do you believe that:
• Psychic ability exists?
• Hypnosis is an altered state of consciousness?
• Magnet therapy is effective for relieving pain?
• Aerobic exercise is an effective treatment for depression?
• UFO’s from outer space have visited earth?

On what do you base your belief or disbelief for the questions above?

Of course, we all know what is meant by the words  think  and  knowledge . You probably also realize that they are not unitary concepts; there are different kinds of thought and knowledge. In this section, let us look at some of these differences. If you are familiar with these different kinds of thought and pay attention to them in your classes, it will help you to focus on the right goals, learn more effectively, and succeed in school. Different assignments and requirements in school call on you to use different kinds of knowledge or thought, so it will be very helpful for you to learn to recognize them (Anderson, et al. 2001).

Factual and conceptual knowledge

Module 5 introduced the idea of declarative memory, which is composed of facts and episodes. If you have ever played a trivia game or watched Jeopardy on TV, you realize that the human brain is able to hold an extraordinary number of facts. Likewise, you realize that each of us has an enormous store of episodes, essentially facts about events that happened in our own lives. It may be difficult to keep that in mind when we are struggling to retrieve one of those facts while taking an exam, however. Part of the problem is that, in contradiction to the advice from Module 5, many students continue to try to memorize course material as a series of unrelated facts (picture a history student simply trying to memorize history as a set of unrelated dates without any coherent story tying them together). Facts in the real world are not random and unorganized, however. It is the way that they are organized that constitutes a second key kind of knowledge, conceptual.

Concepts are nothing more than our mental representations of categories of things in the world. For example, think about dogs. When you do this, you might remember specific facts about dogs, such as they have fur and they bark. You may also recall dogs that you have encountered and picture them in your mind. All of this information (and more) makes up your concept of dog. You can have concepts of simple categories (e.g., triangle), complex categories (e.g., small dogs that sleep all day, eat out of the garbage, and bark at leaves), kinds of people (e.g., psychology professors), events (e.g., birthday parties), and abstract ideas (e.g., justice). Gregory Murphy (2002) refers to concepts as the “glue that holds our mental life together” (p. 1). Very simply, summarizing the world by using concepts is one of the most important cognitive tasks that we do. Our conceptual knowledge  is  our knowledge about the world. Individual concepts are related to each other to form a rich interconnected network of knowledge. For example, think about how the following concepts might be related to each other: dog, pet, play, Frisbee, chew toy, shoe. Or, of more obvious use to you now, how these concepts are related: working memory, long-term memory, declarative memory, procedural memory, and rehearsal? Because our minds have a natural tendency to organize information conceptually, when students try to remember course material as isolated facts, they are working against their strengths.

One last important point about concepts is that they allow you to instantly know a great deal of information about something. For example, if someone hands you a small red object and says, “here is an apple,” they do not have to tell you, “it is something you can eat.” You already know that you can eat it because it is true by virtue of the fact that the object is an apple; this is called drawing an  inference , assuming that something is true on the basis of your previous knowledge (for example, of category membership or of how the world works) or logical reasoning.

Procedural knowledge

Physical skills, such as tying your shoes, doing a cartwheel, and driving a car (or doing all three at the same time, but don’t try this at home) are certainly a kind of knowledge. They are procedural knowledge, the same idea as procedural memory that you saw in Module 5. Mental skills, such as reading, debating, and planning a psychology experiment, are procedural knowledge, as well. In short, procedural knowledge is the knowledge how to do something (Cohen & Eichenbaum, 1993).

Metacognitive knowledge

Floyd used to think that he had a great memory. Now, he has a better memory. Why? Because he finally realized that his memory was not as great as he once thought it was. Because Floyd eventually learned that he often forgets where he put things, he finally developed the habit of putting things in the same place. (Unfortunately, he did not learn this lesson before losing at least 5 watches and a wedding ring.) Because he finally realized that he often forgets to do things, he finally started using the To Do list app on his phone. And so on. Floyd’s insights about the real limitations of his memory have allowed him to remember things that he used to forget.

All of us have knowledge about the way our own minds work. You may know that you have a good memory for people’s names and a poor memory for math formulas. Someone else might realize that they have difficulty remembering to do things, like stopping at the store on the way home. Others still know that they tend to overlook details. This knowledge about our own thinking is actually quite important; it is called metacognitive knowledge, or  metacognition . Like other kinds of thinking skills, it is subject to error. For example, in unpublished research, one of the authors surveyed about 120 General Psychology students on the first day of the term. Among other questions, the students were asked them to predict their grade in the class and report their current Grade Point Average. Two-thirds of the students predicted that their grade in the course would be higher than their GPA. (The reality is that at our college, students tend to earn lower grades in psychology than their overall GPA.) Another example: Students routinely report that they thought they had done well on an exam, only to discover, to their dismay, that they were wrong (more on that important problem in a moment). Both errors reveal a breakdown in metacognition.

The Dunning-Kruger Effect

In general, most college students probably do not study enough. For example, using data from the National Survey of Student Engagement, Fosnacht, McCormack, and Lerma (2018) reported that first-year students at 4-year colleges in the U.S. averaged less than 14 hours per week preparing for classes. The typical suggestion is that you should spend two hours outside of class for every hour in class, or 24 – 30 hours per week for a full-time student. Clearly, students in general are nowhere near that recommended mark. Many observers, including some faculty, believe that this shortfall is a result of students being too busy or lazy. Now, it may be true that many students are too busy, with work and family obligations, for example. Others, are not particularly motivated in school, and therefore might correctly be labeled lazy. A third possible explanation, however, is that some students might not think they need to spend this much time. And this is a matter of metacognition. Consider the scenario that we mentioned above, students thinking they had done well on an exam only to discover that they did not. Justin Kruger and David Dunning examined scenarios very much like this in 1999. Kruger and Dunning gave research participants tests measuring humor, logic, and grammar. Then, they asked the participants to assess their own abilities and test performance in these areas. They found that participants in general tended to overestimate their abilities, already a problem with metacognition. Importantly, the participants who scored the lowest overestimated their abilities the most. Specifically, students who scored in the bottom quarter (averaging in the 12th percentile) thought they had scored in the 62nd percentile. This has become known as the  Dunning-Kruger effect . Many individual faculty members have replicated these results with their own student on their course exams, including the authors of this book. Think about it. Some students who just took an exam and performed poorly believe that they did well before seeing their score. It seems very likely that these are the very same students who stopped studying the night before because they thought they were “done.” Quite simply, it is not just that they did not know the material. They did not know that they did not know the material. That is poor metacognition.

In order to develop good metacognitive skills, you should continually monitor your thinking and seek frequent feedback on the accuracy of your thinking (Medina, Castleberry, & Persky 2017). For example, in classes get in the habit of predicting your exam grades. As soon as possible after taking an exam, try to find out which questions you missed and try to figure out why. If you do this soon enough, you may be able to recall the way it felt when you originally answered the question. Did you feel confident that you had answered the question correctly? Then you have just discovered an opportunity to improve your metacognition. Be on the lookout for that feeling and respond with caution.

concept :  a mental representation of a category of things in the world

Dunning-Kruger effect : individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

inference : an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

metacognition :  knowledge about one’s own cognitive processes; thinking about your thinking

Critical thinking

One particular kind of knowledge or thinking skill that is related to metacognition is  critical thinking (Chew, 2020). You may have noticed that critical thinking is an objective in many college courses, and thus it could be a legitimate topic to cover in nearly any college course. It is particularly appropriate in psychology, however. As the science of (behavior and) mental processes, psychology is obviously well suited to be the discipline through which you should be introduced to this important way of thinking.

More importantly, there is a particular need to use critical thinking in psychology. We are all, in a way, experts in human behavior and mental processes, having engaged in them literally since birth. Thus, perhaps more than in any other class, students typically approach psychology with very clear ideas and opinions about its subject matter. That is, students already “know” a lot about psychology. The problem is, “it ain’t so much the things we don’t know that get us into trouble. It’s the things we know that just ain’t so” (Ward, quoted in Gilovich 1991). Indeed, many of students’ preconceptions about psychology are just plain wrong. Randolph Smith (2002) wrote a book about critical thinking in psychology called  Challenging Your Preconceptions,  highlighting this fact. On the other hand, many of students’ preconceptions about psychology are just plain right! But wait, how do you know which of your preconceptions are right and which are wrong? And when you come across a research finding or theory in this class that contradicts your preconceptions, what will you do? Will you stick to your original idea, discounting the information from the class? Will you immediately change your mind? Critical thinking can help us sort through this confusing mess.

But what is critical thinking? The goal of critical thinking is simple to state (but extraordinarily difficult to achieve): it is to be right, to draw the correct conclusions, to believe in things that are true and to disbelieve things that are false. We will provide two definitions of critical thinking (or, if you like, one large definition with two distinct parts). First, a more conceptual one: Critical thinking is thinking like a scientist in your everyday life (Schmaltz, Jansen, & Wenckowski, 2017).  Our second definition is more operational; it is simply a list of skills that are essential to be a critical thinker. Critical thinking entails solid reasoning and problem solving skills; skepticism; and an ability to identify biases, distortions, omissions, and assumptions. Excellent deductive and inductive reasoning, and problem solving skills contribute to critical thinking. So, you can consider the subject matter of sections 7.2 and 7.3 to be part of critical thinking. Because we will be devoting considerable time to these concepts in the rest of the module, let us begin with a discussion about the other aspects of critical thinking.

Let’s address that first part of the definition. Scientists form hypotheses, or predictions about some possible future observations. Then, they collect data, or information (think of this as making those future observations). They do their best to make unbiased observations using reliable techniques that have been verified by others. Then, and only then, they draw a conclusion about what those observations mean. Oh, and do not forget the most important part. “Conclusion” is probably not the most appropriate word because this conclusion is only tentative. A scientist is always prepared that someone else might come along and produce new observations that would require a new conclusion be drawn. Wow! If you like to be right, you could do a lot worse than using a process like this.

A Critical Thinker’s Toolkit 

Now for the second part of the definition. Good critical thinkers (and scientists) rely on a variety of tools to evaluate information. Perhaps the most recognizable tool for critical thinking is  skepticism (and this term provides the clearest link to the thinking like a scientist definition, as you are about to see). Some people intend it as an insult when they call someone a skeptic. But if someone calls you a skeptic, if they are using the term correctly, you should consider it a great compliment. Simply put, skepticism is a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided. People from Missouri should recognize this principle, as Missouri is known as the Show-Me State. As a skeptic, you are not inclined to believe something just because someone said so, because someone else believes it, or because it sounds reasonable. You must be persuaded by high quality evidence.

Of course, if that evidence is produced, you have a responsibility as a skeptic to change your belief. Failure to change a belief in the face of good evidence is not skepticism; skepticism has open mindedness at its core. M. Neil Browne and Stuart Keeley (2018) use the term weak sense critical thinking to describe critical thinking behaviors that are used only to strengthen a prior belief. Strong sense critical thinking, on the other hand, has as its goal reaching the best conclusion. Sometimes that means strengthening your prior belief, but sometimes it means changing your belief to accommodate the better evidence.

Many times, a failure to think critically or weak sense critical thinking is related to a  bias , an inclination, tendency, leaning, or prejudice. Everybody has biases, but many people are unaware of them. Awareness of your own biases gives you the opportunity to control or counteract them. Unfortunately, however, many people are happy to let their biases creep into their attempts to persuade others; indeed, it is a key part of their persuasive strategy. To see how these biases influence messages, just look at the different descriptions and explanations of the same events given by people of different ages or income brackets, or conservative versus liberal commentators, or by commentators from different parts of the world. Of course, to be successful, these people who are consciously using their biases must disguise them. Even undisguised biases can be difficult to identify, so disguised ones can be nearly impossible.

Here are some common sources of biases:

• Personal values and beliefs.  Some people believe that human beings are basically driven to seek power and that they are typically in competition with one another over scarce resources. These beliefs are similar to the world-view that political scientists call “realism.” Other people believe that human beings prefer to cooperate and that, given the chance, they will do so. These beliefs are similar to the world-view known as “idealism.” For many people, these deeply held beliefs can influence, or bias, their interpretations of such wide ranging situations as the behavior of nations and their leaders or the behavior of the driver in the car ahead of you. For example, if your worldview is that people are typically in competition and someone cuts you off on the highway, you may assume that the driver did it purposely to get ahead of you. Other types of beliefs about the way the world is or the way the world should be, for example, political beliefs, can similarly become a significant source of bias.
• Racism, sexism, ageism and other forms of prejudice and bigotry.  These are, sadly, a common source of bias in many people. They are essentially a special kind of “belief about the way the world is.” These beliefs—for example, that women do not make effective leaders—lead people to ignore contradictory evidence (examples of effective women leaders, or research that disputes the belief) and to interpret ambiguous evidence in a way consistent with the belief.
• Self-interest.  When particular people benefit from things turning out a certain way, they can sometimes be very susceptible to letting that interest bias them. For example, a company that will earn a profit if they sell their product may have a bias in the way that they give information about their product. A union that will benefit if its members get a generous contract might have a bias in the way it presents information about salaries at competing organizations. (Note that our inclusion of examples describing both companies and unions is an explicit attempt to control for our own personal biases). Home buyers are often dismayed to discover that they purchased their dream house from someone whose self-interest led them to lie about flooding problems in the basement or back yard. This principle, the biasing power of self-interest, is likely what led to the famous phrase  Caveat Emptor  (let the buyer beware) .  

Knowing that these types of biases exist will help you evaluate evidence more critically. Do not forget, though, that people are not always keen to let you discover the sources of biases in their arguments. For example, companies or political organizations can sometimes disguise their support of a research study by contracting with a university professor, who comes complete with a seemingly unbiased institutional affiliation, to conduct the study.

People’s biases, conscious or unconscious, can lead them to make omissions, distortions, and assumptions that undermine our ability to correctly evaluate evidence. It is essential that you look for these elements. Always ask, what is missing, what is not as it appears, and what is being assumed here? For example, consider this (fictional) chart from an ad reporting customer satisfaction at 4 local health clubs.

Clearly, from the results of the chart, one would be tempted to give Club C a try, as customer satisfaction is much higher than for the other 3 clubs.

There are so many distortions and omissions in this chart, however, that it is actually quite meaningless. First, how was satisfaction measured? Do the bars represent responses to a survey? If so, how were the questions asked? Most importantly, where is the missing scale for the chart? Although the differences look quite large, are they really?

Well, here is the same chart, with a different scale, this time labeled:

Club C is not so impressive any more, is it? In fact, all of the health clubs have customer satisfaction ratings (whatever that means) between 85% and 88%. In the first chart, the entire scale of the graph included only the percentages between 83 and 89. This “judicious” choice of scale—some would call it a distortion—and omission of that scale from the chart make the tiny differences among the clubs seem important, however.

Also, in order to be a critical thinker, you need to learn to pay attention to the assumptions that underlie a message. Let us briefly illustrate the role of assumptions by touching on some people’s beliefs about the criminal justice system in the US. Some believe that a major problem with our judicial system is that many criminals go free because of legal technicalities. Others believe that a major problem is that many innocent people are convicted of crimes. The simple fact is, both types of errors occur. A person’s conclusion about which flaw in our judicial system is the greater tragedy is based on an assumption about which of these is the more serious error (letting the guilty go free or convicting the innocent). This type of assumption is called a value assumption (Browne and Keeley, 2018). It reflects the differences in values that people develop, differences that may lead us to disregard valid evidence that does not fit in with our particular values.

Oh, by the way, some students probably noticed this, but the seven tips for evaluating information that we shared in Module 1 are related to this. Actually, they are part of this section. The tips are, to a very large degree, set of ideas you can use to help you identify biases, distortions, omissions, and assumptions. If you do not remember this section, we strongly recommend you take a few minutes to review it.

skepticism :  a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

bias : an inclination, tendency, leaning, or prejudice

• Which of your beliefs (or disbeliefs) from the Activate exercise for this section were derived from a process of critical thinking? If some of your beliefs were not based on critical thinking, are you willing to reassess these beliefs? If the answer is no, why do you think that is? If the answer is yes, what concrete steps will you take?

7.2 Reasoning and Judgment

• What percentage of kidnappings are committed by strangers?
• Which area of the house is riskiest: kitchen, bathroom, or stairs?
• What is the most common cancer in the US?
• What percentage of workplace homicides are committed by co-workers?

An essential set of procedural thinking skills is  reasoning , the ability to generate and evaluate solid conclusions from a set of statements or evidence. You should note that these conclusions (when they are generated instead of being evaluated) are one key type of inference that we described in Section 7.1. There are two main types of reasoning, deductive and inductive.

Deductive reasoning

Suppose your teacher tells you that if you get an A on the final exam in a course, you will get an A for the whole course. Then, you get an A on the final exam. What will your final course grade be? Most people can see instantly that you can conclude with certainty that you will get an A for the course. This is a type of reasoning called  deductive reasoning , which is defined as reasoning in which a conclusion is guaranteed to be true as long as the statements leading to it are true. The three statements can be listed as an  argument , with two beginning statements and a conclusion:

Statement 1: If you get an A on the final exam, you will get an A for the course

Statement 2: You get an A on the final exam

Conclusion: You will get an A for the course

This particular arrangement, in which true beginning statements lead to a guaranteed true conclusion, is known as a  deductively valid argument . Although deductive reasoning is often the subject of abstract, brain-teasing, puzzle-like word problems, it is actually an extremely important type of everyday reasoning. It is just hard to recognize sometimes. For example, imagine that you are looking for your car keys and you realize that they are either in the kitchen drawer or in your book bag. After looking in the kitchen drawer, you instantly know that they must be in your book bag. That conclusion results from a simple deductive reasoning argument. In addition, solid deductive reasoning skills are necessary for you to succeed in the sciences, philosophy, math, computer programming, and any endeavor involving the use of logic to persuade others to your point of view or to evaluate others’ arguments.

Cognitive psychologists, and before them philosophers, have been quite interested in deductive reasoning, not so much for its practical applications, but for the insights it can offer them about the ways that human beings think. One of the early ideas to emerge from the examination of deductive reasoning is that people learn (or develop) mental versions of rules that allow them to solve these types of reasoning problems (Braine, 1978; Braine, Reiser, & Rumain, 1984). The best way to see this point of view is to realize that there are different possible rules, and some of them are very simple. For example, consider this rule of logic:

therefore q

Logical rules are often presented abstractly, as letters, in order to imply that they can be used in very many specific situations. Here is a concrete version of the of the same rule:

I’ll either have pizza or a hamburger for dinner tonight (p or q)

I won’t have pizza (not p)

Therefore, I’ll have a hamburger (therefore q)

This kind of reasoning seems so natural, so easy, that it is quite plausible that we would use a version of this rule in our daily lives. At least, it seems more plausible than some of the alternative possibilities—for example, that we need to have experience with the specific situation (pizza or hamburger, in this case) in order to solve this type of problem easily. So perhaps there is a form of natural logic (Rips, 1990) that contains very simple versions of logical rules. When we are faced with a reasoning problem that maps onto one of these rules, we use the rule.

But be very careful; things are not always as easy as they seem. Even these simple rules are not so simple. For example, consider the following rule. Many people fail to realize that this rule is just as valid as the pizza or hamburger rule above.

if p, then q

therefore, not p

Concrete version:

If I eat dinner, then I will have dessert

I did not have dessert

Therefore, I did not eat dinner

The simple fact is, it can be very difficult for people to apply rules of deductive logic correctly; as a result, they make many errors when trying to do so. Is this a deductively valid argument or not?

Students who like school study a lot

Students who study a lot get good grades

Jane does not like school

Therefore, Jane does not get good grades

Many people are surprised to discover that this is not a logically valid argument; the conclusion is not guaranteed to be true from the beginning statements. Although the first statement says that students who like school study a lot, it does NOT say that students who do not like school do not study a lot. In other words, it may very well be possible to study a lot without liking school. Even people who sometimes get problems like this right might not be using the rules of deductive reasoning. Instead, they might just be making judgments for examples they know, in this case, remembering instances of people who get good grades despite not liking school.

Making deductive reasoning even more difficult is the fact that there are two important properties that an argument may have. One, it can be valid or invalid (meaning that the conclusion does or does not follow logically from the statements leading up to it). Two, an argument (or more correctly, its conclusion) can be true or false. Here is an example of an argument that is logically valid, but has a false conclusion (at least we think it is false).

Either you are eleven feet tall or the Grand Canyon was created by a spaceship crashing into the earth.

You are not eleven feet tall

Therefore the Grand Canyon was created by a spaceship crashing into the earth

This argument has the exact same form as the pizza or hamburger argument above, making it is deductively valid. The conclusion is so false, however, that it is absurd (of course, the reason the conclusion is false is that the first statement is false). When people are judging arguments, they tend to not observe the difference between deductive validity and the empirical truth of statements or conclusions. If the elements of an argument happen to be true, people are likely to judge the argument logically valid; if the elements are false, they will very likely judge it invalid (Markovits & Bouffard-Bouchard, 1992; Moshman & Franks, 1986). Thus, it seems a stretch to say that people are using these logical rules to judge the validity of arguments. Many psychologists believe that most people actually have very limited deductive reasoning skills (Johnson-Laird, 1999). They argue that when faced with a problem for which deductive logic is required, people resort to some simpler technique, such as matching terms that appear in the statements and the conclusion (Evans, 1982). This might not seem like a problem, but what if reasoners believe that the elements are true and they happen to be wrong; they will would believe that they are using a form of reasoning that guarantees they are correct and yet be wrong.

deductive reasoning :  a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

argument :  a set of statements in which the beginning statements lead to a conclusion

deductively valid argument :  an argument for which true beginning statements guarantee that the conclusion is true

Inductive reasoning and judgment

Every day, you make many judgments about the likelihood of one thing or another. Whether you realize it or not, you are practicing  inductive reasoning   on a daily basis. In inductive reasoning arguments, a conclusion is likely whenever the statements preceding it are true. The first thing to notice about inductive reasoning is that, by definition, you can never be sure about your conclusion; you can only estimate how likely the conclusion is. Inductive reasoning may lead you to focus on Memory Encoding and Recoding when you study for the exam, but it is possible the instructor will ask more questions about Memory Retrieval instead. Unlike deductive reasoning, the conclusions you reach through inductive reasoning are only probable, not certain. That is why scientists consider inductive reasoning weaker than deductive reasoning. But imagine how hard it would be for us to function if we could not act unless we were certain about the outcome.

Inductive reasoning can be represented as logical arguments consisting of statements and a conclusion, just as deductive reasoning can be. In an inductive argument, you are given some statements and a conclusion (or you are given some statements and must draw a conclusion). An argument is  inductively strong   if the conclusion would be very probable whenever the statements are true. So, for example, here is an inductively strong argument:

• Statement #1: The forecaster on Channel 2 said it is going to rain today.
• Statement #2: The forecaster on Channel 5 said it is going to rain today.
• Statement #3: It is very cloudy and humid.
• Statement #4: You just heard thunder.
• Conclusion (or judgment): It is going to rain today.

Think of the statements as evidence, on the basis of which you will draw a conclusion. So, based on the evidence presented in the four statements, it is very likely that it will rain today. Will it definitely rain today? Certainly not. We can all think of times that the weather forecaster was wrong.

A true story: Some years ago psychology student was watching a baseball playoff game between the St. Louis Cardinals and the Los Angeles Dodgers. A graphic on the screen had just informed the audience that the Cardinal at bat, (Hall of Fame shortstop) Ozzie Smith, a switch hitter batting left-handed for this plate appearance, had never, in nearly 3000 career at-bats, hit a home run left-handed. The student, who had just learned about inductive reasoning in his psychology class, turned to his companion (a Cardinals fan) and smugly said, “It is an inductively strong argument that Ozzie Smith will not hit a home run.” He turned back to face the television just in time to watch the ball sail over the right field fence for a home run. Although the student felt foolish at the time, he was not wrong. It was an inductively strong argument; 3000 at-bats is an awful lot of evidence suggesting that the Wizard of Ozz (as he was known) would not be hitting one out of the park (think of each at-bat without a home run as a statement in an inductive argument). Sadly (for the die-hard Cubs fan and Cardinals-hating student), despite the strength of the argument, the conclusion was wrong.

Given the possibility that we might draw an incorrect conclusion even with an inductively strong argument, we really want to be sure that we do, in fact, make inductively strong arguments. If we judge something probable, it had better be probable. If we judge something nearly impossible, it had better not happen. Think of inductive reasoning, then, as making reasonably accurate judgments of the probability of some conclusion given a set of evidence.

We base many decisions in our lives on inductive reasoning. For example:

Statement #1: Psychology is not my best subject

Statement #2: My psychology instructor has a reputation for giving difficult exams

Statement #3: My first psychology exam was much harder than I expected

Judgment: The next exam will probably be very difficult.

Decision: I will study tonight instead of watching Netflix.

Some other examples of judgments that people commonly make in a school context include judgments of the likelihood that:

• A particular class will be interesting/useful/difficult
• You will be able to finish writing a paper by next week if you go out tonight
• Your laptop’s battery will last through the next trip to the library
• You will not miss anything important if you skip class tomorrow
• Your instructor will not notice if you skip class tomorrow
• You will be able to find a book that you will need for a paper
• There will be an essay question about Memory Encoding on the next exam

Tversky and Kahneman (1983) recognized that there are two general ways that we might make these judgments; they termed them extensional (i.e., following the laws of probability) and intuitive (i.e., using shortcuts or heuristics, see below). We will use a similar distinction between Type 1 and Type 2 thinking, as described by Keith Stanovich and his colleagues (Evans and Stanovich, 2013; Stanovich and West, 2000). Type 1 thinking is fast, automatic, effortful, and emotional. In fact, it is hardly fair to call it reasoning at all, as judgments just seem to pop into one’s head. Type 2 thinking , on the other hand, is slow, effortful, and logical. So obviously, it is more likely to lead to a correct judgment, or an optimal decision. The problem is, we tend to over-rely on Type 1. Now, we are not saying that Type 2 is the right way to go for every decision or judgment we make. It seems a bit much, for example, to engage in a step-by-step logical reasoning procedure to decide whether we will have chicken or fish for dinner tonight.

Many bad decisions in some very important contexts, however, can be traced back to poor judgments of the likelihood of certain risks or outcomes that result from the use of Type 1 when a more logical reasoning process would have been more appropriate. For example:

Statement #1: It is late at night.

Statement #2: Albert has been drinking beer for the past five hours at a party.

Statement #3: Albert is not exactly sure where he is or how far away home is.

Judgment: Albert will have no difficulty walking home.

Decision: He walks home alone.

As you can see in this example, the three statements backing up the judgment do not really support it. In other words, this argument is not inductively strong because it is based on judgments that ignore the laws of probability. What are the chances that someone facing these conditions will be able to walk home alone easily? And one need not be drunk to make poor decisions based on judgments that just pop into our heads.

The truth is that many of our probability judgments do not come very close to what the laws of probability say they should be. Think about it. In order for us to reason in accordance with these laws, we would need to know the laws of probability, which would allow us to calculate the relationship between particular pieces of evidence and the probability of some outcome (i.e., how much likelihood should change given a piece of evidence), and we would have to do these heavy math calculations in our heads. After all, that is what Type 2 requires. Needless to say, even if we were motivated, we often do not even know how to apply Type 2 reasoning in many cases.

So what do we do when we don’t have the knowledge, skills, or time required to make the correct mathematical judgment? Do we hold off and wait until we can get better evidence? Do we read up on probability and fire up our calculator app so we can compute the correct probability? Of course not. We rely on Type 1 thinking. We “wing it.” That is, we come up with a likelihood estimate using some means at our disposal. Psychologists use the term heuristic to describe the type of “winging it” we are talking about. A  heuristic   is a shortcut strategy that we use to make some judgment or solve some problem (see Section 7.3). Heuristics are easy and quick, think of them as the basic procedures that are characteristic of Type 1.  They can absolutely lead to reasonably good judgments and decisions in some situations (like choosing between chicken and fish for dinner). They are, however, far from foolproof. There are, in fact, quite a lot of situations in which heuristics can lead us to make incorrect judgments, and in many cases the decisions based on those judgments can have serious consequences.

Let us return to the activity that begins this section. You were asked to judge the likelihood (or frequency) of certain events and risks. You were free to come up with your own evidence (or statements) to make these judgments. This is where a heuristic crops up. As a judgment shortcut, we tend to generate specific examples of those very events to help us decide their likelihood or frequency. For example, if we are asked to judge how common, frequent, or likely a particular type of cancer is, many of our statements would be examples of specific cancer cases:

Statement #1: Andy Kaufman (comedian) had lung cancer.

Statement #2: Colin Powell (US Secretary of State) had prostate cancer.

Statement #3: Bob Marley (musician) had skin and brain cancer

Statement #4: Sandra Day O’Connor (Supreme Court Justice) had breast cancer.

Statement #5: Fred Rogers (children’s entertainer) had stomach cancer.

Statement #6: Robin Roberts (news anchor) had breast cancer.

Statement #7: Bette Davis (actress) had breast cancer.

Judgment: Breast cancer is the most common type.

Your own experience or memory may also tell you that breast cancer is the most common type. But it is not (although it is common). Actually, skin cancer is the most common type in the US. We make the same types of misjudgments all the time because we do not generate the examples or evidence according to their actual frequencies or probabilities. Instead, we have a tendency (or bias) to search for the examples in memory; if they are easy to retrieve, we assume that they are common. To rephrase this in the language of the heuristic, events seem more likely to the extent that they are available to memory. This bias has been termed the  availability heuristic   (Kahneman and Tversky, 1974).

The fact that we use the availability heuristic does not automatically mean that our judgment is wrong. The reason we use heuristics in the first place is that they work fairly well in many cases (and, of course that they are easy to use). So, the easiest examples to think of sometimes are the most common ones. Is it more likely that a member of the U.S. Senate is a man or a woman? Most people have a much easier time generating examples of male senators. And as it turns out, the U.S. Senate has many more men than women (74 to 26 in 2020). In this case, then, the availability heuristic would lead you to make the correct judgment; it is far more likely that a senator would be a man.

In many other cases, however, the availability heuristic will lead us astray. This is because events can be memorable for many reasons other than their frequency. Section 5.2, Encoding Meaning, suggested that one good way to encode the meaning of some information is to form a mental image of it. Thus, information that has been pictured mentally will be more available to memory. Indeed, an event that is vivid and easily pictured will trick many people into supposing that type of event is more common than it actually is. Repetition of information will also make it more memorable. So, if the same event is described to you in a magazine, on the evening news, on a podcast that you listen to, and in your Facebook feed; it will be very available to memory. Again, the availability heuristic will cause you to misperceive the frequency of these types of events.

Most interestingly, information that is unusual is more memorable. Suppose we give you the following list of words to remember: box, flower, letter, platypus, oven, boat, newspaper, purse, drum, car. Very likely, the easiest word to remember would be platypus, the unusual one. The same thing occurs with memories of events. An event may be available to memory because it is unusual, yet the availability heuristic leads us to judge that the event is common. Did you catch that? In these cases, the availability heuristic makes us think the exact opposite of the true frequency. We end up thinking something is common because it is unusual (and therefore memorable). Yikes.

The misapplication of the availability heuristic sometimes has unfortunate results. For example, if you went to K-12 school in the US over the past 10 years, it is extremely likely that you have participated in lockdown and active shooter drills. Of course, everyone is trying to prevent the tragedy of another school shooting. And believe us, we are not trying to minimize how terrible the tragedy is. But the truth of the matter is, school shootings are extremely rare. Because the federal government does not keep a database of school shootings, the Washington Post has maintained their own running tally. Between 1999 and January 2020 (the date of the most recent school shooting with a death in the US at of the time this paragraph was written), the Post reported a total of 254 people died in school shootings in the US. Not 254 per year, 254 total. That is an average of 12 per year. Of course, that is 254 people who should not have died (particularly because many were children), but in a country with approximately 60,000,000 students and teachers, this is a very small risk.

But many students and teachers are terrified that they will be victims of school shootings because of the availability heuristic. It is so easy to think of examples (they are very available to memory) that people believe the event is very common. It is not. And there is a downside to this. We happen to believe that there is an enormous gun violence problem in the United States. According the the Centers for Disease Control and Prevention, there were 39,773 firearm deaths in the US in 2017. Fifteen of those deaths were in school shootings, according to the Post. 60% of those deaths were suicides. When people pay attention to the school shooting risk (low), they often fail to notice the much larger risk.

And examples like this are by no means unique. The authors of this book have been teaching psychology since the 1990’s. We have been able to make the exact same arguments about the misapplication of the availability heuristics and keep them current by simply swapping out for the “fear of the day.” In the 1990’s it was children being kidnapped by strangers (it was known as “stranger danger”) despite the facts that kidnappings accounted for only 2% of the violent crimes committed against children, and only 24% of kidnappings are committed by strangers (US Department of Justice, 2007). This fear overlapped with the fear of terrorism that gripped the country after the 2001 terrorist attacks on the World Trade Center and US Pentagon and still plagues the population of the US somewhat in 2020. After a well-publicized, sensational act of violence, people are extremely likely to increase their estimates of the chances that they, too, will be victims of terror. Think about the reality, however. In October of 2001, a terrorist mailed anthrax spores to members of the US government and a number of media companies. A total of five people died as a result of this attack. The nation was nearly paralyzed by the fear of dying from the attack; in reality the probability of an individual person dying was 0.00000002.

The availability heuristic can lead you to make incorrect judgments in a school setting as well. For example, suppose you are trying to decide if you should take a class from a particular math professor. You might try to make a judgment of how good a teacher she is by recalling instances of friends and acquaintances making comments about her teaching skill. You may have some examples that suggest that she is a poor teacher very available to memory, so on the basis of the availability heuristic you judge her a poor teacher and decide to take the class from someone else. What if, however, the instances you recalled were all from the same person, and this person happens to be a very colorful storyteller? The subsequent ease of remembering the instances might not indicate that the professor is a poor teacher after all.

Although the availability heuristic is obviously important, it is not the only judgment heuristic we use. Amos Tversky and Daniel Kahneman examined the role of heuristics in inductive reasoning in a long series of studies. Kahneman received a Nobel Prize in Economics for this research in 2002, and Tversky would have certainly received one as well if he had not died of melanoma at age 59 in 1996 (Nobel Prizes are not awarded posthumously). Kahneman and Tversky demonstrated repeatedly that people do not reason in ways that are consistent with the laws of probability. They identified several heuristic strategies that people use instead to make judgments about likelihood. The importance of this work for economics (and the reason that Kahneman was awarded the Nobel Prize) is that earlier economic theories had assumed that people do make judgments rationally, that is, in agreement with the laws of probability.

Another common heuristic that people use for making judgments is the  representativeness heuristic (Kahneman & Tversky 1973). Suppose we describe a person to you. He is quiet and shy, has an unassuming personality, and likes to work with numbers. Is this person more likely to be an accountant or an attorney? If you said accountant, you were probably using the representativeness heuristic. Our imaginary person is judged likely to be an accountant because he resembles, or is representative of the concept of, an accountant. When research participants are asked to make judgments such as these, the only thing that seems to matter is the representativeness of the description. For example, if told that the person described is in a room that contains 70 attorneys and 30 accountants, participants will still assume that he is an accountant.

inductive reasoning :  a type of reasoning in which we make judgments about likelihood from sets of evidence

inductively strong argument :  an inductive argument in which the beginning statements lead to a conclusion that is probably true

heuristic :  a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

availability heuristic :  judging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

representativeness heuristic:   judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

Type 1 thinking : fast, automatic, and emotional thinking.

Type 2 thinking : slow, effortful, and logical thinking.

• What percentage of workplace homicides are co-worker violence?

Many people get these questions wrong. The answers are 10%; stairs; skin; 6%. How close were your answers? Explain how the availability heuristic might have led you to make the incorrect judgments.

• Can you think of some other judgments that you have made (or beliefs that you have) that might have been influenced by the availability heuristic?

7.3 Problem Solving

• Please take a few minutes to list a number of problems that you are facing right now.
• Now write about a problem that you recently solved.
• What is your definition of a problem?

Mary has a problem. Her daughter, ordinarily quite eager to please, appears to delight in being the last person to do anything. Whether getting ready for school, going to piano lessons or karate class, or even going out with her friends, she seems unwilling or unable to get ready on time. Other people have different kinds of problems. For example, many students work at jobs, have numerous family commitments, and are facing a course schedule full of difficult exams, assignments, papers, and speeches. How can they find enough time to devote to their studies and still fulfill their other obligations? Speaking of students and their problems: Show that a ball thrown vertically upward with initial velocity v0 takes twice as much time to return as to reach the highest point (from Spiegel, 1981).

These are three very different situations, but we have called them all problems. What makes them all the same, despite the differences? A psychologist might define a  problem   as a situation with an initial state, a goal state, and a set of possible intermediate states. Somewhat more meaningfully, we might consider a problem a situation in which you are in here one state (e.g., daughter is always late), you want to be there in another state (e.g., daughter is not always late), and with no obvious way to get from here to there. Defined this way, each of the three situations we outlined can now be seen as an example of the same general concept, a problem. At this point, you might begin to wonder what is not a problem, given such a general definition. It seems that nearly every non-routine task we engage in could qualify as a problem. As long as you realize that problems are not necessarily bad (it can be quite fun and satisfying to rise to the challenge and solve a problem), this may be a useful way to think about it.

Can we identify a set of problem-solving skills that would apply to these very different kinds of situations? That task, in a nutshell, is a major goal of this section. Let us try to begin to make sense of the wide variety of ways that problems can be solved with an important observation: the process of solving problems can be divided into two key parts. First, people have to notice, comprehend, and represent the problem properly in their minds (called  problem representation ). Second, they have to apply some kind of solution strategy to the problem. Psychologists have studied both of these key parts of the process in detail.

When you first think about the problem-solving process, you might guess that most of our difficulties would occur because we are failing in the second step, the application of strategies. Although this can be a significant difficulty much of the time, the more important source of difficulty is probably problem representation. In short, we often fail to solve a problem because we are looking at it, or thinking about it, the wrong way.

problem :  a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

problem representation :  noticing, comprehending and forming a mental conception of a problem

Defining and Mentally Representing Problems in Order to Solve Them

So, the main obstacle to solving a problem is that we do not clearly understand exactly what the problem is. Recall the problem with Mary’s daughter always being late. One way to represent, or to think about, this problem is that she is being defiant. She refuses to get ready in time. This type of representation or definition suggests a particular type of solution. Another way to think about the problem, however, is to consider the possibility that she is simply being sidetracked by interesting diversions. This different conception of what the problem is (i.e., different representation) suggests a very different solution strategy. For example, if Mary defines the problem as defiance, she may be tempted to solve the problem using some kind of coercive tactics, that is, to assert her authority as her mother and force her to listen. On the other hand, if Mary defines the problem as distraction, she may try to solve it by simply removing the distracting objects.

As you might guess, when a problem is represented one way, the solution may seem very difficult, or even impossible. Seen another way, the solution might be very easy. For example, consider the following problem (from Nasar, 1998):

Two bicyclists start 20 miles apart and head toward each other, each going at a steady rate of 10 miles per hour. At the same time, a fly that travels at a steady 15 miles per hour starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner until he is crushed between the two front wheels. Question: what total distance did the fly cover?

Please take a few minutes to try to solve this problem.

Most people represent this problem as a question about a fly because, well, that is how the question is asked. The solution, using this representation, is to figure out how far the fly travels on the first leg of its journey, then add this total to how far it travels on the second leg of its journey (when it turns around and returns to the first bicycle), then continue to add the smaller distance from each leg of the journey until you converge on the correct answer. You would have to be quite skilled at math to solve this problem, and you would probably need some time and pencil and paper to do it.

If you consider a different representation, however, you can solve this problem in your head. Instead of thinking about it as a question about a fly, think about it as a question about the bicycles. They are 20 miles apart, and each is traveling 10 miles per hour. How long will it take for the bicycles to reach each other? Right, one hour. The fly is traveling 15 miles per hour; therefore, it will travel a total of 15 miles back and forth in the hour before the bicycles meet. Represented one way (as a problem about a fly), the problem is quite difficult. Represented another way (as a problem about two bicycles), it is easy. Changing your representation of a problem is sometimes the best—sometimes the only—way to solve it.

Unfortunately, however, changing a problem’s representation is not the easiest thing in the world to do. Often, problem solvers get stuck looking at a problem one way. This is called  fixation . Most people who represent the preceding problem as a problem about a fly probably do not pause to reconsider, and consequently change, their representation. A parent who thinks her daughter is being defiant is unlikely to consider the possibility that her behavior is far less purposeful.

Problem-solving fixation was examined by a group of German psychologists called Gestalt psychologists during the 1930’s and 1940’s. Karl Dunker, for example, discovered an important type of failure to take a different perspective called  functional fixedness . Imagine being a participant in one of his experiments. You are asked to figure out how to mount two candles on a door and are given an assortment of odds and ends, including a small empty cardboard box and some thumbtacks. Perhaps you have already figured out a solution: tack the box to the door so it forms a platform, then put the candles on top of the box. Most people are able to arrive at this solution. Imagine a slight variation of the procedure, however. What if, instead of being empty, the box had matches in it? Most people given this version of the problem do not arrive at the solution given above. Why? Because it seems to people that when the box contains matches, it already has a function; it is a matchbox. People are unlikely to consider a new function for an object that already has a function. This is functional fixedness.

Mental set is a type of fixation in which the problem solver gets stuck using the same solution strategy that has been successful in the past, even though the solution may no longer be useful. It is commonly seen when students do math problems for homework. Often, several problems in a row require the reapplication of the same solution strategy. Then, without warning, the next problem in the set requires a new strategy. Many students attempt to apply the formerly successful strategy on the new problem and therefore cannot come up with a correct answer.

The thing to remember is that you cannot solve a problem unless you correctly identify what it is to begin with (initial state) and what you want the end result to be (goal state). That may mean looking at the problem from a different angle and representing it in a new way. The correct representation does not guarantee a successful solution, but it certainly puts you on the right track.

A bit more optimistically, the Gestalt psychologists discovered what may be considered the opposite of fixation, namely  insight . Sometimes the solution to a problem just seems to pop into your head. Wolfgang Kohler examined insight by posing many different problems to chimpanzees, principally problems pertaining to their acquisition of out-of-reach food. In one version, a banana was placed outside of a chimpanzee’s cage and a short stick inside the cage. The stick was too short to retrieve the banana, but was long enough to retrieve a longer stick also located outside of the cage. This second stick was long enough to retrieve the banana. After trying, and failing, to reach the banana with the shorter stick, the chimpanzee would try a couple of random-seeming attempts, react with some apparent frustration or anger, then suddenly rush to the longer stick, the correct solution fully realized at this point. This sudden appearance of the solution, observed many times with many different problems, was termed insight by Kohler.

Lest you think it pertains to chimpanzees only, Karl Dunker demonstrated that children also solve problems through insight in the 1930s. More importantly, you have probably experienced insight yourself. Think back to a time when you were trying to solve a difficult problem. After struggling for a while, you gave up. Hours later, the solution just popped into your head, perhaps when you were taking a walk, eating dinner, or lying in bed.

fixation :  when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

functional fixedness :  a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

mental set :  a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

insight :  a sudden realization of a solution to a problem

Solving Problems by Trial and Error

Correctly identifying the problem and your goal for a solution is a good start, but recall the psychologist’s definition of a problem: it includes a set of possible intermediate states. Viewed this way, a problem can be solved satisfactorily only if one can find a path through some of these intermediate states to the goal. Imagine a fairly routine problem, finding a new route to school when your ordinary route is blocked (by road construction, for example). At each intersection, you may turn left, turn right, or go straight. A satisfactory solution to the problem (of getting to school) is a sequence of selections at each intersection that allows you to wind up at school.

If you had all the time in the world to get to school, you might try choosing intermediate states randomly. At one corner you turn left, the next you go straight, then you go left again, then right, then right, then straight. Unfortunately, trial and error will not necessarily get you where you want to go, and even if it does, it is not the fastest way to get there. For example, when a friend of ours was in college, he got lost on the way to a concert and attempted to find the venue by choosing streets to turn onto randomly (this was long before the use of GPS). Amazingly enough, the strategy worked, although he did end up missing two out of the three bands who played that night.

Trial and error is not all bad, however. B.F. Skinner, a prominent behaviorist psychologist, suggested that people often behave randomly in order to see what effect the behavior has on the environment and what subsequent effect this environmental change has on them. This seems particularly true for the very young person. Picture a child filling a household’s fish tank with toilet paper, for example. To a child trying to develop a repertoire of creative problem-solving strategies, an odd and random behavior might be just the ticket. Eventually, the exasperated parent hopes, the child will discover that many of these random behaviors do not successfully solve problems; in fact, in many cases they create problems. Thus, one would expect a decrease in this random behavior as a child matures. You should realize, however, that the opposite extreme is equally counterproductive. If the children become too rigid, never trying something unexpected and new, their problem solving skills can become too limited.

Effective problem solving seems to call for a happy medium that strikes a balance between using well-founded old strategies and trying new ground and territory. The individual who recognizes a situation in which an old problem-solving strategy would work best, and who can also recognize a situation in which a new untested strategy is necessary is halfway to success.

Solving Problems with Algorithms and Heuristics

For many problems there is a possible strategy available that will guarantee a correct solution. For example, think about math problems. Math lessons often consist of step-by-step procedures that can be used to solve the problems. If you apply the strategy without error, you are guaranteed to arrive at the correct solution to the problem. This approach is called using an  algorithm , a term that denotes the step-by-step procedure that guarantees a correct solution. Because algorithms are sometimes available and come with a guarantee, you might think that most people use them frequently. Unfortunately, however, they do not. As the experience of many students who have struggled through math classes can attest, algorithms can be extremely difficult to use, even when the problem solver knows which algorithm is supposed to work in solving the problem. In problems outside of math class, we often do not even know if an algorithm is available. It is probably fair to say, then, that algorithms are rarely used when people try to solve problems.

Because algorithms are so difficult to use, people often pass up the opportunity to guarantee a correct solution in favor of a strategy that is much easier to use and yields a reasonable chance of coming up with a correct solution. These strategies are called  problem solving heuristics . Similar to what you saw in section 6.2 with reasoning heuristics, a problem solving heuristic is a shortcut strategy that people use when trying to solve problems. It usually works pretty well, but does not guarantee a correct solution to the problem. For example, one problem solving heuristic might be “always move toward the goal” (so when trying to get to school when your regular route is blocked, you would always turn in the direction you think the school is). A heuristic that people might use when doing math homework is “use the same solution strategy that you just used for the previous problem.”

By the way, we hope these last two paragraphs feel familiar to you. They seem to parallel a distinction that you recently learned. Indeed, algorithms and problem-solving heuristics are another example of the distinction between Type 1 thinking and Type 2 thinking.

Although it is probably not worth describing a large number of specific heuristics, two observations about heuristics are worth mentioning. First, heuristics can be very general or they can be very specific, pertaining to a particular type of problem only. For example, “always move toward the goal” is a general strategy that you can apply to countless problem situations. On the other hand, “when you are lost without a functioning gps, pick the most expensive car you can see and follow it” is specific to the problem of being lost. Second, all heuristics are not equally useful. One heuristic that many students know is “when in doubt, choose c for a question on a multiple-choice exam.” This is a dreadful strategy because many instructors intentionally randomize the order of answer choices. Another test-taking heuristic, somewhat more useful, is “look for the answer to one question somewhere else on the exam.”

You really should pay attention to the application of heuristics to test taking. Imagine that while reviewing your answers for a multiple-choice exam before turning it in, you come across a question for which you originally thought the answer was c. Upon reflection, you now think that the answer might be b. Should you change the answer to b, or should you stick with your first impression? Most people will apply the heuristic strategy to “stick with your first impression.” What they do not realize, of course, is that this is a very poor strategy (Lilienfeld et al, 2009). Most of the errors on exams come on questions that were answered wrong originally and were not changed (so they remain wrong). There are many fewer errors where we change a correct answer to an incorrect answer. And, of course, sometimes we change an incorrect answer to a correct answer. In fact, research has shown that it is more common to change a wrong answer to a right answer than vice versa (Bruno, 2001).

The belief in this poor test-taking strategy (stick with your first impression) is based on the  confirmation bias   (Nickerson, 1998; Wason, 1960). You first saw the confirmation bias in Module 1, but because it is so important, we will repeat the information here. People have a bias, or tendency, to notice information that confirms what they already believe. Somebody at one time told you to stick with your first impression, so when you look at the results of an exam you have taken, you will tend to notice the cases that are consistent with that belief. That is, you will notice the cases in which you originally had an answer correct and changed it to the wrong answer. You tend not to notice the other two important (and more common) cases, changing an answer from wrong to right, and leaving a wrong answer unchanged.

Because heuristics by definition do not guarantee a correct solution to a problem, mistakes are bound to occur when we employ them. A poor choice of a specific heuristic will lead to an even higher likelihood of making an error.

algorithm :  a step-by-step procedure that guarantees a correct solution to a problem

problem solving heuristic :  a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

confirmation bias :  people’s tendency to notice information that confirms what they already believe

An Effective Problem-Solving Sequence

You may be left with a big question: If algorithms are hard to use and heuristics often don’t work, how am I supposed to solve problems? Robert Sternberg (1996), as part of his theory of what makes people successfully intelligent (Module 8) described a problem-solving sequence that has been shown to work rather well:

• Identify the existence of a problem.  In school, problem identification is often easy; problems that you encounter in math classes, for example, are conveniently labeled as problems for you. Outside of school, however, realizing that you have a problem is a key difficulty that you must get past in order to begin solving it. You must be very sensitive to the symptoms that indicate a problem.
• Define the problem.  Suppose you realize that you have been having many headaches recently. Very likely, you would identify this as a problem. If you define the problem as “headaches,” the solution would probably be to take aspirin or ibuprofen or some other anti-inflammatory medication. If the headaches keep returning, however, you have not really solved the problem—likely because you have mistaken a symptom for the problem itself. Instead, you must find the root cause of the headaches. Stress might be the real problem. For you to successfully solve many problems it may be necessary for you to overcome your fixations and represent the problems differently. One specific strategy that you might find useful is to try to define the problem from someone else’s perspective. How would your parents, spouse, significant other, doctor, etc. define the problem? Somewhere in these different perspectives may lurk the key definition that will allow you to find an easier and permanent solution.
• Formulate strategy.  Now it is time to begin planning exactly how the problem will be solved. Is there an algorithm or heuristic available for you to use? Remember, heuristics by their very nature guarantee that occasionally you will not be able to solve the problem. One point to keep in mind is that you should look for long-range solutions, which are more likely to address the root cause of a problem than short-range solutions.
• Represent and organize information.  Similar to the way that the problem itself can be defined, or represented in multiple ways, information within the problem is open to different interpretations. Suppose you are studying for a big exam. You have chapters from a textbook and from a supplemental reader, along with lecture notes that all need to be studied. How should you (represent and) organize these materials? Should you separate them by type of material (text versus reader versus lecture notes), or should you separate them by topic? To solve problems effectively, you must learn to find the most useful representation and organization of information.
• Allocate resources.  This is perhaps the simplest principle of the problem solving sequence, but it is extremely difficult for many people. First, you must decide whether time, money, skills, effort, goodwill, or some other resource would help to solve the problem Then, you must make the hard choice of deciding which resources to use, realizing that you cannot devote maximum resources to every problem. Very often, the solution to problem is simply to change how resources are allocated (for example, spending more time studying in order to improve grades).
• Monitor and evaluate solutions.  Pay attention to the solution strategy while you are applying it. If it is not working, you may be able to select another strategy. Another fact you should realize about problem solving is that it never does end. Solving one problem frequently brings up new ones. Good monitoring and evaluation of your problem solutions can help you to anticipate and get a jump on solving the inevitable new problems that will arise.

Please note that this as  an  effective problem-solving sequence, not  the  effective problem solving sequence. Just as you can become fixated and end up representing the problem incorrectly or trying an inefficient solution, you can become stuck applying the problem-solving sequence in an inflexible way. Clearly there are problem situations that can be solved without using these skills in this order.

Additionally, many real-world problems may require that you go back and redefine a problem several times as the situation changes (Sternberg et al. 2000). For example, consider the problem with Mary’s daughter one last time. At first, Mary did represent the problem as one of defiance. When her early strategy of pleading and threatening punishment was unsuccessful, Mary began to observe her daughter more carefully. She noticed that, indeed, her daughter’s attention would be drawn by an irresistible distraction or book. Fresh with a re-representation of the problem, she began a new solution strategy. She began to remind her daughter every few minutes to stay on task and remind her that if she is ready before it is time to leave, she may return to the book or other distracting object at that time. Fortunately, this strategy was successful, so Mary did not have to go back and redefine the problem again.

Pick one or two of the problems that you listed when you first started studying this section and try to work out the steps of Sternberg’s problem solving sequence for each one.

a mental representation of a category of things in the world

an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

knowledge about one’s own cognitive processes; thinking about your thinking

individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

Thinking like a scientist in your everyday life for the purpose of drawing correct conclusions. It entails skepticism; an ability to identify biases, distortions, omissions, and assumptions; and excellent deductive and inductive reasoning, and problem solving skills.

a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

an inclination, tendency, leaning, or prejudice

a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

a set of statements in which the beginning statements lead to a conclusion

an argument for which true beginning statements guarantee that the conclusion is true

a type of reasoning in which we make judgments about likelihood from sets of evidence

an inductive argument in which the beginning statements lead to a conclusion that is probably true

fast, automatic, and emotional thinking

slow, effortful, and logical thinking

a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

udging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

noticing, comprehending and forming a mental conception of a problem

when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

a sudden realization of a solution to a problem

a step-by-step procedure that guarantees a correct solution to a problem

The tendency to notice and pay attention to information that confirms your prior beliefs and to ignore information that disconfirms them.

a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

Introduction to Psychology Copyright © 2020 by Ken Gray; Elizabeth Arnott-Hill; and Or'Shaundra Benson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Definition:

Problem Solving is the process of identifying, analyzing, and finding effective solutions to complex issues or challenges.

Key Steps in Problem Solving:

• Identification of the problem: Recognizing and clearly defining the issue that needs to be resolved.
• Analysis and research: Gathering relevant information, data, and facts to understand the problem in-depth.
• Formulating strategies: Developing various approaches and plans to tackle the problem effectively.
• Evaluation and selection: Assessing the viability and potential outcomes of the proposed solutions and selecting the most appropriate one.
• Implementation: Putting the chosen solution into action and executing the necessary steps to resolve the problem.
• Monitoring and feedback: Continuously evaluating the implemented solution and obtaining feedback to ensure its effectiveness.
• Adaptation and improvement: Modifying and refining the solution as needed to optimize results and prevent similar problems from arising in the future.

Skills and Qualities for Effective Problem Solving:

• Analytical thinking: The ability to break down complex problems into smaller, manageable components and analyze them thoroughly.
• Creativity: Thinking outside the box and generating innovative solutions.
• Decision making: Making logical and informed choices based on available data and critical thinking.
• Communication: Clearly conveying ideas, listening actively, and collaborating with others to solve problems as a team.
• Resilience: Maintaining a positive mindset, perseverance, and adaptability in the face of challenges.
• Resourcefulness: Utilizing available resources and seeking new approaches when confronted with obstacles.
• Time management: Effectively organizing and prioritizing tasks to optimize problem-solving efficiency.

Problem Solving

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• Cite this reference work entry

• David H. Jonassen 2 &
• Woei Hung 3  

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Cognition ; Problem typology ; Problem-based learning ; Problems ; Reasoning

Problem solving is the process of constructing and applying mental representations of problems to finding solutions to those problems that are encountered in nearly every context.

Theoretical Background

Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to vexing and complex social problems, such as violence in society (see Problem Typology ). Second, finding or solving for the unknown must have some social, cultural, or intellectual value. That is, someone believes that it is worth finding the unknown. If no one perceives an unknown or a need to determine an unknown, there is no perceived problem. Finding...

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10 Best Problem-Solving Therapy Worksheets & Activities

Cognitive science tells us that we regularly face not only well-defined problems but, importantly, many that are ill defined (Eysenck & Keane, 2015).

Sometimes, we find ourselves unable to overcome our daily problems or the inevitable (though hopefully infrequent) life traumas we face.

Problem-Solving Therapy aims to reduce the incidence and impact of mental health disorders and improve wellbeing by helping clients face life’s difficulties (Dobson, 2011).

This article introduces Problem-Solving Therapy and offers techniques, activities, and worksheets that mental health professionals can use with clients.

Before you continue, we thought you might like to download our three Positive Psychology Exercises for free . These science-based exercises explore fundamental aspects of positive psychology, including strengths, values, and self-compassion, and will give you the tools to enhance the wellbeing of your clients, students, or employees.

This Article Contains:

What is problem-solving therapy, 14 steps for problem-solving therapy, 3 best interventions and techniques, 7 activities and worksheets for your session, fascinating books on the topic, resources from positivepsychology.com, a take-home message.

Problem-Solving Therapy assumes that mental disorders arise in response to ineffective or maladaptive coping. By adopting a more realistic and optimistic view of coping, individuals can understand the role of emotions and develop actions to reduce distress and maintain mental wellbeing (Nezu & Nezu, 2009).

“Problem-solving therapy (PST) is a psychosocial intervention, generally considered to be under a cognitive-behavioral umbrella” (Nezu, Nezu, & D’Zurilla, 2013, p. ix). It aims to encourage the client to cope better with day-to-day problems and traumatic events and reduce their impact on mental and physical wellbeing.

Clinical research, counseling, and health psychology have shown PST to be highly effective in clients of all ages, ranging from children to the elderly, across multiple clinical settings, including schizophrenia, stress, and anxiety disorders (Dobson, 2011).

Can it help with depression?

PST appears particularly helpful in treating clients with depression. A recent analysis of 30 studies found that PST was an effective treatment with a similar degree of success as other successful therapies targeting depression (Cuijpers, Wit, Kleiboer, Karyotaki, & Ebert, 2020).

Other studies confirm the value of PST and its effectiveness at treating depression in multiple age groups and its capacity to combine with other therapies, including drug treatments (Dobson, 2011).

The major concepts

Effective coping varies depending on the situation, and treatment typically focuses on improving the environment and reducing emotional distress (Dobson, 2011).

PST is based on two overlapping models:

Social problem-solving model

This model focuses on solving the problem “as it occurs in the natural social environment,” combined with a general coping strategy and a method of self-control (Dobson, 2011, p. 198).

The model includes three central concepts:

• Social problem-solving
• The problem
• The solution

The model is a “self-directed cognitive-behavioral process by which an individual, couple, or group attempts to identify or discover effective solutions for specific problems encountered in everyday living” (Dobson, 2011, p. 199).

Relational problem-solving model

The theory of PST is underpinned by a relational problem-solving model, whereby stress is viewed in terms of the relationships between three factors:

• Stressful life events
• Emotional distress and wellbeing
• Problem-solving coping

Therefore, when a significant adverse life event occurs, it may require “sweeping readjustments in a person’s life” (Dobson, 2011, p. 202).

• Enhance positive problem orientation
• Decrease negative orientation
• Foster ability to apply rational problem-solving skills
• Reduce the tendency to avoid problem-solving
• Minimize the tendency to be careless and impulsive

D’Zurilla’s and Nezu’s model includes (modified from Dobson, 2011):

• Initial structuring Establish a positive therapeutic relationship that encourages optimism and explains the PST approach.
• Assessment Formally and informally assess areas of stress in the client’s life and their problem-solving strengths and weaknesses.
• Obstacles to effective problem-solving Explore typically human challenges to problem-solving, such as multitasking and the negative impact of stress. Introduce tools that can help, such as making lists, visualization, and breaking complex problems down.
• Problem orientation – fostering self-efficacy Introduce the importance of a positive problem orientation, adopting tools, such as visualization, to promote self-efficacy.
• Problem orientation – recognizing problems Help clients recognize issues as they occur and use problem checklists to ‘normalize’ the experience.
• Problem orientation – seeing problems as challenges Encourage clients to break free of harmful and restricted ways of thinking while learning how to argue from another point of view.
• Problem orientation – use and control emotions Help clients understand the role of emotions in problem-solving, including using feelings to inform the process and managing disruptive emotions (such as cognitive reframing and relaxation exercises).
• Problem orientation – stop and think Teach clients how to reduce impulsive and avoidance tendencies (visualizing a stop sign or traffic light).
• Problem definition and formulation Encourage an understanding of the nature of problems and set realistic goals and objectives.
• Generation of alternatives Work with clients to help them recognize the wide range of potential solutions to each problem (for example, brainstorming).
• Decision-making Encourage better decision-making through an improved understanding of the consequences of decisions and the value and likelihood of different outcomes.
• Solution implementation and verification Foster the client’s ability to carry out a solution plan, monitor its outcome, evaluate its effectiveness, and use self-reinforcement to increase the chance of success.
• Guided practice Encourage the application of problem-solving skills across multiple domains and future stressful problems.
• Rapid problem-solving Teach clients how to apply problem-solving questions and guidelines quickly in any given situation.

Success in PST depends on the effectiveness of its implementation; using the right approach is crucial (Dobson, 2011).

Problem-solving therapy – Baycrest

The following interventions and techniques are helpful when implementing more effective problem-solving approaches in client’s lives.

First, it is essential to consider if PST is the best approach for the client, based on the problems they present.

Is PPT appropriate?

It is vital to consider whether PST is appropriate for the client’s situation. Therapists new to the approach may require additional guidance (Nezu et al., 2013).

Therapists should consider the following questions before beginning PST with a client (modified from Nezu et al., 2013):

• Has PST proven effective in the past for the problem? For example, research has shown success with depression, generalized anxiety, back pain, Alzheimer’s disease, cancer, and supporting caregivers (Nezu et al., 2013).
• Is PST acceptable to the client?
• Is the individual experiencing a significant mental or physical health problem?

All affirmative answers suggest that PST would be a helpful technique to apply in this instance.

Five problem-solving steps

The following five steps are valuable when working with clients to help them cope with and manage their environment (modified from Dobson, 2011).

Ask the client to consider the following points (forming the acronym ADAPT) when confronted by a problem:

• Attitude Aim to adopt a positive, optimistic attitude to the problem and problem-solving process.
• Define Obtain all required facts and details of potential obstacles to define the problem.
• Alternatives Identify various alternative solutions and actions to overcome the obstacle and achieve the problem-solving goal.
• Predict Predict each alternative’s positive and negative outcomes and choose the one most likely to achieve the goal and maximize the benefits.
• Try out Once selected, try out the solution and monitor its effectiveness while engaging in self-reinforcement.

If the client is not satisfied with their solution, they can return to step ‘A’ and find a more appropriate solution.

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Positive self-statements

When dealing with clients facing negative self-beliefs, it can be helpful for them to use positive self-statements.

Use the following (or add new) self-statements to replace harmful, negative thinking (modified from Dobson, 2011):

• I can solve this problem; I’ve tackled similar ones before.
• I can cope with this.
• I just need to take a breath and relax.
• Once I start, it will be easier.
• It’s okay to look out for myself.
• I can get help if needed.
• Other people feel the same way I do.
• I’ll take one piece of the problem at a time.
• I can keep my fears in check.
• I don’t need to please everyone.

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PST practitioners have many different techniques available to support clients as they learn to tackle day-to-day or one-off trauma.

5 Worksheets and workbooks

Problem-solving self-monitoring form.

Ask the client to complete the following:

• Describe the problem you are facing.
• What is your goal?
• What have you tried so far to solve the problem?
• What was the outcome?

Reactions to Stress

It can be helpful for the client to recognize their own experiences of stress. Do they react angrily, withdraw, or give up (Dobson, 2011)?

The Reactions to Stress worksheet can be given to the client as homework to capture stressful events and their reactions. By recording how they felt, behaved, and thought, they can recognize repeating patterns.

What Are Your Unique Triggers?

Helping clients capture triggers for their stressful reactions can encourage emotional regulation.

When clients can identify triggers that may lead to a negative response, they can stop the experience or slow down their emotional reaction (Dobson, 2011).

The What Are Your Unique Triggers ? worksheet helps the client identify their triggers (e.g., conflict, relationships, physical environment, etc.).

Problem-Solving worksheet

Imagining an existing or potential problem and working through how to resolve it can be a powerful exercise for the client.

Use the Problem-Solving worksheet to state a problem and goal and consider the obstacles in the way. Then explore options for achieving the goal, along with their pros and cons, to assess the best action plan.

Getting the Facts

Clients can become better equipped to tackle problems and choose the right course of action by recognizing facts versus assumptions and gathering all the necessary information (Dobson, 2011).

Use the Getting the Facts worksheet to answer the following questions clearly and unambiguously:

• Who is involved?
• What did or did not happen, and how did it bother you?
• Where did it happen?
• When did it happen?
• Why did it happen?
• How did you respond?

2 Helpful Group Activities

While therapists can use the worksheets above in group situations, the following two interventions work particularly well with more than one person.

Generating Alternative Solutions and Better Decision-Making

A group setting can provide an ideal opportunity to share a problem and identify potential solutions arising from multiple perspectives.

Use the Generating Alternative Solutions and Better Decision-Making worksheet and ask the client to explain the situation or problem to the group and the obstacles in the way.

Once the approaches are captured and reviewed, the individual can share their decision-making process with the group if they want further feedback.

Visualization

Visualization can be performed with individuals or in a group setting to help clients solve problems in multiple ways, including (Dobson, 2011):

• Clarifying the problem by looking at it from multiple perspectives
• Rehearsing a solution in the mind to improve and get more practice
• Visualizing a ‘safe place’ for relaxation, slowing down, and stress management

Guided imagery is particularly valuable for encouraging the group to take a ‘mental vacation’ and let go of stress.

Ask the group to begin with slow, deep breathing that fills the entire diaphragm. Then ask them to visualize a favorite scene (real or imagined) that makes them feel relaxed, perhaps beside a gently flowing river, a summer meadow, or at the beach.

The more the senses are engaged, the more real the experience. Ask the group to think about what they can hear, see, touch, smell, and even taste.

Encourage them to experience the situation as fully as possible, immersing themselves and enjoying their place of safety.

Such feelings of relaxation may be able to help clients fall asleep, relieve stress, and become more ready to solve problems.

We have included three of our favorite books on the subject of Problem-Solving Therapy below.

1. Problem-Solving Therapy: A Treatment Manual – Arthur Nezu, Christine Maguth Nezu, and Thomas D’Zurilla

This is an incredibly valuable book for anyone wishing to understand the principles and practice behind PST.

Written by the co-developers of PST, the manual provides powerful toolkits to overcome cognitive overload, emotional dysregulation, and the barriers to practical problem-solving.

Find the book on Amazon .

2. Emotion-Centered Problem-Solving Therapy: Treatment Guidelines – Arthur Nezu and Christine Maguth Nezu

Another, more recent, book from the creators of PST, this text includes important advances in neuroscience underpinning the role of emotion in behavioral treatment.

Along with clinical examples, the book also includes crucial toolkits that form part of a stepped model for the application of PST.

3. Handbook of Cognitive-Behavioral Therapies – Keith Dobson and David Dozois

This is the fourth edition of a hugely popular guide to Cognitive-Behavioral Therapies and includes a valuable and insightful section on Problem-Solving Therapy.

This is an important book for students and more experienced therapists wishing to form a high-level and in-depth understanding of the tools and techniques available to Cognitive-Behavioral Therapists.

For even more tools to help strengthen your clients’ problem-solving skills, check out the following free worksheets from our blog.

• Case Formulation Worksheet This worksheet presents a four-step framework to help therapists and their clients come to a shared understanding of the client’s presenting problem.
• Understanding Your Default Problem-Solving Approach This worksheet poses a series of questions helping clients reflect on their typical cognitive, emotional, and behavioral responses to problems.
• Social Problem Solving: Step by Step This worksheet presents a streamlined template to help clients define a problem, generate possible courses of action, and evaluate the effectiveness of an implemented solution.

If you’re looking for more science-based ways to help others enhance their wellbeing, check out this signature collection of 17 validated positive psychology tools for practitioners. Use them to help others flourish and thrive.

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While we are born problem-solvers, facing an incredibly diverse set of challenges daily, we sometimes need support.

Problem-Solving Therapy aims to reduce stress and associated mental health disorders and improve wellbeing by improving our ability to cope. PST is valuable in diverse clinical settings, ranging from depression to schizophrenia, with research suggesting it as a highly effective treatment for teaching coping strategies and reducing emotional distress.

Many PST techniques are available to help improve clients’ positive outlook on obstacles while reducing avoidance of problem situations and the tendency to be careless and impulsive.

The PST model typically assesses the client’s strengths, weaknesses, and coping strategies when facing problems before encouraging a healthy experience of and relationship with problem-solving.

Why not use this article to explore the theory behind PST and try out some of our powerful tools and interventions with your clients to help them with their decision-making, coping, and problem-solving?

We hope you enjoyed reading this article. Don’t forget to download our three Positive Psychology Exercises for free .

• Cuijpers, P., Wit, L., Kleiboer, A., Karyotaki, E., & Ebert, D. (2020). Problem-solving therapy for adult depression: An updated meta-analysis. European P sychiatry ,  48 (1), 27–37.
• Dobson, K. S. (2011). Handbook of cognitive-behavioral therapies (3rd ed.). Guilford Press.
• Dobson, K. S., & Dozois, D. J. A. (2021). Handbook of cognitive-behavioral therapies  (4th ed.). Guilford Press.
• Eysenck, M. W., & Keane, M. T. (2015). Cognitive psychology: A student’s handbook . Psychology Press.
• Nezu, A. M., & Nezu, C. M. (2009). Problem-solving therapy DVD . Retrieved September 13, 2021, from https://www.apa.org/pubs/videos/4310852
• Nezu, A. M., & Nezu, C. M. (2018). Emotion-centered problem-solving therapy: Treatment guidelines. Springer.
• Nezu, A. M., Nezu, C. M., & D’Zurilla, T. J. (2013). Problem-solving therapy: A treatment manual . Springer.

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“One thing is sure. We have to do something. We have to do the best we know how at the moment… If it doesn’t turn out right, we can modify it as we go along.” –  Franklin D.Roosevelt

P roblems in life can take on a variety of forms, but many of them share common characteristics that serve as cues, alerting us to the presence of a bonafide problem. The attitude that we choose to take toward the problem can serve as a powerful determinant of our ability to reduce distress and use emotional information in helpful ways. Many of the problems or chaos that we invite , create, or have thrust upon us become less intimidating and paralyzing when we take a proactive stance toward solving them. A mindfully open and alert stance can serve as a stable foundation as you begin the process of confronting the problem and moving toward a solution.

Part of the wisdom inherent in effective problem solving is discerning between solvable and unsolvable problems … and being willing to radically accept and let go of those problems which are truly out of your control. For all of the problems that you have the power to solve, remember that quite often a puzzling or painful problem is actually just a very difficult decision that is waiting to be made. It is possible that the looming “problem” in your life has taken on its imposing or frightening form due to a conscious or unconscious un willingness on your part to make a tough decision.

Brief Mindfulness Exercise:

Before you begin the following five steps of problem solving from your base of mindfulness, allow yourself a few moments to slow down and take a some slow deep breaths. Bring your full awareness to this  moment. Allow your thoughts, emotions, and sensations to naturally emerge; notice them just as they are, accept their presence, and release them with each breath that leaves your lungs. If confusing or unsettling thoughts enter into awareness, observe them with an open heart and nonjudgmental mind. Allow yourself to become disentangled from those thoughts as you notice that they are just thoughts … not “facts” or absolute truth.

Notice your emotions as they arise naturally from within. Perhaps you sense a deep-seated fear as you approach this problem. Observe this experience and direct compassion toward your fear, anxiety , or doubt. Embrace your suffering , rather than push it away. Notice what useful information is embedded within those painful disavowed experiences. Observe any physical sensations that emerge at this time, reconnecting with your body . Direct your full awareness in a nonjudgmental, accepting, and curious way toward those sensations. Perhaps there is a tightness in your throat or chest, shaking in your hands, a racing heart, or queasiness at your core.

Be kind toward yourself and notice the delicate way that your thoughts, emotions, and sensations are all coming together in a nuanced dance as you approach solving this problem. Allow wise mind to guide you, bringing together reason with emotion, as you begin to become open, reflective, and alert to the problem. When you are ready, direct your mindful awareness and focus  completely to the problem you are facing. Remember that part of being mindful involves directing your full presence toward one thing at a time , so give yourself the gift of slowing down as you go through this five step process of problem solving.

Mindful Problem Solving

R ead through the following five steps of problem solving and write down your authentic responses at each step along the way. Let go of the notion of “right” or “wrong” responses and trust yourself . As you go through these steps, make a commitment to yourself to follow through with your plan. When you take the time to move through solving a difficult problem with an open heart and awakened mind, you may begin to see that the right path out of the woods was there all along… just waiting for you to notice it and summon the courage to make the journey.

(1) State your problem

Problems cannot be solved and decisions cannot be made effectively before you have clearly and accurately identified the problem. If this step is easy for you, simply write down in simple and concise terms exactly what problem you are facing. If it seems challenging to identify the problem, try writing down some characteristics of the problem or common themes. For example, “health issues: illness, sleep, diet, mental health” or “relationship issues: conflict, loneliness, dissatisfaction.”

Once you have clearly identified and stated your current problem, take the time to engage in a bit of “ problem analysis ” to help you understand the various dimensions of the problem with greater clarity:

• What is the problem?
• Who is involved?
• What happens? What bothers you?
• Where does the problem occur?
• When does it occur?
• How does it happen? (Is there a pattern ?)
• Why do you think it happens?
• What else is important in this situation?
• How do you respond to the situation? (List your behaviors .)
• How does it make you feel?
• What outcome do you want to see?

(2) Outline your solutions

Once you have sufficiently identified the problem from various perspectives, you are ready to start identifying the best solutions available. Maintain a mindfully open attitude as you approach potential solutions from a place of creativity. Even if your “ideal” solution may not be realistic at this present moment, stay open to making the most out of the tools you do  have to work with at this point in time. Notice if any potential solutions come to you as you reflect on your responses to the last three questions from step one, regarding what you do , what you feel , and what you truly want .

Try coming up with and writing down three possible solutions based on those responses. For example, possible solutions may be worded in some of the following ways: “Figure out better ways to respond when I feel confused or frozen by the problem,” or  “Learn how to manage intense emotions more effectively when the problem occurs,” or  “Deliver painful news or express authentic feelings , no matter how scary it may feel.”

As you begin to set goals that will move you closer to your desired solution , remember to describe what you do want  to happen, as opposed to what you don’t want  to happen. For example, instead of “I don’t want to feel sad and confused,” rephrase that as, “I do want to feel happiness and a sense of clarity.” It is easier to move toward desired goals when they are stated in positive terms. If your goals feel general or vague (e.g., “I want to feel happier”), simply notice this for now – you will develop specific strategies intended to help you realize your goals in the next step.

Remember to state your intended goal from your own point of view, taking responsibility and ownership… this is what you  want to do. For example, instead of “I don’t want my friend to get angry with me so easily,” rephrase it as, “I want to learn how to develop a better relationship with my friend.” When goals are stated in these terms, you can become empowered by realizing the amount of control you have in reaching your goal, instead of depending on or wondering about the thoughts or behaviors of others.

(3) List your strategies

Maintain the creative mindful attitude that you took while generating possible solutions, as you allow your heart and mind to fully open to the process of recognizing strategies that will move you closer toward your goals. As you begin the process of coming up with ideas that may or may not help you reach your goal(s), remember: (1) don’t criticize/judge your ideas, (2) allow yourself to generate lots  of ideas/possibilities, (3) think creatively – allow yourself to be free of censorship, and (4) integrate and improve on ideas if needed – perhaps a few of your strategies have the potential to integrate into one amazing idea.

As you begin to create a brainstorm list of potential strategies, reflect back on your three possible solutions from the previous step. This exercise in brainstorming possible strategies involves the following steps:

• Write down the clearly stated/defined problem
• List your three possible solutions
• Underneath each solution, write at least 10 possible strategies

Part of engaging in this process of brainstorming from a centered place of mindfulness involves giving yourself permission to take your time, slow down your mind , and allow creative and productive strategies to emerge naturally into conscious awareness. Creative, effective, and mindful problem solving allows for strategies/ideas to be borne out of your authentic self … from your innermost sense of values , intuition, and alert wisdom.

(4) View the consequences of your strategies

At this step in the problem solving process, you have clearly stated the problem, come up with three possible solutions (think of them as solutions A, B, & C), and at least 10 possible strategies for each. Now that you are equipped with at least 30 problem-solving strategies, you are prepared to narrow down that list as you evaluate the potential (realistic) consequences of putting them into action.

• Look at the three lists of strategies you created for solutions A, B, and C. Notice which solution has generated the most strategies that appear to have the greatest chances of actually  succeeding.
• After you mindfully evaluate which of the three lists contains strategies that seem most effective (likely to bring about the desired outcome), choose the solution that you believe has the greatest chance of bringing success.
• Using the solution you chose (A, B, or C), begin to narrow down the strategies to three. These three strategies should be the best strategies for that particular solution; bear in mind you can always combine a few strategies into an even more powerful one. During the process of narrowing down your list, cross out any ideas that strike you as exceedingly unrealistic or not aligned with your true values or authentic self.
• In order to evaluate the consequences of each strategy, reflect on how each may positively and negative impact yourself, others, and your short-term/long-term goals.
• Write down each of your three narrowed down strategies in specific terms and list the positive and negative consequences in two columns underneath each strategy.
• If the best strategy does not become readily apparent to you at this point, try rating the positive and negative consequences for each of the three strategies on a scale of 1 to 4 (1 = not too important or significant, 4 = very important or significant).
• You can now go through all three strategies and add up those scores. The idea is that the most effective strategy is the one with the highest positive/lowest negative consequence score.
• If you feel at peace and content with the strategy that yielded the greatest positive consequences for yourself/others and your short-term/long-term goals, carry this knowledge and confidence with you to the final step of this problem-solving process.

(5) Evaluate your results

Now that you have selected the best strategy as a result of your deliberate, focused, and mindful process of problem solving, the time has come to put that strategy into action . It is time to take your carefully selected strategy and break it down into simple, specific, realistic steps that you will commit to enacting. Remember to insert different/specific words into the following example that allow you to connect this final step to the personal problem you are currently facing. A specific example of breaking down your chosen strategy into concrete steps can be found at step five of the following example.

General example of final outcome – “Five steps of effective and mindful problem solving” :

(1) Problem : “I’m at a major crossroads in my life and don’t know what to do.”

(2) Best solution – based on which of the three primary solutions generated the most effective list of strategies: “Figure out better ways to respond when I feel confused or frozen by the problem.”

(3) Best strategy – based on greatest/realistic chances of success and mindful weighing of potential consequences: “Practice mindfulness meditation , emotion regulation exercises , & interpersonal assertiveness .”

(4) Awareness of consequences  – accurate recognition of short-term/long-term consequences to yourself/others based on enacting the best strategy: “ Positive : feel more centered/relaxed/in touch with my authentic experience, increased ability to effectively identify/respond to emotions in myself and others, & increased confidence in ability to take a stand and speak my true feelings with healthy assertiveness ; Negative : fears of becoming lost within the process of meditation, temporary discomfort with allowing and responding to uncomfortable emotions authentically, & potential that expressing authentic thoughts/feelings may cause short-term/long-term hurt to others.”

(5)   Evaluate & break down strategy into manageable steps  – consider desired actions based on chosen strategy and commit to specific steps you will take toward putting that strategy into action: “Read about simple mindfulness exercise s and set aside 20 minutes each morning/evening to practice, write out specific emotion regulation coping skills onto flashcards and practice using them when feeling calm/centered as well as during times of emotional distress, & learn about interpersonal effectiveness and assertiveness skills – actively practice clearly stating thoughts, feelings, and needs on a daily basis.”

P roblem solving becomes significantly easier and less intimidating when you take a proactive approach toward solving the problem and become mindfully attuned with your authentic inner experience (focusing less on what others may think, want, or do as you determine what you  are feeling). Give yourself the opportunity go through this type of deliberate, thoughtful, and wise process of reaching healthy resolutions to your problems.

Remember that even when taking a mindful approach, problems aren’t always solved in the first, second, or even third attempts. This is because there are so many unknowns inherent within life’s mysteries and the only person’s behaviors you can ultimately control are your own. If your initial attempts at problem solving go awry, choose to reframe that perceived failure as a learning opportunity and a valuable chance to do things differently next time. The sooner you start taking active steps toward solving problems and recognize what works and what doesn’t work… the sooner you can shed the heavy robes of indecision and emotional paralysis and begin to live your most authentic life.

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Wood, J.C. (2010). The cognitive behavioral therapy workbook for personality disorders.  Oakland, CA: New Harbinger Publications, Inc.

Featured image: For What It’s Worth by Adam Swank / CC BY-SA 2.0

About Laura K. Schenck, Ph.D., LPC

I am a Licensed Professional Counselor (LPC) with a Ph.D. in Counseling Psychology from the University of Northern Colorado. Some of my academic interests include: Dialectical Behavior Therapy, mindfulness, stress reduction, work/life balance, mood disorders, identity development, supervision & training, and self-care.

Extremely helpful, Laura. Thank you so much.

I would so enjoy seeing more about problem-solving and decision-making.

What's On Your Mind? Cancel reply

How to develop a problem-solving mindset

May 14, 2023 Leaders today are confronted with more problems, of greater magnitude, than ever before. In these volatile times, it’s natural to react based on what’s worked best in the past. But when you’re solving the toughest business challenges on an ongoing basis, it’s crucial to start from a place of awareness. “If you are in an uncertain situation, the most important thing you can do is calm down,” says senior partner Aaron De Smet , who coauthored Deliberate Calm  with Jacqueline Brassey  and Michiel Kruyt. “Take a breath. Take stock. ‘Is the thing I’m about to do the right thing to do?’ And in many cases, the answer is no. If you were in a truly uncertain environment, if you’re in new territory, the thing you would normally do might not be the right thing.” Practicing deliberate calm not only prepares you to deal with the toughest problems, but it enhances the quality of your decisions, makes you more productive, and enables you to be a better leader. Check out these insights to learn how to develop a problem-solving mindset—and understand why the solution to any problem starts with you.

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How to Build Your Problem-Solving Skills

Get curious, think big, and get outside of your comfort zone..

Posted March 4, 2022 | Reviewed by Tyler Woods

• What Is a Career
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• Get curious to alternative perspectives and viewpoints.
• Daydream without restrictions to break thought patterns.
• Think of alternative ways to do things should you need to be flexible.

People say you can't teach an old dog new tricks. I prefer the expression "it takes more effort to teach an old dog new tricks." Any time you want to learn something new it takes your brain a great amount of energy to build new neural pathways. If you are trying to change something you've already learned, it takes extra effort to build pathways that override the previous ones.

There are many ways to help build new skills, particularly problem-solving skills; they start with getting curious, thinking big, and then trying new things.

Get Curious

It will be hard to learn anything unless you are genuinely interested in it. So find ways to get curious. You can align the new topic to something that already motivates you—this can be a passion, a value, an attribute you like about yourself, or a goal you have. For example, you may want to be that go-to expert or may want to develop deeper relationships with others. Choose whatever will keep you engaged in the learning and build upon that. From there, here are some tips on how to get curious:

• Block out time in your calendar to get curious, either in isolation or with others
• Ponder and expose yourself to how people from an opposing viewpoint see a topic
• Ask others their opinion or their input before making a choice
• Ask people to walk you through how they made previous decisions
• Reflect back on successes and failures: were there themes?
• Have coffee with colleagues once-removed to understand what they do and figure out how your roles may intertwine
• Find connections between others or the bigger picture. For example, how do the other department's objectives impact your day-to-day? How do your customers' actions impact your role?
• Read the news and determine how events/laws/policies impact you or your organization

To see if you are building on your knowledge from someone else's viewpoint, say summary statements of what you have heard and whether you have heard them correctly.

Once you have had time to get curious and gather information, it's time to dream big. What would you do with unlimited time, money, and resources? What would you do if there were no office politics or bureaucracy? "Blue sky" thinking can help you get outside existing processes and thought patterns to find new solutions. Some tips on how to build daydreaming into your routine are:

• Schedule time for daydreaming and block out distractions (either individually or as part of a team)
• Break the adrenaline rush of firefighting the small problems. The quick checklist items feel good in the moment but don't contribute to your sense of meaning or purpose in your work
• Think one step ahead, about how others may react to your moves
• Become a student of the competitor. Act as if you are an employee of the competitor and try to understand why they are choosing their strategy
• Consider how your daydreams could become reality. How much effort and resources are needed and compare it to the potential payoff

To check yourself on this is to see whether you are actually spending the time daydreaming. Whether it's weekly/monthly/quarterly, hold yourself accountable for achieving this goal.

Work outside your comfort zone

It's one thing to have a well-thought-out plan, but it's another to be able to flex that plan at a moment's notice. If you have done your due diligence in getting curious and daydreaming, you will know the pros/cons of contingency plans by understanding the drivers, the downstream implications, and who needs to be looped in. Here are some ideas and tips on how to try different solutions:

• Make "what if" plans for likely risks/bumps in the process
• Take on a task that is ambiguous or has a high likelihood of failing
• Do a feasibility study to determine potential risks/rewards of a new idea
• If and when resources are limited, look for alternatives (e.g., what tasks can be done with tightened budgets)
• Offer to do the budget or forecast
• Get out of perfectionist thinking and recognize when 80 percent is good enough

You will know your problem-solving skills are developing when you begin to get excited about change and ambiguity rather than anxious .

As learning and trying new things becomes more exciting and second nature, you will find that this energy transfers across your whole life. You are more likely to gain empathy for others , you can build resilience during stressful times , and you gain confidence and self-esteem to take on bigger challenges.

Lauren Florko has a Ph.D. in Industrial/Organizational Psychology. She also owns her own company, Triple Threat Consulting, based out of Vancouver, British Columbia.

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Human intelligence and brain networks

Inteligencia humana y redes cerebrales, intelligence humaine et réseaux cérébraux, roberto colom.

Universidad Autónoma de Madrid, Spain

Sherif Karama

McGill University, Montreal, Quebec, Canada

Rex E. Jung

The MIND Research Network, Albuquerque, New Mexico, USA

Richard J. Haier

University of California, Irvine, California, USA

Intelligence can be defined as a general mental ability for reasoning, problem solving, and learning. Because of its general nature, intelligence integrates cognitive functions such as perception, attention, memory, language, or planning. On the basis of this definition, intelligence can be reliably measured by standardized tests with obtained scores predicting several broad social outcomes such as educational achievement, job performance, health, and longevity. A detailed understanding of the brain mechanisms underlying this general mental ability could provide significant individual and societal benefits. Structural and functional neuroimaging studies have generally supported a frontoparietal network relevant for intelligence. This same network has also been found to underlie cognitive functions related to perception, short-term memory storage, and language. The distributed nature of this network and its involvement in a wide range of cognitive functions fits well with the integrative nature of intelligence. A new key phase of research is beginning to investigate how functional networks relate to structural networks, with emphasis on how distributed brain areas communicate with each other.

La inteligencia se puede definir como una capacidad mental general para razonar, resolver problemas y aprender. Dada su naturaleza general, la inteligencia integra funciones cognitivas como perceptión, atención, memoria, lenguaje o planificatión. De acuerdo con esta definitión la inteligencia se puede medir confiablemente mediante pruebas estandarizadas en que los puntajes obtenidos predicen algunas repercusiones sociales generales como éxito educacional, rendimiento laboral, salud y longevidad. Una comprensión detallada de los mecanismos cerebrales a la base de esta capacidad mental general podría entregar significativos beneficios individuales y sociales. Los estudios de neuroimágenes estructurales y funcionales en general le han dado soporte a una red frontoparietal como relevante para la inteligencia. Esta misma red se ha encontrado a la base de las funciones cognitivas relacionadas con la perceptión, el almacenamiento de la memoria de corto plazo y el lenguaje. La forma en que se distribuye esta red y su participatión en una amplia gama de funciones cognitivas se ajusta bien con la característica integradora de la inteligencia. Se está iniciando una nueva fase clave de la investigatión para estudiar cómo se relacionan las redes funcionales con las redes estructurales, con un énfasis en cómo las áreas cerebrales dispersas se comunican unas con otras.

L'intelligence peut se définir comme une capacité mentale générale de raisonnement, de résolution de problèmes et d'apprentissage. Sa nature généraliste lui permet d'intégrer des fonctions cognitives comme la perception, l'attention, la mémoire, le langage ou l'organisation. Selon cette définition, l'intelligence peut être mesurée de façon fiable par des tests standardisés dont les scores prédisent plusieurs données sociales importantes comme le niveau d'éducation, la performance professionnelle, la santé et la longévité. Une compréhension précise des mécanismes cérébraux sous-tendant cette aptitude mentale générale pourrait bénéficier de façon significative à l'individu et à la société. Des études de neuro-imagerie structurale et fonctionnelle sont dans l'ensemble en faveur d'un réseau frontopariétal pour l'intelligence. Ce même réseau est également à la base des fonctions cognitives liées à la perception, à la mémorisation à court terme et au langage. La nature multifocale de ce réseau et son implication dans de nombreuses fonctions cognitives cadre bien avec la démarche d'ensemble de l'intelligence. Une nouvelle phase clé de la recherche commence à s'intéresser aux rapports entre les réseaux fonctionnels et les réseaux structuraux, en insistant sur la façon dont les différentes aires cérébrales communiquent entre elles.

Human intelligence: definition, measurement, and structure

Reasoning, problem solving, and learning are crucial facets of human intelligence. People can reason about virtually any issue, and many problems may be solved. Simple and highly complex behavioral repertoires can be learned throughout the lifespan. Importantly, there are widespread individual differences in the ability to reason, solve problems, and learn which lead to human differences in the general ability to cope with challenging situations. These differences: (i) become more salient as the cognitive complexity of the situation becomes greater 1 - 3 ; (ii) are stable over time 4 ; and (iii) are partially mediated by genetic factors. 5

Various definitions of intelligence tend to converge around similar notions designed to capture the essence of this psychological factor. Jensen 6 notes Carl Bereiter's definition of intelligence: “what you use when you don't know what to do” (p 111). After their extensive survey, Snyderman and Rothman 7 underscored reasoning, problem solving, and learning as crucial for intelligence. The “mainstream science on intelligence” report coordinated by Gottfredson 8 highlights reasoning, planning, solving problems, thinking abstractly, comprehending complex ideas, learning quickly, and learning from experience. The American Psychological Association (APA) report on intelligence acknowledges that “individuals differ from one another in their ability to understand complex ideas, to adapt effectively to the environment, to learn from experience, to engage in various forms of reasoning, to overcome obstacles by taking thought” (p 77). 9

Humans perceive the environment, attend to relevant stimuli, memorize episodic and semantic information, communicate, and so forth. However, these activities must be integrated in some way for: (i) adapting our behavior to the environment; (ii) selecting the most appropriate contexts; or (iii) changing the world when adaptation and selection are not an option. 10 In our view, the integration of cognitive functions and abilities is dependent on the very general mental ability we call “general intelligence” or g for short. This integration is consistent with g as ability 11 or as an emergent property of the brain. 12

Any cognitive ability refers to variations in performance on some defined class of mental or cognitive tasks ( Figure 1 ). Abilities reflect observable differences in individuals' performance on certain tests or tasks. However, this performance involves the synthesis of a variety of abilities: “spatial ability,” for instance, can be regarded as an inexact concept that has no formal scientific meaning unless it refers to the structure of abilities that compose it. The problem of defining (and measuring) intelligence is the problem of defining the constructs that underlie it and of specifying their structure. 13 - 15

For more than a century, psychologists have developed hundreds of tests for the standardized measurement of intelligence with varying degrees of reliability and validity 16 The resulting measures allowed for the organization of taxonomies identifying minor and major cognitive abilities. J. B. Carroll, 17 , 18 for example, proposed a threestratum theory of intelligence after the extensive reanalysis of more than 400 datasets with thousands of subjects from almost 20 different countries around the world. Figure 2 . shows a simplified depiction of the taxonomy of cognitive abilities.

This survey of factor analytic studies supports the view that intelligence has a hierarchical structure (ie, like a pyramid). There is strong evidence for a factor representing general intelligence (g) located at the apex of the hierarchy (stratum III). This g factor provides an index of the level of difficulty that an individual can handle in performing induction, reasoning, visualization, or language comprehension tests. At a lower order in the hierarchy (stratum II), several broad ability factors are distinguished: fluid intelligence, crystallized intelligence, general memory, visual perception, auditory perception, retrieval, or cognitive speed. Lastly, stratum I is based on specific abilities, such as induction, lexical knowledge, associative memory, spatial relations, general sound discrimination, or ideational fluency.

Factor analytic surveys reveal two main findings: (i) the g factor constitutes more than half of the total common factor variance in a cognitive test or task in samples representative of the population; and (ii) various specific cognitive abilities can be identified, including the cognitive domains of language, memory, and learning, visual perception, information processing, knowledge and so forth, indicating certain generalizations of abilities; actually, there are more than 60 specific or narrow abilities. Available test batteries (a good example would be the Wechsler Adult Intelligence Scale - WAIS) measure g in addition to several cognitive abilities and specific skills. We know how to separate these influences over cognitive performance by means of statistical analyses. There are some measures which are highly g-loaded (eg, the Vocabulary subtest of the WAIS), while others are less g-loaded (eg, the Digit Symbol Subtest of the WAIS). ( Figure 3 ). shows how gray matter correlates become more prominent with increased g loadings of the intelligence measures. Moreover, the same measure can load differently on general and specific cognitive factors/abilities depending on the sample analyzed. 19 , 20

Human intelligence and the brain

Exploring the relationships between human intelligence and the brain requires a careful consideration of the structure of human intelligence. As evident from above, when researchers state that they are measuring intelligence by means of the Standard Progressive Matrices Test (SPM - as another example) they are telling an imprecise story because the SPM measures g plus spatial and reasoning abilities plus SPM specificity. The exact combination of these “ingredients” for the analyzed sample must be computed before saying something clear about the measured performance. This requires that studies use a battery of tests rather than just one test. Although this was not usually done for the early functional imaging studies of intelligence, 21 - 25 it is now more common. 26 - 29 Results from the older and the newer studies, however, point to the importance of both whole brain and specific brain networks.

Brain size and human intelligence

Wickett et al 30 state:

“There is no longer any doubt that a larger brain predicts greater intelligence. Several research teams, using differing scan protocols, populations, and cognitive measures, have all shown that IQ and brain volume correlate at about the 0.40 level ( ...) obviously replication of this effect is no longer required. What is required now is a more fine-grained analysis of why it is that a larger brain predicts greater intelligence, and what it is about intelligence that is most directly related to brain volume” (p 1096, emphasis added).

The meta-analysis by McDaniel 31 studied the relationship between in vivo brain volume and intelligence. Thirty-seven samples comprising a total of 1530 participants were considered simultaneously. These were the main findings: (i) the average correlation is 0.33; (ii) subsets of the 37 studies that allow partitioning by gender revealed that the correlation is higher for females (0.40) than for males (0.34); and (iii) the correlation does not change across age (0.33). The report concludes that these results resolve a 169-year-old debate: it is clear that intelligence and brain volumes are positively related.

Going one step further, several studies measured the volume of regions of interest (ROIs) showing the most significant correlations (controlling for total brain volumes) in frontal, parietal, and temporal brain regions, along with the hippocampus and the cerebellum. 32 , 33 Nevertheless, regional correlations are moderate (ranging from 0.25 to 0.50) which implies that measures of total or local brain size are far from telling the whole story.

From this perspective, gray and white matter must be distinguished. In keeping with this, voxel-by-voxel (a voxel is a volume element analogous to a pixel) analyses also showed specific areas where the amount of gray and white matter was correlated with intelligence scores. 24 , 25 The amount of gray matter is considered to reflect number and density of neuronal bodies and dendritic arborization, whereas the amount of white matter is considered to capture number and thickness of axons and their degree of myelination. Gray matter could support information processing capacity, while white matter might support the efficient flow of information in the brain. Available reports are consistent with the statement that both gray and white matter volumes are positively related to intelligence, but that the latter relationship is somewhat greater (unweighted mean correlation values =.27 and .31 respectively). 34 It is noteworthy that new studies using diffusion tensor imaging (DTI), which is the best method to date for assessing white matter, have reported DTI correlations with intelligence scores (see white matter section below).

A distributed brain network for human intelligence

Jung and Haier 35 reviewed 37 structural and functional neuroimaging studies published between 1988 and 2007. Based on the commonalities found in their analysis, they proposed the Parieto-Frontal Integration Theory (PFIT), identifying several brain areas distributed across the brain. These P-FIT regions support distinguishable information processing stages ( Figure 4 ).

This is a summary of the proposed stages.

• Occipital and temporal areas process sensory information in the first processing stage: the extrastriate cortex (Brodmann areas - BAs - 18 and 19) and the fusiform gyrus (BA 37), involved with recognition, imagery and elaboration of visual inputs, as well as Wernicke's area (BA 22) for analysis and elaboration of syntax of auditory information.
• Integration and abstraction of the sensory information by parietal BAs 39 (angular gyrus), 40 (supramarginal gyrus), and 7 (superior parietal lobule) correspond to the second processing stage.
• The parietal areas interact with the frontal lobes in the third processing stage and this interaction underlies problem solving, evaluation, and hypothesis testing. Frontal BAs 6, 9, 10, 45, 46, and 47 are underscored by the model.
• The anterior cingulate (BA 32) is implicated for response selection and inhibition of alternative responses, once the best solution is determined in the previous stage.

White matter, especially the arcuate fasciculus, is thought to play a critical role in reliable communication of information across the brain processing units. Nevertheless, note that the “Geschwind area” (underlying the angular gyrus) within the arcuate fasciculus may be even more important than the entire track. 36

Frontal, parietal, temporal, and occipital areas are depicted in Figure 4. However, Jung and Haier 35 suggest that not all these areas are equally necessary in all individuals for intelligence. Discrete brain regions of the dorsolateral prefrontal cortex (BAs 9, 45, 46, and 47) and the parietal cortex (BAs 7 and 40) could be considered most important for human intelligence.

A frontoparietal network may be relevant for intelligence, but also for working memory. 37 A study by Gray et al 38 tested whether fluid or reasoning ability (Gf) was mediated by neural mechanisms supporting working memory. Sixty participants performed verbal and nonverbal working memory tasks. They had to indicate if a current item matched the item they saw 3 items previously (3-back). Brain activity was measured by event-related functional magnetic resonance imaging (fMRI). The demand for working memory varied across trials. Results showed that: (i) participants scoring higher on the Progressive Matrices Test (a measure related to fluid g - Gf) were more accurate in the 3-back task; and (ii) only lateral prefrontal and parietal regions mediated the correlation between Gf and 3-back performance.

These fMRI results are consistent with the voxel-based morphometry (VBM) study reported by Colom et al (N = 48). 39 In agreement with the well established fact that the g factor and working memory capacity are very highly correlated, 40 - 45 these researchers predicted that g and working memory would share significant common neural networks. Therefore, using a VBM approach they quantified the overlap in brain areas where regional gray matter was correlated with measures of general intelligence and working memory, finding a common neuroanatomic framework supported by frontal gray matter regions belonging to BA 10 and by the right inferior parietal lobule (BA 40). Of note, this study also showed: (i) more gray matter recruitment for the more cognitively complex tasks (= more highly g loaded); and (ii) the complex span task (backward digit span) showed more gray matter overlap with the general factor of intelligence than the simple span task (forward digit span, ( Figure 5 ). These results were interpreted after the theory proposed by Cowan, 46 namely that parietal regions support “capacity limitations,” whereas frontal areas underlie the “control of attention.”

A similar commonality between intelligence and working memory was found in animal studies. Matzel and Kolata 47 reviewed several reports in which performance of laboratory mice was measured in a variety of attention and learning tasks. These are their most prominent conclusions:

• The “positive manifold” (eg, scores on cognitive tasks of various kinds are positively correlated) found in humans also applied to mice
• Storage and processing components of working memory accounted for the strong relationship between this cognitive function and g
• Networks involved in working memory overlap with those relevant for intelligence. These findings support an evolutionary conservation process of the structure and determinants of intelligence beyond humans. 48

Giftedness has been also investigated with related findings. Lee et al 49 used an fMRI approach to investigate the neural bases of superior intelligence. Eighteen gifted and 18 nongifted adolescents were analyzed. They solved reasoning problems, having high (complex) and low (simple) loadings on g. Increased bilateral frontoparietal activations (lateral prefrontal, anterior cingulate, and posterior parietal cortices) were found for both groups, but the gifted subjects showed greater activations in the posterior parietal cortex. Furthermore, activations in BAs 7 and 40 (superior and intraparietal cortices) correlated with intelligence differences. Therefore, high intelligence was associated with increased involvement of the frontoparietal network through preferential activation of the posterior parietal regions.

Gläscher et al 28 investigated the neural substrates of g in 241 patients with focal brain damage, using voxel-based lesion-symptom mapping. Statistically significant associations between g and damage within a distributed network in frontal and parietal brain regions were found. Further, damage of white matter association tracts in frontopolar areas was also shown to be associated with differences in g. They concluded that g draws on connections between regions integrating verbal, visuospatial, working memory, and executive processes.

Going one step further, Gläscher et al 28 asked whether or not there was a neural region whose damage uniquely impacts g beyond subtests contributing to the general score. They examined this question by analyzing the nonoverlap between a disjunction of subtests and the reported lesion pattern for g. A single region was found in the left frontal pole (BA 10) showing a significant effect unique to g. This result complements the distributed nature of g and suggests a hierarchical control mechanism. This unique area for g may be involved in the allocation of the working memory resources necessary for successful performance on specific cognitive tasks. However, this finding should be placed within context since there are studies showing no decline in intelligence associated with prefrontal lobotomy, presumably including the frontopolar cortex. 35 Therefore, future studies are necessary to determine the specific necessity of the frontal poles to g. The comparison between lesion cohorts and normal cohorts must be done carefully.

The structural studies reported by Colom et al 27 and Karama et al 50 are also consistent with the P-FIT model. In the first study (N =100) the general factor of intelligence was estimated after nine tests measuring reasoning, verbal, and nonverbal intelligence. Their VBM approach revealed several clusters of voxels correlating with individual differences in g scores. The main regions included the dorsolateral prefrontal cortex, Broca's and Wernicke's areas, the somatosensory association cortex, and the visual association cortex. The design matrix in this study controlled for sex, but when total gray matter was controlled for instead of sex, significant correlations were concentrated in frontal and parietal areas only ( Figure 6 ): superior, middle, and frontal gyrus, along with the postcentral gyrus and the superior parietal lobule.

Karama et al 50 used an automated cortical thickness protocol (CIVET51) to analyze a large sample of children and adolescents representative of the population (N=216). The most consistent areas of association between g scores and cortical thickness were found in lateral prefrontal, occipital extrastriate, and parahippocampal areas. Similar to the study reported by Colom et al, 27 Karama et al 50 identified more brain regions related to g than those in the P-FIT model, likely resulting from the synthesizing nature of the P-FIT approach (ie, if all regions implicated in intelligence across all 37 studies were included, they would have numbered in the hundreds) as opposed to the experimental/exploratory approach employed by these studies.

There are three other studies applying a cortical thickness approach (the third will be discussed later). Shaw et al 52 analyzed the trajectory of change in the thickness of the cerebral cortex on a sample of 307 children and adolescents. Intelligence was measured by four subtests from the Wechsler scales (vocabulary, similarities, block design, and matrix reasoning). They found that changes in thickness are more related to intelligence than thickness itself: negative correlations were found in early childhood, whereas the correlation was positive in late adolescence (these positive correlations were identified in frontal BAs 4, 6, 8, 10, 11, and 44-46, in parietal BAs 1-3, 5, 39, 40, in temporal BAs 21, 37, and in occipital BAs 17, 18, and 19). Further, intelligence differences were associated with the trajectory of cortical development in frontal brain regions. Finally, children with higher scores on intelligence showed more change in estimated cortical thickness along the developmental process.

Narr et al 53 studied a sample of 65 participants. They found positive associations between cortical thickness and intelligence bilaterally in prefrontal BAs 10/11 and 47, as well as in posterior temporal BAs 36/37. These researchers also analyzed males and females separately, finding that males showed correlations in temporaloccipital association cortices, whereas females exhibited correlations in prefrontal and temporal association cortices. These results are not entirely consistent with the parietofrontal framework and emphasize the importance of separate analyses for males and females. 25 , 54 , 55

Functional networks and neurotransmitters

Using an fMRI approach, Bishop et al 56 reported a study based on previous evidence showing that a polymorphism (val158met) in the catechol-O-methyltransferase (COMT) gene regulates catecholaminergic signaling in prefrontal cortex. The val158 allele is associated with higher COMT activity than the met158 allele-therefore, a lesser conten of dopamine. Twenty-two participants, genotyped for the COMT val158met polymorphism, performed verbal and spatial fluid intelligence (Gf) items, classified according to their cognitive complexity, as estimated from the loadings on g (see ref 57). These researchers were particularly interested in the analysis of the frontoparietal network related to fluid intelligence (the lateral prefrontal cortex, the presupplementary motor area/anterior cingulate cortex, and the intraparietal sulcus).

Findings revealed a positive effect of COMT val allele load upon the BOLD signal in regions belonging to this brain network when items showing distinguishable cognitive complexity were compared. This result suggests that the COMT val158met polymorphism impacts on the neural network supporting fluid intelligence. The finding is a demonstration that the effect of single genes can impact blood oxygen level dependent signal as assessed by fMRI. Further evidence linking catecholamine modulation within the identified network may help explain individual differences in the neural response to high levels of cognitive complexity, irrespective of the content domain (verbal or nonverbal).

White matter

The relationship between human intelligence and the integrity of white matter has been much less investigated, although this trend is changing rapidly. Diffusion tensor imaging (DTI) is based on the diffusion of water molecules in the brain and provides information about the size, orientation, and geometry of myelinated axons. DTI can produce measures that include fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RA), and axial diffusivity (AD), which allow for the assessment of myelin and axonal integrity (see Figure 7 ).

DTI is useful for fine-grained deterministic and probabilistic tractography to capture underlying cortical connectivity patterns. This can be used for the quantitative analysis of local and global network properties using graph-theoretical approaches (eg, analysis of small-world properties). 58 , 59

Using DTI, Schmithorst et al 60 analyzed the relationship between intelligence and white matter structure. The sample comprised 47 children and adolescents (age range 5 to 18). White matter structure was studied using fractional anisotropy (FA) and mean diffusivity (MD) indices. These indices were correlated with intelligence scores obtained from the Wechsler scales. These researchers found positive correlations bilaterally for FA in white matter association areas (frontal and parietooccipital areas). These correlations were thought to reflect a positive relationship between fiber organization-density and intelligence.

Also using a DTI approach, Yu et al 61 computed correlations between the integrity of several tracts (corpus callosum, cingulum, uncinate fasciculus, optic radiation, and corticospinal tract) and intelligence. On the basis of their scores on the Wechsler scales, 79 participants were divided in two groups: average and high intelligence. White matter integrity was assessed by fractional anisotropy (FA). The results showed that high intelligence participants display more white matter integrity than average intelligence participants only in the right uncinate fasciculus. Therefore, the right uncinate fasciculus might be an important neural basis for intelligence differences. A sample of 15 participants with mental retardation was also analyzed. These participants were compared with the 79 healthy controls and they showed extensive damage in the integrity of several white matter tracts: corpus callosum, uncinate fasciculus, optic radiation, and corticospinal tract.

Tang et al 62 used both DTI and fMRI during an n-back memory task in 40 young adults who had also completed a battery of intelligence tests. Correlations between the BOLD signal obtained from the n-back task and intelligence were mainly concentrated in the right prefrontal and bilateral parietal cortices. These correlations were negative (the higher the intelligence, the lower the activation during the n-back task) which supports the efficiency model of brain function. Further, white matter tracts connecting these areas also showed correlations to g. Specifically, integrity of interhemispheric connections was positively correlated to some intelligence factors in females but negatively correlated in males.

Chiang et al 63 have reported the first study combining a genetic informative design and a DTI approach for analyzing the relationships between white matter integrity and human intelligence. Intelligence was assessed by the Multidimensional Aptitude Battery, which provides measures of general intelligence, verbal (information, vocabulary, and arithmetic), and nonverbal intelligence (spatial and object assembly). The sample comprised 23 pairs of identical twins and 23 pairs of fraternal twins. White matter integrity, quantified using FA, was used to fit structural equation models (SEM) at each point in the brain. Afterwards three-dimensional maps of heritability were generated. White matter integrity was found to be under significant genetic control in bilateral frontal, bilateral parietal, and left occipital lobes (values ranging from .55 to .85). FA measures were correlated with the estimate of general intelligence and with nonverbal intelligence in the cingulum, optic radiations, superior fronto-occipital fasciculus, internal capsule, the isthmus of the corpus callosum, and the corona radiata. Further, common genetic factors mediated the correlation between intelligence and white matter integrity which suggests a common physiological mechanism and common genetic determination.

Networks for human intelligence

As noted above, gray matter supports information processing capacity and white matter promotes efficient flow of information across the brain. Connections are relevant for intelligence and these connections might be organized in networks. From this perspective, Li et al 64 reported a study testing the hypothesis that high levels of intelligence involve more efficient information transfer in the brain. 21 , 65 , 66 Studying a sample of 79 participants, brain anatomical networks were constructed by means of diffusion tensor tractography. These networks included intrahemispheric and interhemispheric connections. Six white-matter tracts were further constructed: the genu of the corpus callosum, the body of the corpus callosum, the splenium of the corpus callosum, the cingulum, the corticospinal tract, and the inferior fronto-occipital fasciculus. Thereafter, they calculated the topological properties of the networks for every participant. The sample was divided between average and high intelligence according to scores on the Wechsler scales. Higher global efficiencies were revealed for the latter group: higher intelligence was found to display shorter characteristic path length and a higher global efficiency of the networks. This was interpreted as a characteristic of a more efficient parallel information transfer in the brain anatomy. Therefore, the efficiency of brain structural organization could be an important biological basis for human intelligence, as originally proposed by Haier et al. 21 , 66

Song et al 67 analyzed 59 adults for studying the relationships between spontaneous brain activity at rest and individual differences in intelligence. Intelligence was assessed by the Wechsler scales. Using fMRI, the bilateral dorsolateral prefrontal cortices were the seed regions for investigating the correlations across subjects between individual intelligence scores and the strength of the functional connectivity between the seed regions and the remaining brain regions. These researchers found that brain regions in which the strength of the functional connectivity significantly correlated with intelligence scores were distributed in the frontal, parietal, occipital and limbic lobes. Furthermore, functional connectivity within the frontal lobe and between the frontal and posterior brain regions predicted differences in intelligence. These results are consistent with the relevance of a network view for human intelligence.

van den Heuvel et al 68 used resting state fMRI and graph analysis for exploring the presumed organization of the brain network. Functional connections of this brain network were analyzed computing correlations among the spontaneous signals of different brain regions during rest. The sample comprised 19 subjects and intelligence was measured by the Wechsler scales. They found associations between global communication efficiency - more long-distance connections - and scores of intelligence. This was interpreted as suggesting that a difference in the efficiency with which the brain integrates information between brain regions is related to differences in human intelligence. The strongest effects were found in frontal and parietal regions. Furthermore, intelligence differences were not related to the level of local information processing (local neighborhood clustering) and to the total number of functional connections of the brain network.

Beyond these specific studies, the so-called “connectome project” deserves close attention. 69 There is strong agreement regarding the fact that the human brain comprises a wide variety of functional systems. Obtaining brain images during rest shows large-amplitude spontaneous low frequency fluctuations in the fMRI signal. These fluctuations are related across areas sharing functions and the correlations show up as an individual's functional connectome. Biswall et al 69 report findings obtained from 1414 participants from 35 laboratories. Their main results were: (i) there is a universal functional architecture; (ii) there are substantial sex differences and age-related gradients; and (iii) it is possible to establish normative maps for the functional boundaries among identified networks.

Integration of intelligence and cognitive findings

The frontoparietal network is relevant for intelligence, but also for other cognitive functions. 70 Thus, for instance, Wager and Smith 71 reported a meta-analysis of 60 positron-emission tomography (PET) and fMRI studies of working memory. The effect of three content domains (verbal, spatial, and object), three executive functions (updating, temporal order, and manipulation) along with their interactions were analyzed. Brain areas most involved in all these cognitive facets were located in the frontal and parietal lobes: (i) spatial and nonspatial contents were separated in posterior, but not anterior areas; (ii) executive manipulation evoked more frontal activations, but with some exceptions; and (iii) the parietal cortex was always implicated in executive processing. The meta-analysis by Wager, Jonides, and Reading 72 after 31 PET and fMRI studies of shifting attention also highlights this fronto-parietal network (medial prefrontal, superior and inferior parietal, medial parietal, and premotor cortices).

Similarly, Marois and Ivanoff 3 analyzed the capacity limits of information processing in the brain. Three basic limitations for perception, working memory, and action were explicitly considered. Their revision was based mainly on fMRI evidence and these were the basic conclusions: (i) perception and action limitations are related to fronto-parietal brain networks; and (ii) working memory capacity limitations are associated to parieto-ccipital brain networks. The lateral prefrontal cortex may support general target consolidation and response selection, using a flexible coding system for processing relevant information in any given task. In contrast, the lateral parietal cortex might provide support to more specific processing goals. This brain region is more sensitive to perception than to action.

Thus, core cognitive functions (especially working memory) and intelligence share a frontoparietal brain network. If this network is involved for most individuals, it could be possible to predict individual differences in intelligence based on brain data. 74 This was attempted by Choi et al 75 using structural (cortical thickness) and functional magnetic resonance imaging. Their regression model explained 50% of the variance in IQ scores. Even when this figure may be questioned on several grounds, the main approach underscores that brain images might be employed for estimating intelligence levels in some instances using a neurometric approach.

Finally, experimental confirmatory approaches should be welcomed to increase refinement of ongoing research efforts. In this regard, transcranial magnetic stimulation (TMS) may help test hypotheses aimed at determining whether or not specific brain regions are really important for understanding individual differences in human intelligence. TMS induces transient changes in brain activity noninvasively. It does this by producing changes in a magnetic field that, in turn, evoke electric currents in the brain which promote depolarization of cellular membranes. Cognitive neuroscience often relies on a correlation approach, whereas TMS allows studying (almost) causal brain-behavior relationships in higher cognitive functions. 76 , 77 The study reported by Aleman and van't Wout 78 exemplifies this approach using a working memory task (forward and backward digit span). Working memory (and intelligence) performance is partially supported by the dorsolateral prefrontal cortex. Using repetitive TMS (rTMS) - adapted in the Hz band for suppressing cognitive processing - over the right dorsolateral prefrontal cortex, a significant decrease of performance in the forward and backward digit span test was found. Thus, regional suppression (or enhancement) might be produced to experimentally test specific predictions.

Regardless of the use of exploratory (correlation) or confirmatory (experimental) approaches, we do agree with Kennedy 79 : “as with more _eras', it is the underlying technology that makes the era possible [...] new advances in acquisition, analysis, databasing, modeling, and sharing will continue to be necessary.” This is especially true for analyzing human intelligence because this psychological factor is undoubtedly rooted in widely distributed regions in the brain. Frontal and parietal lobes likely comprise crucial processing areas for intelligence, but integrity of hard connections across the entire brain or spontaneous harmonic coactivation among distant regions appear also to be relevant. Creating a comprehensive picture for what can be called “neuro-intelligence” 80 should prove as challenging as it is exciting.

Acknowledgments

RC was partly supported by grant PSI2010-20364 from the Ministerio de Ciencia e Innovación (Spain).

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Theories of Intelligence in Psychology

Learn How to Define and Test Intelligence

• What is Intelligence?
• Foundational Theories

Other Types of Intelligence

Intelligence (iq) testing, frequently asked questions.

Intelligence is one of the most talked-about subjects in psychology , but no standard definition exists. Some researchers have suggested that intelligence is a single, general ability. Other theories of intelligence hold that intelligence encompasses a range of aptitudes, skills, and talents.

How Do We Define Intelligence?

Despite substantial interest in the subject, there still isn't a consensus among experts about the components of intelligence or whether accurate measurements of intelligence are even possible.

Although contemporary definitions of intelligence vary considerably, experts generally agree that intelligence involves mental abilities such as logic, reasoning, problem-solving , and planning. Specifically, current definitions tend to suggest that intelligence is the ability to:

• Learn from experience :   The acquisition , retention, and use of knowledge is an essential component of intelligence.
• Recognize problems : To use knowledge, people first must identify the problems it might address.
• Solve problems :   People must then use what they have learned to come up with solutions to problems.

Research on intelligence plays a significant role in many areas, including educational program funding, job applicant screening, and testing to identify children who need additional academic help.

Main Theories of Intelligence in Psychology

Given the intense interest in the concept of intelligence, some of the field's greatest minds have explored it from numerous angles. Following are some of the major theories of intelligence that have emerged in the last 100 years.

Major Types of Intelligence Theories

• General intelligence
• Primary mental abilities
• Multiple intelligences
• The triarchic approach to intelligence

General Intelligence

British psychologist Charles Spearman (1863–1945) described the concept of general intelligence , or the "g factor." After using factor analysis to examine mental aptitude tests, Spearman concluded that scores on these tests were remarkably similar.

People who performed well on one cognitive test tended to perform well on other tests, while those who scored poorly on one test tended to score poorly on others. He concluded that intelligence is a general cognitive ability that researchers can measure and express numerically.

Primary Mental Abilities

Psychologist Louis L. Thurstone (1887–1955) focused on seven primary mental abilities rather than a single, general ability. These include:

• Associative memory : The ability to memorize and recall
• Numerical ability : The ability to solve mathematical problems
• Perceptual speed : The ability to see differences and similarities among objects
• Reasoning : The ability to find rules
• Spatial visualization : The ability to visualize relationships
• Verbal comprehension : The ability to define and understand words
• Word fluency : The ability to produce words rapidly

Multiple Intelligences

Among more recent ideas about intelligence is Howard Gardner's theory of multiple intelligences . He proposed that traditional IQ testing does not fully and accurately depict a person's abilities. He proposed eight different intelligences based on skills and abilities that are valued in various cultures:

• Bodily-kinesthetic intelligence : The ability to control body movements and handle objects skillfully
• Interpersonal intelligence : The capacity to detect and respond appropriately to the moods, motivations, and desires of others
• Intrapersonal intelligence : The capacity to be self-aware and in tune with inner feelings, values, beliefs, and thinking processes
• Logical-mathematical intelligence : The ability to think conceptually and abstractly, as well as discern logical or numerical patterns
• Musical intelligence : The ability to produce and appreciate rhythm, pitch, and timbre
• Naturalistic intelligence : The ability to recognize and categorize animals, plants, and other objects in nature
• Verbal-linguistic intelligence : Well-developed verbal skills and sensitivity to the sounds, meanings, and rhythms of words
• Visual-spatial intelligence : The capacity to think in images and visualize accurately and abstractly

What Kind of Intelligence Do You Have?

If you'd like to know more about your intelligence style, try our fast and free quiz to learn more about what makes you tick.

The Triarchic Approach to Intelligence

Psychologist Robert Sternberg defined intelligence as "mental activity directed toward purposive adaptation to, selection, and shaping of real-world environments relevant to one's life."

Although he agreed with Gardner that intelligence is much broader than a single, general ability, he suggested that some of Gardner's types of intelligence are better viewed as individual talents. Sternberg proposed the concept of "successful intelligence," which involves three factors:

• Analytical intelligence : The ability to evaluate information and solve problems
• Creative intelligence : The ability to come up with new ideas
• Practical intelligence : The ability to adapt to a changing environment

Of course, there are many other theories on the types of intelligence humans possess.

Fluid vs. Crystallized Intelligence

Psychologist Raymon Cattell, along with his student John Horn, created the theory of fluid vs. crystallized intelligence . Fluid intelligence involves the ability to solve new problems without relying on knowledge from previous experiences.

According to the theory, a person's fluid intelligence declines as they get older. Crystallized intelligence, on the other hand, increases with age—this type of intelligence is based on concrete facts and experiences.

Emotional Intelligence

Emotional intelligence (sometimes called EQ) was initially coined by psychologist Daniel Goleman. It refers to a person's ability to regulate emotions and use their emotions to relate to others. Signs of emotional intelligence include strong self-awareness , empathy , embracing change, and managing emotions in difficult situations.

Efforts to quantify intelligence took a significant leap forward when German psychologist William Stern first coined the term "intelligence quotient" (IQ) in the early 20th century.

Psychologist Alfred Binet developed the very first intelligence tests to help the French government identify schoolchildren who needed extra academic assistance.

Binet was the first to introduce the concept of mental age: a set of abilities that children of a certain age possess.

Since then, intelligence testing has emerged as a widely used tool, which has led to many other tests of skill and aptitude.

However, IQ testing continues to spur debate over its use, cultural biases, influences on intelligence, and even the very way we define intelligence.

How Psychologists and Psychiatrists Measure Intelligence

Experts use a variety of standardized tests to measure intelligence. Some are aptitude tests administered in a group setting, such as the Scholastic Assessment Test (SAT) and the American College Test (ACT). Others are IQ tests given to individuals.

IQ test scores average around 100. Most children with intellectual disabilities (85%) score between 55 and 70. Severe disabilities usually correspond to still lower scores.

The following is a brief history of IQ tests as they were developed:

• Binet-Simon intelligence scale : This was the first IQ test ever made and was developed in 1905 by Alfred Binet and Theodore Simon.
• Stanford-Binet IQ test : This was psychologist Lewis Terman's adaptation of the Binet-Simon test. Scores are based on a person's mental age divided by their chronological age (mental age/chronological age x 100).
• Wechsler Adult Intelligence Scale (WAIS) : This was the first intelligence test for adults, developed by David Wechsler in 1939. It was the first to use standardized normal distribution in scoring and is commonly used today. It is divided into verbal and performance measures. Like most modern tests, it scores on a bell curve.

Other tests that psychologists and psychiatrists use today include the Woodcock-Johnson Tests of Cognitive Abilities, the Kaufman Assessment Battery for Children, the Cognitive Assessment System, and the Differential Ability Scale.

Questions About IQ Testing

The study of the human mind is complex, in part because the most important tool in the effort is the same as the subject itself.

As humans, researchers bring not only their knowledge and expertise but also their biases, experiences, cultural backgrounds, and beliefs to the table; like all scientific experts, they must combat their own humanness to strive for objectivity.

In addition, there's the sheer complexity of the human mind and the challenges of measuring a trait with so many conflicting definitions and nuances. No single standard for intelligence or its quantification exists as yet.

It's no surprise, then, that important questions about intelligence and IQ testing remain unanswered, at least in part. Some of these include:

• Are intelligence tests biased?
• Is intelligence a single ability, or does it involve multiple skills and abilities?
• Is intelligence inherited, or does the environment play a more significant role?
• What do intelligence scores predict, if anything?

To explore these questions, psychologists continue to research the nature, influences, and effects of intelligence. Their ongoing findings resonate across society, from education and the workplace to medical and behavioral diagnostic and therapeutic approaches.

Final Thoughts

Despite considerable debate, no definitive conceptualization of intelligence has emerged in the field of psychology. Today, psychologists often account for the many theoretical viewpoints when discussing intelligence and acknowledge that the debate is ongoing.

Early theories of intelligence focused on logic, problem-solving abilities, and critical thinking skills. In 1920, Edward Thorndike postulated three kinds of intelligence: social, mechanical, and abstract. Building on this, contemporary theories such as that proposed by Harvard psychologist  Howard Gardner tend to break intelligence into separate categories (e.g., emotional, musical, spatial, etc.).

Emotional intelligence (EI or EQ) is the ability to perceive, control, and evaluate emotions. Some researchers suggest that emotional intelligence can be learned and strengthened; others claim it's an inborn characteristic. Generally, EI is measured by self-report and ability tests.

Fluid intelligence is the ability to apply logic and think flexibly. Raymond Cattell defined fluid intelligence as "the ability to perceive relationships independent of previous specific practice or instruction concerning those relationships."

Intelligence develops and changes throughout life, generally peaking in midlife . A study published in  Psychological Science suggested that certain elements of fluid intelligence peak as late as 40.

Jaarsveld S, Lachmann T. Intelligence and creativity in problem solving: The importance of test features in cognition research .  Front Psychol . 2017;8. doi:10.3389/fpsyg.2017.00134

Spearman C. "General intelligence," objectively determined and measured .  The American Journal of Psychology . 1904;15(2):201. doi:10.2307/1412107

Thurstone LL.  Primary Mental Abilities . University of Chicago Press; 1938.

Gardner H. Frames of Mind: The Theory of Multiple Intelligences . Basic Books; 2011.

Sternberg RJ. Beyond IQ: A Triarchic Theory of Human Intelligence . CUP Archive; 1985.

Horn JL, Cattell RB. Refinement and test of the theory of fluid and crystallized general intelligences .  Journal of Educational Psychology . 1966;57(5):253-270. doi:10.1037/h0023816

Ghisletta P, Rabbitt P, Lunn M, Lindenberger U.  Two thirds of the age-based changes in fluid and crystallized intelligence, perceptual speed, and memory in adulthood are shared .  Intelligence . 2012;40(3):260-268. doi:10.1016/j.intell.2012.02.008

Barbey AK.  Network neuroscience theory of human intelligence .  Trends Cogn Sci (Regul Ed) . 2018;22(1):8-20. doi:10.1016/j.tics.2017.10.001

Drigas AS, Papoutsi C.  A new layered model on emotional intelligence . Behav Sci (Basel). 2018;8(5):45. doi:10.3390/bs8050045

Nicolas S, Andrieu B, Croizet JC, Sanitioso RB, Burman JT. Sick? Or slow? On the origins of intelligence as a psychological object .  Intelligence . 2013;41(5):699-711. doi:10.1016/j.intell.2013.08.006

HealthyChildren.org. Children with intellectual disabilities . American Academy of Pediatrics.

Richardson K, Norgate SH. Does IQ really predict job performance?   Applied Developmental Science . 2015;19(3):153-169. doi:10.1080/10888691.2014.983635

Hartshorne JK, Germine LT.  When does cognitive functioning peak? The asynchronous rise and fall of different cognitive abilities across the life span .  Psychol Sci . 2015;26(4):433-443. doi:10.1177/0956797614567339

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Problem solving

Worrying is a natural response to life's problems. But when it takes over and we can start to feel overwhelmed, it can really help to take a step back and break things down.

Learning new ways to work through your problems can make them feel more manageable, and improve your mental and physical wellbeing.

Video: Problem solving

The tips in this video can help you to find strategies and solutions for tackling the problems that can be solved, and learning how to manage and cope with those that cannot.

Steps and strategies to help you solve problems

1. focus on your values.

Feeling like you have lots of problems to solve in different areas of your life can make it difficult to know how and where to start.

A great way to focus is to write down a few areas of your life that are most important to you right now – for example, a relationship, finances or a long-term goal like studying or developing your career.

This can make it easier to prioritise which problems to tackle.

2. Tackle problems with possible solutions first

It's important to work out if your problem can be solved or is a "hypothetical worry" – things that are out of your control even though you might think about them often.

They might be based on something that happened in the past that cannot be changed or a worry about the future that starts with "what if…".

Ask yourself whether a problem can be dealt with by doing something practical. If the answer is no, it's a hypothetical worry.

Make a list of your problems, and work out which are solvable and which are hypothetical.

3. Set aside time to work through solvable problems

Set aside 5 or 10 minutes to think about possible solutions for one of your solvable problems.

Try to be as open-minded as you can, even if some ideas feel silly. Thinking broadly and creatively is often when the best solutions come to mind.

It may feel difficult at first but, over time, this approach can start to feel easier.

Once you have some ideas, think through or write down:

• the pros and cons of each solution
• whether it's likely to work
• if you have everything you need to try it

4. Make a plan

The next step is to choose a solution you want to try and make a plan for putting it into action. Try to be specific:

• What are you going to do?
• Do you need the support of anybody else?
• How much time do you need?
• When will you do it?

5. Try 'worry time'

Not all of our problems can be solved right away, but it can be difficult to switch off and stop ourselves from dwelling on them.

Using the "worry time" technique to stick to a short set time – say 10 to 15 minutes in the evening – for worrying can make this much easier to manage.

You can learn more about the worry time technique on tackling your worries .

6. Find time to relax

Worrying about our problems can make it harder to relax, but there are lots of things you can try to help you clear your mind and feel calmer.

The most important thing is to find what works for you. It might be getting active, spending time on an existing hobby or trying a new one, or techniques like mindfulness, meditation or our progressive muscle relaxation exercise.

Video: Progressive muscle relaxation

This video will guide you through an exercise to help you recognise when you're starting to get tense, and relax your body and mind.

7. Review and reflect

Once you start trying new approaches to solving and managing problems, consider setting aside time to review what went well with your solutions or anything else you noticed.

Make notes of the problems you face and any strategies you use to overcome them. This can come in handy later on and also be a good reminder of what works best for you.

Ticking off on a checklist any problems you manage to solve is a great way to recognise your achievements and boost your confidence.

8. Give journaling a go

Sometimes getting our thoughts out of our head – and down onto paper, our phones or anything else – is a great way to stop our worries and "what ifs" from spiralling out of control.

Expressing ourselves in this way can also make it easier to spot when our thoughts are unhelpful and we may benefit from a more balanced outlook. Give it a go to see if this works for you.

More self-help CBT techniques you can try

Bouncing back from life's challenges.

Taking steps to stay on top of your mental wellbeing and build resilience can really help you deal with problems when times are tougher. Learn more, and see tips and techniques you can use.

Tackling your worries

Facing your fears

Staying on top of things

Find more ideas to try in self-help CBT techniques

The Practical Value of Studying Philosophy

Posted in: Why Study Philosophy?

Transferable Skills

By studying philosophy, students develop cognitive transferable skills that pay off in a variety of professions—transferable skills such as Logical Reasoning • Analysis • Abstract Conceptualization • Problem-Solving • Creative Thinking • Clear and Persuasive Writing • Mental Dexterity • An Ability to Assess Different Perspectives and Frameworks • Information Management.

Earning Potential

The national median salary of Philosophy graduates is higher than nearly every other major in the social sciences, humanities, and higher than many other majors—higher than Psychology, Criminology, Communication, Special Education, Early Childhood Education, Business Management, Political Science, History, English, and so on (data source:  payscale.com ).

Which professions do philosophy graduates pursue? • Technology • Business • Law • Publishing • Government • Advertising • Journalism • Teaching • Sales • Human Resources • Public Relations • Activism • Public Policy, and so on.

Read about the practical value of studying philosophy

• Forbes  (2017) – “ A Case For Majoring In Philosophy ”

“Every year, college students choose their majors with an eye toward the return on investment. Among the usual lucrative suspects like finance and engineering, one liberal arts field stands out: philosophy. It turns out that philosophy majors earn significantly more than most majors, especially over the long term.”

“The surprisingly robust ROI [return on investment] for philosophy majors can be traced to its intellectual rigor. Philosophers are taught to seek out the pressure points in arguments and to reason for themselves. They dive into highly technical conversations, construct their own positions and arguments, and analyze relevant problems from multiple perspectives.”

“Beyond finances, the study of philosophy can also help students learn for themselves how they define the good life and how to go about living it.”

• U.S. News & World Report  (2020) – “ What You Can Do With a Philosophy Degree ”

“Philosophy students learn how to question conventional thinking, which is a marketable skill.”

“A Wall Street Journal analysis of the long-term earning potential of people with various college majors revealed that philosophy majors tend to get raises and promotions more quickly than individuals with other majors, and a result of this rapid career progression is that philosophy majors’ mid-career earnings are usually double the size of their starting salaries.”

• CNBC  (2018) – “ Mark Cuban says studying philosophy may soon be worth more than computer science—here’s why ”

“’I’m going to make a prediction’, Cuban told AOL in 2017. ‘In 10 years, a liberal arts degree in philosophy will be worth more than a traditional programming degree’…He views previously lucrative jobs in industries like accounting and computer programming as subject to the powers of automation. To remain competitive, Cuban advises ditching degrees that teach specific skills or professions and opting for degrees that teach you to think in a big picture way, like philosophy.”

• Times Higher Education  (2019) – “ What Can You Do with a Philosophy Degree? ”

“Philosophy graduates have highly transferable skills that are valuable to employers.”

“Graduates secure work in a variety of disciplines after their degree, such as teaching, PR or politics. Communications, publishing, HR and advertising can be attractive options for philosophy graduates, as well as law, banking, the civil service, business and science. Others go on to further study, research, academia and/or lecturing in philosophy or a related field.”

• Entrepreneur Magazine  (2017) – “ 5 Reasons Why Philosophy Majors Make Great Entrepreneurs ”

“When accomplished entrepreneurs like Reid Hoffman, Peter Thiel and Carly Fiorina credit their philosophy backgrounds for their success, you have to wonder if they’re on to something.”

• New York Times  (2018) – “ A Wall Street Giant Makes a $75 Million Bet on Academic Philosophy ”

“Philosophy, he [Bill Miller] added, ‘has made a huge difference both to my life outside business, in terms of adding a great degree of richness and knowledge, and to the actual decisions I’ve made in investing’.”

“Mr. Miller, 67, is not the only old-guard Wall Street figure with a background in philosophy. George Soros was heavily influenced by the Austrian philosopher Karl Popper. Carl Icahn was a philosophy major at Princeton . . . (On the watchdog side of the street, Sheila Bair, the former chair of the Federal Deposit Insurance Corporation, was also a philosophy major.)”

• Harvard Business Review  (2014) – “ How Philosophy Makes You a Better Leader ”

“A CEO client . . . found that contemplating the teachings of an ancient philosopher (Socrates) and a 20th century philosopher (Habermas) empowered him to implement an enhanced process of dialogue, consensus building, and ‘communicative rationality’ with his leadership team.”

• National Bureau Of Economic Research  (2017) – “ The Costs Of And Net Returns To College Major ”

“Health and Engineering majors, where earnings returns are large on a per graduate basis, have per-dollar returns similar to those observed in education, math, philosophy , and language degrees. .  .”

Graduate Study

Some philosophy majors go on to graduate studies in philosophy in order to pursue an academic career. The philosophy major is also exceptional training for many other post-graduate paths, such as law school. In fact, statistics indicate that philosophy majors perform very well on standardized tests for post-graduate and professional study.

• The GRE (“the SAT for graduate school”) – Philosophy majors come out on top.

“When students are compared by major on how far above average they do on the Graduate Record Examinations (GRE), a standardized test used in many disciplines to assess applicants to graduate programs, philosophy majors come out on top , according to a new look at test score data over the past few years.” (Daily Nous)

• Our philosophy department and Montclair State’s Feliciano School of Business have partnered for a “4 + 1” Philosophy BA/MBA program .
• The LSAT (the entrance exam for law school admissions) – Philosophy majors tie for first place with Economics majors.
• Medical School – The Philosophy major is a solid path to medical school. Consider the data and facts as explained by Paul Jung, M.D: “ If you think biochemistry is your ticket into medical school, think again. “

The University of Chicago The Law School

Meet the class: simon whiteman, ’27, former professional baseball player ready to take on business law.

As a former Major League Baseball player with a chemical engineering degree from Yale, Simon Whiteman, ’27, has an unusual CV. The Trumbull, Connecticut native is excited to put his intellect and the skills he learned as an athlete to work in the legal field.

Please describe your professional background and path.

I graduated from Yale University in 2019 with a degree in chemical engineering. One month later, the San Francisco Giants selected me in the ninth round of that year’s amateur draft. I played professional baseball in the Giants’ organization for five years across four levels as high as AA.

What key experiences have shaped you?

Playing professional baseball exposed me to a host of different personalities, backgrounds, and cultures. I learned how to collaborate with peers from many walks of life. Living in various states and playing on many teams with players of assorted ages, I learned how to communicate and compete alongside many different teammates.

What motivated your decision to go to law school?

My approach to problem-solving is extremely analytical, stemming from my engineering background as an undergraduate. Studying law will give me an entirely new toolset to tackle problems at the intersection of business and policy.

Why did you select the University of Chicago Law School?

I am looking forward to learning from brilliant faculty who are at the top of a myriad of fields. Additionally, the University’s commitment to the pursuit of truth through free speech discussion excites me.

What do you plan to do with your legal education?

I’d like to work as in-house counsel for a corporation, executing strategies and making decisions while using my law background to structure business solutions.

What is the thing you are most looking forward to about being a law student?

For the last five years, I’ve been training and competing physically, using my intellectual abilities in service of optimizing my physical strength, mobility, and efficiency. I’m looking forward to competing intellectually using my mental skillset for its own benefit.

What are some of your hobbies or interests?

Outside of baseball and physical fitness, I’m interested in psychological horror in both literature and film, and the gothic genre.

What is a “fun fact” about you?

In my last year of professional baseball, in AA, my top sprint speed of 31.3 ft/sec would have placed me top three in the Major Leagues. I stole ninety-seven bases with the Giants and another seventy in a four-year college career.