waiting at a subway station

Cognition and Mental Abilities7

Enduring Issues in Cognition and Mental Abilities

Building Blocks of Thought • Language • Images • Concepts Language, Thought, and Culture • Is Language Male Dominated? Nonhuman Language and Thought • The Question of Language • Animal Cognition

Problem Solving • Interpreting Problems • Implementing Strategies and

Evaluating Progress • Obstacles to Solving


Decision Making • Compensatory Decision

Making • Decision-Making

Heuristics • Framing • Explaining Our Decisions


Intelligence and Mental Abilities • Theories of Intelligence • Intelligence Tests • What Makes a Good


Heredity, Environment, and Intelligence • Heredity • Environment • The IQ Debate: A Useful


• Mental Abilities and Human Diversity: Gender and Culture

• Extremes of Intelligence

Creativity • Intelligence and

Creativity • Creativity Tests Answers to Problems in the Chapter Answers to Intelligence Test Questions



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“At the Braefield School for the Deaf, I met Joseph, a boyof 11 who had just entered school for the first time—an11-year-old with no language whatever. He had been born deaf, but this had not been realized until he was in his fourth year. His failure to talk, or understand speech, at the normal age was put down to ‘retardation,’ then to ‘autism,’ and these diagnoses had clung to him. When his deafness finally became apparent he was seen as ‘deaf and dumb,’ dumb not only literally, but metaphorically, and there was never any attempt to teach him language.

Joseph longed to communicate, but could not. Neither speaking nor writing nor signing was available to him, only ges- tures and pantomimes, and a marked ability to draw. What has happened to him? I kept asking myself. What is going on inside, how has he come to such a pass? He looked alive and ani- mated, but profoundly baffled: His eyes were attracted to speaking mouths and signing hands—they darted to our mouths and hands, inquisitively, uncomprehendingly, and, it seemed to me, yearningly. He perceived that something was ‘going on’ between us, but he could not comprehend what it was—he had, as yet, almost no idea of symbolic communica- tion, of what it was to have a symbolic currency, to exchange meaning. . . .

Joseph was unable, for example, to communicate how he had spent the weekend. . . . It was not only language that was


missing: there was not, it was evident, a clear sense of the past, of ‘a day ago’ as distinct from ‘a year ago.’ There was a strange lack of historical sense, the feeling of a life that lacked autobio- graphical and historical dimension . . .a life that only existed in the moment, in the present. . . .

Joseph saw, distinguished, categorized, used; he had no problems with perceptual categorization or generalization, but he could not, it seemed, go much beyond this, hold abstract ideas in mind, reflect, play, plan. He seemed completely literal—unable to juggle images or hypotheses or possibilities, unable to enter an imaginative or figurative realm. And yet, one still felt, he was of normal intelligence, despite the manifest lim- itations of intellectual functioning. It was not that he lacked a mind, but that he was not using his mind fully. . . .” (Sacks, 2000, pp. 32–34)

As Sacks suggests, language and thought are intertwined. We find it difficult to imagine one without the other, and we con- sider both part of what it means to be human. Psychologists use the term cognition to refer to all the processes that we use to acquire and apply information. We have already considered the cognitive processes of perception, learning, and memory. In this chapter, we focus on three cognitive processes that we think of as characteristically human: thinking, problem solving, and decision making. We also discuss two mental abilities that psy- chologists have tried to measure: intelligence and creativity.

ENDURING ISSUES IN COGNITION AND MENTAL ABILITIES The “Enduring Issues” in this chapter are highlighted in four prominent places. We will encounter the diversity–universality theme when we explore the differences and similari- ties in the way people process information and again when we discuss exceptional abilities. We make two additional references to the enduring issues as we discuss the stability–change of intelligence test scores over time and again when we explore how mea- sures of intelligence and performance sometimes vary as a function of expectations and situations (person–situation).

BUILDING BLOCKS OF THOUGHT What are the three most important building blocks of thought?

When you think about a close friend, you may have in mind complex statements about her, such as “I’d like to talk to her soon” or “I wish I could be more like her.” You may also have an image of her—probably her face, but perhaps the sound of her voice as well. Or you may think of your friend by using various concepts or categories such as woman, kind, strong, dynamic, and gentle. When we think, we make use of all these things—language, images, and concepts—often simultaneously. These are the three most important building blocks of thought.

L E A R N I N G O B J E C T I V E • Describe the three basic building

blocks of thought and give an example of each. Explain how phonemes, morphemes, and grammar (syntax and semantics) work together to form a language.

cognition The processes whereby we acquire and use knowledge.


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218 Chapter 7

Language What steps do we go through to turn a thought into a statement?

Human language is a flexible system of symbols that enables us to communicate our ideas, thoughts, and feelings. Joseph, the deaf boy described at the beginning of this chapter, had great difficulty communicating because he knew no languages. Although all animals com- municate with each other, language is unique to humans (MacWhinney, 2005).

One way to understand language is to consider its basic structure. Spoken language is based on units of sound called phonemes. The sounds of t, th, and k, for instance, are all phonemes in English. By themselves, phonemes are meaningless and seldom play an important role in help- ing us to think. But phonemes can be grouped together to form words, prefixes (such as un- and pre-), and suffixes (such as -ed and -ing). These meaningful combinations of phonemes are known as morphemes—the smallest meaningful units in a language. Unlike phonemes, mor- phemes play a key role in human thought. They can represent important ideas such as “red” or “calm” or “hot.” The suffix -ed captures the idea of “in the past” (as in visited or liked). The pre- fix pre- conveys the idea of “before” or “prior to” (as in preview or predetermined).

We can combine morphemes to create words that represent quite complex ideas, such as pre-exist-ing, un-excell-ed, psycho-logy. In turn, words can be arranged to form sentences according to the rules of grammar. The two major components of grammar are syntax and semantics. Syntax is the system of rules that governs how we combine words to form mean- ingful phrases and sentences. For example, in English and many other languages, the mean- ing of a sentence is often determined by word order. “Sally hit the car” means one thing; “The car hit Sally” means something quite different; and “Hit Sally car the” is meaningless.

Semantics describes how we assign meaning to morphemes, words, phrases, and sentences—in other words, the content of language. When we are thinking about something—say, the ocean—our ideas often consist of phrases and sentences, such as “The ocean is unusually calm tonight.” Sentences have both a surface structure—the partic- ular words and phrases—and a deep structure—the underlying meaning. The same deep structure can be conveyed by different surface structures:

The ocean is unusually calm tonight. Tonight the ocean is particularly calm. Compared with most other nights, tonight the ocean is calm.

Alternatively, the same surface structure can convey different meanings or deep structures, but a knowledge of language permits one to know what is meant within a given context:

Surface Structure Might mean. . . Or. . .

Flying planes can be dangerous. An airborne plane. . .

The profession of pilot. . .

Visiting relatives can be a nuisance. Relatives who are visiting. . .

The obligation to visit relatives. . .

The chicken is ready to eat. Food has been cooked sufficiently. . .

The bird is hungry. . .

Syntax and semantics enable speakers and listeners to perform what linguist Noam Chomsky calls transformations between surface structure and deep structure. According to Chomsky (1957; Chomsky, Place, & Schoneberger, 2000), when you want to communicate an idea, you start with a thought, then choose words and phrases that will express the idea, and finally, produce the speech sounds that make up those words and phrases, as shown by the left arrow in Figure 7–1. When you want to understand a sentence, your task is reversed. You must start with speech sounds and work your way up to the meaning of those sounds, as represented by the right arrow in Figure 7–1.

Our remarkable ability to perform these transformations becomes clear when you attempt to comprehend the following sentence: when lettres wihtin wrods are jubmled or trnasposed (as

language A flexible system of communication that uses sounds, rules, gestures, or symbols to convey information.

phonemes The basic sounds that make up any language.

morphemes The smallest meaningful units of speech, such as simple words, prefixes, and suffixes.

grammar The language rules that determine how sounds and words can be combined and used to communicate meaning within a language.


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Cognition and Mental Abilities 219

they are in this sentence), raeding speed is redcued, though not as much as you might expect (approx- imately 11%–26%). However, it is much more dif- ficult to extract the meaning of a sentence when letter substitutions are made (such as “qroblem” or “problnc”for “problem”) (Rayner,White, Johnson, & Liversedge, 2006).

Images What role do images play in thinking?

Using language is not the only way to think about things. Think for a moment about Abraham Lincoln. Your thoughts of Lincoln may have included such phrases as “wrote the Gettysburg Address” and “president during the Civil War.” But you probably also had some mental images about him: bearded face, lanky body, or log cabin. An image is a mental representation of some sensory experience, and it can be used to think about things. We can visualize the Statue of Liberty; we can smell Thanksgiving dinner; we can hear Martin Luther King, Jr., saying, “I have a dream!” Images also allow us to use concrete forms to represent complex and abstract ideas, as when newspapers use pie charts and graphs to illus- trate how people voted in an election (Stylianou, 2002; C. C. Yang, Chen, & Hong, 2003).

Concepts How do concepts help us to think more efficiently?

Concepts are mental categories for classifying specific people, things, or events. Dogs, books, fast, beautiful, and interesting are all concepts. When you think about a specific thing—say, Mt. Everest—you may think of facts, such as that it is 29,029 feet high or that it is on the border between Nepal, Tibet, and China. You may also have an image of it. But you are also likely to think of the concepts that apply to it, such as mountain, highest, dangerous, and snow-covered. Concepts help us to think efficiently about things and how they relate to one another. They also give meaning to new experiences and allow us to organize our experiences. For example, most children soon develop a concept of fish that allows them to recognize, think about and understand new kinds of fish when they see them for the first time. And over time, we often find it necessary to modify some of our concepts to better match our experiences. Thus, as they grow older, children come to understand that whales and dolphins are not fish (though, like fish, they swim in water) and they modify their concepts of fish and mammals accordingly. Conversely, for most of us there is no need to understand that killer whales and pilot whales are actually dolphins and thus no need to modify our concepts of dolphins and whales accordingly.

Although it is tempting to think of concepts as simple and clear-cut, most of the concepts that we use are rather “fuzzy”: They overlap one another and are often poorly defined. For example, most people can tell a mouse from a rat, but listing the critical differences between the two would be difficult (Rosch, 1973, 2002). If we cannot explain the difference between mouse and rat, how can we use these fuzzy concepts in our thinking? It turns out that we often construct a prototype (or model) of a representative mouse and one of a representative rat, and then use those prototypes in our thinking (Rosch, 1978, 2002; Voorspoels, Vanpaemel, & Storms, 2008). For example, when thinking about birds, most of us have a prototype, in mind—such as a robin or a sparrow—that captures for us the essence of bird. When we encounter new objects, we compare them with this prototype to determine whether they are, in fact, birds. And when we think about birds, we usually think about our prototypical bird.

Concepts, then, like words and images, help us to formulate thoughts. But human cog- nition involves more than just passively thinking about things. It also involves actively

Figure 7–1 The direction of movement in speech production and comprehension. Producing a sentence involves movement from thoughts and ideas to basic sounds; compre- hending a sentence requires movement from basic sounds back to the underlying thoughts and ideas.

Meaning (thought, idea)

Sentences (phrases)

Morphemes (words, prefixes, suffixes)

Phonemes (basic sounds)

Producing speech

Co m

pr eh

en di

ng s

pe ec


“Well, you don’t look like an experimental psychologist to me.” Source: © The New Yorker Collection, 1994, Sam Gross from cartoonbank.com. All Rights Reserved.

image A mental representation of a sensory experience.

concepts Mental categories for classifying objects, people, or experiences.

prototype (or model) According to Rosch, a mental model containing the most typical features of a concept.


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220 Chapter 7


1. ____________, ____________, and ____________ are the three most important building blocks of thought.

2. In language, units of sound, called ____________, are combined to form the smallest units of meaning, called ____________. These smallest meaningful units can then be combined to create words, which in turn can be used to build phrases and whole ____________.

3. Language rules that specify how sounds and words can be combined into meaningful sentences are called rules of ____________.

4. Indicate whether the following statements are true (T) or false (F). a. _____ Images help us to think about things because images use concrete forms to

represent complex ideas. b. _____ People decide which objects belong to a concept by comparing the object’s

features to a model or prototype of the concept. c. _____ Concepts help us give meaning to new experiences.

Pablo Picasso, the great 20th-century artist, developed a style of painting known as Cubism. In paintings such as Nude with Bunch of Irises and Mirror, 1934, shown here, he re-formed objects into basic geometric shapes. We recognize the figure in this paint- ing as a woman because its shapes repre- sent the “concept” of a female.

Answers:1. language, images, concepts.2. phonemes, morphemes, sentences. 3. grammar.4. a. (T);b. (T);c. (T).

Answers:1. d.2. a.


1. “I will spend tonight studying.” “Tonight I will be studying.” These two sentences exhibit the same

a. surface structure. b. syntax. c. phonology. d. deep structure.

2. Harry cannot list the essential differences between dogs and cats, but he has no trouble thinking about dogs and cats. This is most likely due to the fact that he

a. has a prototype of a representative dog and another of a representative cat. b. has developed a morpheme for a dog and another morpheme for a cat. c. is exhibiting functional fixedness. d. is using heuristics.

using words, images, and concepts to fashion an understanding of the world, to solve prob- lems, and to make decisions. In the next three sections, we see how this is done.

LANGUAGE, THOUGHT, AND CULTURE How do language, thought, and culture influence each other?

Diversity–Universality Do We All Think Alike? For at least 100 years, psychologists and philosophers assumed the basic processes of human cognition are universal. They accepted that cultural differences affect thought— thus, Masai elders in the Serengeti count their wealth in heads of cattle, whereas Wall Street bankers measure theirs in stocks and bonds. But habits of thought—the ways peo- ple process information—were assumed to be the same everywhere. The tendency to cat- egorize objects and experiences, the ability to reason logically, and the desire to understand situations in terms of cause and effect were thought to be part of human nature, regardless of cultural setting (Goode, 2000a). In this section, we will examine the validity of these viewpoints. ■

L E A R N I N G O B J E C T I V E • Summarize the evidence for the idea that

people in different cultures perceive and think about the world in different ways. Explain what is meant by “linguistic determinism” and summarize the evidence for and against it.


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Cognition and Mental Abilities 221

Do people from different cultures perceive and think about the world in different ways? A series of controlled experi- ments suggests they do. In one experiment (Nisbett, Peng, Choi, & Norenzayan, 2001), American and Japanese students were shown an underwater scene and asked to describe what they saw. Most Japanese participants described the scene as a whole, beginning with the background; by contrast, most American participants described the biggest, brightest, fastest fish. Nisbett and his colleagues concluded these stud- ies reflect fundamental, qualitative differences in how East- erners and Westerners perceive and think about the world. They also emphasized that the origin of these differences is cultural rather than genetic, because the cognitive approach of U.S.-born Asian Americans is indistinguishable from that of European Americans (Peng & Nisbett, 1999; Nisbett et al., 2001; Nisbett & Norenzayan, 2002).

As we have seen, language is one of the building blocks of thought. Can language influence how we think and what we can think about? Benjamin Whorf (1956) strongly believed that it does. According to Whorf ’s linguistic relativity hypothesis, the language we speak determines the pattern of our thinking and our view of the world—a position known more generally as linguistic determinism. For Whorf, if a language lacks a particular expression, the corre- sponding thought will probably not occur to speakers of that language. For example, the Hopi of the southwestern United States have only two nouns for things that fly. One noun refers to birds; the other is used for everything else. A plane and a dragonfly, for instance, are both referred to with the same noun. According to Whorf, Hopi speakers would not see as great a difference between planes and dragonflies as we do, because their language labels the two similarly.

The linguistic relativity hypothesis has intuitive appeal—it makes sense to think that limits of language will produce limits in thinking. However, research indicates that lan- guage doesn’t seem to restrict thinking to the extent that some linguistic determinists believed. For example, the Dani of New Guinea have only two words for colors—dark and light—yet they see and can easily learn to label other basic colors like red, yellow, and green. They also judge the similarity of colors much as English-speaking people do (E. R. Heider & Oliver, 1972). Thus, the ability to think about colors is quite similar across cultures, even when these cultures have quite different color terms in their languages (Roberson, Davies, & Davidoff, 2000; P. E. Ross, 2004). Moreover, experience and thought actually influence language. For example, the growth of personal computers and the Internet has inspired a vocabulary of its own, such as RAM, gigabyte, online, CPU, and blogs. In short, people cre- ate new words when they need them.

Psychologists have not dismissed the Whorf hypothesis altogether, but rather have softened it, recognizing that language, thought, and culture are intertwined (Chiu, Leung, & Kwan, 2007; Bennardo, 2003). Experience shapes language; and language, in turn, affects sub- sequent experience (K. Fiedler, 2008). This realization has caused us to examine our use of language more carefully, as we will see in the next section.

Is Language Male Dominated? Does language contribute to gender stereotyping?

The English language has traditionally used masculine terms such as man and he to refer to all people—female as well as male. Several studies suggest that this affects the way English speakers think. Hyde (1984) discovered that the use of “he” or “she” to describe a factory worker affected how children assessed the performance of male and female workers. Chil- dren who heard workers described by the masculine pronoun “he” rated female workers poorly; those who heard workers identified by the pronoun “she” judged female workers

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linguistic relativity hypothesis Whorf ’s idea that patterns of thinking are determined by the specific language one speaks.

linguistic determinism The belief that thought and experience are determined by language.

The Dani of New Guinea can perceive and remember the many colors of their world just as readily as you can, even though their lan- guage has only two color terms—light and dark. Human thought is not limited to the words in a person’s language. Language may indeed influence thought, but it doesn’t seem to restrict thought to the extent that Whorf believed.

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222 Chapter 7

most positively; and the ratings of children who heard gender-neutral descriptions of workers fell in between those of the two other groups.

More recent research has focused on the unconscious, automatic nature of gender stereotyping and language (Palomares, 2004; Parks & Roberton, 2004). In an experiment requiring men and women to respond rapidly to gender-neutral and gender-specific pro- nouns, both sexes responded more quickly to stimuli containing traditional gender stereo- types (e.g., nurse/she) than to stimuli containing nontraditional ones (e.g., nurse/he). This occurred even among participants who were explicitly opposed to gender stereotyping (Banaji & Hardin, 1996).

As we have seen, language, cognition, and culture are interrelated in a complex fashion, each contributing to how people communicate, think, and behave. However, as we noted at the beginning of this chapter, nonhumans do communicate with one another. The nature of communication and cognition in nonhuman animals is a topic to which we will now turn.


1. According to Whorf’s ____________ ____________ hypothesis, the language we speak shapes our thinking.

2. Indicate whether the following statements are true (T) or false (F). a. _____ Many words in our language correspond to concepts. b. _____ Experience shapes language. c. _____ Thoughts are limited to the words in the language that a person speaks.

Answer:1. b.


1. Cross-cultural studies indicate that people from different cultures with very different languages nonetheless perceive and are able to think about such things as colors in very similar ways even if their language contains no words for these things. These data ________ Whorf’s theory.

a. support b. contradict c. neither support nor contradict

Answers:1. linguistic relativity.2. a. (T);b. (T);c.(F).

NONHUMAN LANGUAGE AND THOUGHT Can scientists learn what is on an animal’s mind?

The Question of Language What kind of communication and language do other animals use?

The forms of animal communication vary widely. Honeybees enact an intricate waggle dance that tells their hive mates not only exactly where to find pollen, but also the quality of that pollen (Biesmeijer & Seeley, 2005). Humpback whales perform long, haunting solos ranging from deep bass rumblings to high soprano squeaks. The technical term for such messages is signs, general or global statements about the animal’s current state. But fixed, stereotyped signs don’t constitute a language. The distinguishing features of language are meaningfulness (or semantics), displacement (talking or thinking about the past or the future), and productivity (the ability to produce and understand new and unique words and expressions such as slang terms). Using these criteria, as far as we know, no other species has its own language.

For more than two decades, however, Francine Patterson (Bonvillian & Patterson, 1997; F. G. Patterson, 1981) used American Sign Language with a lowland gorilla named Koko. By age 5, Koko had a working vocabulary of 500 signs—similar to a 5-year-old deaf

L E A R N I N G O B J E C T I V E • Summarize research evidence that

supports the statement that “nonhuman animals have some humanlike cognitive capacities.” Explain the following statement: “All animals communicate, but only humans use language to communicate.”

signs Stereotyped communications about an animal’s current state.

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Cognition and Mental Abilities 223

child using sign language, though far lower than a hearing, speaking child’s vocabulary of 1,000–5,000 words (F. G. Patterson & Cohn, 1990). In her mid-20s, Koko signed about her own and her companions’ happy, sad, or angry emotions. Most interesting, Koko referred to the past and the future (displacement). Using signs before and later, yesterday and tomorrow appropriately, she mourned the death of her pet kitten and expressed a desire to become a mother.

Critics suggest that researchers such as Patterson may be reading meaning and intentions into simple gestures. To reduce the ambiguity of hand signs, other researchers have used computer keyboards to teach and record com- munications with apes (Rumbaugh, 1977; Rumbaugh & Savage-Rumbaugh, 1978); to document behavior with and without humans on camera; to use double-blind pro- cedures; and also to study another ape species, bonobos. Most impressive—and surprising—was a bonobo named Kanzi (Savage-Rumbaugh & Lewin, 1994). Initially in the lab, Kanzi was adopted by an older female who lacked keyboard skills. Some months later, Kanzi, who had been accompanying his “mother” to lessons but who was not receiving formal training, was learning keyboard symbols and spoken English on his own—much as children do.

That apes can learn signs without intensive training or rewards from human trainers is clear. Whether they can grasp the deep structure of language is less clear (Blumberg & Wasserman, 1995). Moreover, at best, apes have reached the linguistic level of a 2- to 2-1/2- year-old child. Critics see this as evidence of severe limitations, whereas others view it as an extraordinary accomplishment.

Animal Cognition Do some animals think like humans?

As we have seen, language is only one of the building blocks of thought. Without language, can nonhumans nonetheless think? The question is particularly difficult to answer because psychologists have only recently developed techniques for learning how other animals use their brains and for identifying the similarities and differences between human and non- human thought (Bolhuis & Giraldeau, 2005).

Numerous studies indicate that other animals have some humanlike cognitive capaci- ties. Parrots, for example, are exceptionally good vocal mimics. But do parrots know what they are saying? According to Irene Pepperberg (2000, 2006, 2007), Alex, an African gray parrot, did. Alex could count to 6; identify more than 50 different objects; and classify objects according to color, shape, material, and relative size. Pepperberg contends that rather than demonstrating simple mimicry, the parrot’s actions reflected reasoning, choice, and, to some extent, thinking.

Other researchers have taught dolphins to select which of two objects is identical to a sample object—the basis of the concepts same and different (Harley, Roitblat, & Nachtigall, 1996; Herman, Uyeyama, & Pack, 2008)—and to respond accurately to numerical concepts such as more and less (Jaakkola, Fellner, Erb, Rodriguez, & Guarino, 2005). What’s more, rhesus and capuchin monkeys can learn the concept of numeration, or the capacity to use numbers, and serialization, or the ability to place objects in a specific order based on a con- cept (Terrace, Son, & Brannon, 2003; A. A. Wright & Katz, 2007). In short, humans are not unique in their ability to form concepts.

But do chimps, dolphins, and parrots know what they know? Do nonhuman animals have a sense of self (Bard, Todd, Bernier, Love, & Leavens, 2006; Herman, 2002)? George Gallup (1985, 1998) noticed that after a few days’ exposure, captive chimpanzees began making faces in front of a mirror and used it to examine and groom parts of their bodies they had never seen before. To test whether the animals understood that they were seeing

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Professor Sue Savage-Rumbaugh and Kanzi. Savage-Rumbaugh continued Kanzi’s natural- istic education through social interaction during walks outside. Kanzi now understands spoken English and more than 200 keyboard symbols. He responds to completely new vocal and keyboard requests and uses the keyboard to make requests, comment on his surroundings, state his intentions, and— sometimes—indicate what he is thinking about.

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themselves, Gallup anesthetized them and painted a bright red mark above the eyebrow ridge and on the top of one ear. The first time the chimps looked at the mirror after awaken- ing, they reached up and touched the red marks, presumably recognizing themselves.

Since Gallup’s initial study, hundreds of researchers have used the mirror test and more recently live video displays with many other animals (Hirata, 2007). Only four nonhuman species—chimpanzees, bonobos (formerly called “pygmy chimpanzees”), orangutans, and less frequently gorillas—show signs of self-awareness (Bard et. al., 2006; Boysen & Himes, 1999; Gallup, 1985; Heschl & Burkart, 2006; Vauclair, 1996). For that matter, even human infants do not demonstrate mirror-recognition until 18 to 24 months of age.

If chimpanzees possess self-awareness, do they understand that others have information, thoughts, and emotions that may differ from their own? Observational studies suggest they do have at least a limited sense of other-awareness (Goodall, 1971; Parr, 2003; Savage-Rumbaugh & Fields, 2000). One measure of other-awareness is deception. For example, if a chimpanzee discovers a hidden store of food and another chimpanzee happens along, the first may begin idly grooming himself. Presumably, the first chimpanzee recognizes that the second (a) is equally interested in food, and (b) will interpret the grooming behavior as meaning there is nothing interesting nearby. Both in the wild and in captive colonies, chimpanzees frequently practice deception in matters of food, receptive females, and power or dominance.

So far, we have been talking about what humans and nonhumans think about. As we will see in the next section, cognitive psychologists are equally interested in how people use thinking to solve problems and make decisions.

224 Chapter 7


1. Chimpanzees, orangutans, and bonobos are the only two nonhuman species to consistently show

a. self-awareness. b. problem-solving ability. c. numeration comprehension.

2. Humans use language to communicate. What is the nonhuman animal equivalent of language?

a. grunts b. squeaks c. signs

Answer:1. a.


1. When you visit the zoo, you notice a chimpanzee using a mirror to groom itself. This is a sign of:

a. self-awareness b. numeration c. displacement

Answers:1. a.2. c.

PROBLEM SOLVING What are three general aspects of the problem-solving process?

Solve the following problems:

PROBLEM 1 You have three measuring spoons. (See Figure 7–2.) One is filled with 8 teaspoons of salt; the other two are empty, but have a capacity of 2 teaspoons each. Divide the salt among the spoons so that only 4 teaspoons of salt remain in the largest spoon.

Most people find this problem easy. Now try solving a more complex problem (the answers to all of the problems are at the end of this chapter).

L E A R N I N G O B J E C T I V E S • Explain why problem representation is

an important first step in solving problems. In your explanation include divergent and convergent thinking, verbal, mathematical and visual representation, and problem categorization.

• Distinguish between trial and error, information retrieval, algorithms, and heuristics as ways of solving problems. Give an example of hill-climbing, subgoals, means-end analysis, and working backward. Explain how “mental sets” can help or hinder problem solving.

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PROBLEM 2 You have three measuring spoons. (See Figure 7–3.) One (spoon A) is filled with 8 teaspoons of salt. The second and third spoons are both empty. The second spoon (spoon B) can hold 5 teaspoons, and the third (spoon C) can hold 3 teaspoons. Divide the salt among the spoons so that spoon A and spoon B each have exactly 4 tea- spoons of salt and spoon C is empty.

Most people find this problem much more difficult than the first one. Why? The answer lies in interpretation, strategy, and evaluation. Problem 1 is considered trivial because interpreting what is needed is easy, the strategies for solving it are simple, and the steps required to move closer to a solution can be verified effortlessly. Problem 2, by con- trast, requires some thought to interpret what is needed; the strategies for solving it are not immediately apparent; and the steps required to see actual progress toward the goal are harder to evaluate. These three aspects of problem solving—interpretation, strategy, and evaluation—provide a useful framework for investigating this topic.

Interpreting Problems Why is representing the problem so important to finding an effective solution?

The first step in solving a problem is called problem representation, which means inter- preting or defining the problem. It is tempting to leap ahead and try to solve a problem just as it is presented, but this impulse often leads to poor solutions. For example, if your busi- ness is losing money, you might define the problem as deciphering how to cut costs. But by defining the problem so narrowly, you have ruled out other options. A better representa- tion of this problem would be to figure out ways to boost profits—by cutting costs, by increasing income, or both. Problems that have no single correct solution and that require a flexible, inventive approach call for divergent thinking—or thinking that involves gener- ating many different possible answers. In contrast, convergent thinking is thinking that narrows its focus in a particular direction, assuming that there is only one solution (or at most a limited number of right solutions).

To see the importance of problem representation, consider the next two problems.

PROBLEM 3 You have four pieces of chain, each of which is made up of three links. (See Figure 7–4.) All links are closed at the beginning of the problem. It costs 2 cents to open a link and 3 cents to close a link. How can you join all 12 links together into a single, contin- uous circle without paying more than 15 cents?

Problem 3 is difficult because people assume that the best way to proceed is to open and close the end links on the pieces of chain. As long as they persist with this “conceptual block,” they will be unable to solve the problem. If the problem is represented differently, the solu- tion is obvious almost immediately (see Answer Key at the end of this chapter for solutions).

If you have successfully interpreted Problem 3, give Problem 4 a try.

PROBLEM 4 A monk wishes to get to a retreat at the top of a mountain. He starts climbing the mountain at sunrise and arrives at the top at sunset of the same day. During the course of his ascent, he travels at various speeds and stops often to rest. He spends the night engaged in meditation. The next day, he starts his descent at sunrise, following the same narrow path that he used to climb the mountain. As before, he travels at various speeds and stops often to rest. Because he takes great care not to trip and fall on the way down, the descent takes as long as the ascent, and he does not arrive at the bottom until sunset. Prove that there is one place on the path that the monk passes at exactly the same time of day on the ascent and on the descent.

This problem is extremely difficult to solve if it is represented verbally or mathemati- cally. It is considerably easier to solve if it is represented visually, as you can see from the explanation that appears at the end of this chapter. Interestingly, Albert Einstein relied heav- ily on his powers of visualization to understand phenomena that he would later describe by using complex mathematical formulas. This great thinker believed his extraordinary genius resulted in part from his skill in representing problems visually (Kosslyn, 2002).

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Figure 7–2 Figure for Problem 1

Figure 7–3 Figure for Problem 2




problem representation The first step in solving a problem; it involves interpreting or defining the problem.

divergent thinking Thinking that meets the criteria of originality, inventiveness, and flexibility.

convergent thinking Thinking that is directed toward one correct solution to a problem.


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Another aspect of successfully representing a problem is deciding to which cate- gory the problem belongs. In fact, gaining expertise in any field consists primarily of increasing your ability to represent and categorize problems so that they can be solved quickly and effectively (Tanaka, Curran, & Sheinberg, 2005). Star chess play- ers, for example, can readily categorize a game situation by comparing it with various standard situations stored in their long-term memories (Huffman, Matthews, & Gagne, 2001; A. J. Waters, Gobet, & Leyden, 2002). This strategy helps them interpret the current pattern of chess pieces with greater speed and precision than a novice chess player can.

Implementing Strategies and Evaluating Progress Why are heuristics usually better for solving problems than is trial and error?

Once you have properly interpreted a problem, the next steps are to select a solution strat- egy and evaluate progress toward your goal. A solution strategy can be anything from sim- ple trial and error, to information retrieval based on similar problems, to a set of step-by-step procedures guaranteed to work (called an algorithm), to rule-of-thumb approaches known as heuristics.

Trial and Error Trial and error is a strategy that works best when choices are limited. For example, if you have only three or four keys to choose from, trial and error is the best way to find out which one unlocks your friend’s front door. In most cases, however, trial and error wastes time because there are many different options to test.

Information Retrieval One approach is to retrieve information from long-term memory about how such a problem was solved in the past. Information retrieval is an espe- cially important option when a solution is needed quickly. For example, pilots simply memorize the slowest speed at which a particular airplane can fly before it stalls.

Algorithms Complex problems require complex strategies. An algorithm is a problem- solving method that guarantees a solution if it is appropriate for the problem and is prop- erly carried out. For example, to calculate the product of 323 and 546, we multiply the

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Figure 7–4 Figure for Problem 3

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algorithm A step-by-step method of problem solving that guarantees a correct solution.

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numbers according to the rules of multiplication (the algorithm). If we do it accurately, we are guaranteed to get the right answer.

Heuristics Because we don’t have algorithms for every kind of problem, we often turn to heuristics, or rules of thumb. Heuristics do not guarantee a solution, but they may bring it within reach.

A very simple heuristic is hill climbing: We try to move continually closer to our goal without going backward. At each step, we evaluate how far “up the hill” we have come, how far we still have to go, and precisely what the next step should be. On a multiple-choice test, for example, one useful hill-climbing strategy is first to eliminate the alternatives that are obviously incorrect.

Another problem-solving heuristic is to create subgoals, which involves breaking a prob- lem into smaller, more manageable pieces that are easier to solve individually than the prob- lem as a whole (Nunokawa, 2001; S. K. Reed, 2003). Consider the problem of the Hobbits and the Orcs.

PROBLEM 5 Three Hobbits and three Orcs are on the bank of a river. They all want to get to the other side, but their boat will carry only two creatures at a time. Moreover, if at any time the Orcs outnumber the Hobbits, the Orcs will attack the Hobbits. How can all the creatures get across the river without danger to the Hobbits?

You can find the solution to this problem by thinking of it in terms of a series of sub- goals. What has to be done to get just one or two creatures across the river safely, temporar- ily leaving aside the main goal of getting everyone across? We could first send two of the Orcs across and have one of them return. That gets one Orc across the river. Now we can think about the next trip. It’s clear that we can’t then send a single Hobbit across with an Orc, because the Hobbit would be outnumbered as soon as the boat landed. Therefore, we have to send either two Hobbits or two Orcs. By working on the problem in this fashion— concentrating on subgoals—we can eventually get everyone across.

Once you have solved Problem 5, try Problem 6, which is considerably more difficult (the answers to both problems are at the end of the chapter).

PROBLEM 6 This problem is identical to Problem 5, except that there are five Hobbits and five Orcs, and the boat can carry only three creatures at a time.

Subgoals are often helpful in solving a variety of everyday problems. For example, a stu- dent whose goal is to write a term paper might set subgoals by breaking the project into a series of separate tasks: choosing a topic, doing research, writing the first draft, editing, and so on. Even the subgoals can sometimes be broken down into separate tasks: Writing the first draft might break down into the subgoals of writing the introduction, describing the position to be taken, supporting the position with evidence, drawing conclusions, writing a summary, and writing a bibliography. Subgoals make problem solving more manageable because they free us from the burden of having to “get to the other side of the river” all at once.

One of the most frequently used heuristics, called means-end analysis, combines hill climbing and subgoals. Like hill climbing, means-end analysis involves analyzing the dif- ference between the current situation and the desired end, and then doing something to reduce that difference. But in contrast to hill climbing—which does not permit detours away from the final goal in order to solve the problem—means-end analysis takes into account the entire problem situation. It formulates subgoals in such a way as to allow us temporarily to take a step that appears to be backward in order to reach our goal in the end. One example is the pitcher’s strategy in a baseball game when confronted with the best batter in the league. The pitcher might opt to walk this batter intentionally even though doing so moves away from the major subgoal of keeping runners off base. Inten- tional walking might enable the pitcher to keep a run from scoring and so contribute to the ultimate goal of winning the game. This flexibility in thinking is a major benefit of means-end analysis.

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heuristics Rules of thumb that help in simplifying and solving problems, although they do not guarantee a correct solution.

hill climbing A heuristic, problem-solving strategy in which each step moves you progressively closer to the final goal.

subgoals Intermediate, more manageable goals used in one heuristic strategy to make it easier to reach the final goal.

means-end analysis A heuristic strategy that aims to reduce the discrepancy between the current situation and the desired goal at a number of intermediate points.


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But means-end analysis also poses the danger of straying so far from the end goal that the goal disappears altogether. One way of avoiding this situation is to use the heuristic of working backward. With this strategy, the search for a solution begins at the goal and works backward toward the “givens.” Working backward is often used when the goal has more information than the givens and when the operations involved can work in two directions. For example, if you wanted to spend exactly $100 on clothing, it would be difficult to reach that goal simply by buying some items and hoping that they totaled exactly $100. A better strategy would be to buy one item, subtract its cost from $100 to determine how much money you have left, then purchase another item, subtract its cost, and so on, until you have spent $100.

Obstacles to Solving Problems How can a “mental set” both help and hinder problem solving?

Many factors can either help or hinder problem solving. One factor is a person’s level of motivation, or emotional arousal. Generally, we must generate a certain surge of excite- ment to motivate ourselves to solve a problem, yet too much arousal can hamper our abil- ity to find a solution. (See Chapter 8, “Motivation and Emotion.”)

Another factor that can either help or hinder problem solving is mental set—our ten- dency to perceive and to approach problems in certain ways. A mental set can be helpful if we have learned operations that can legitimately be applied to the present situation. In fact, much of our formal education involves learning useful mental sets. But sets can also create obstacles, especially when a novel approach is needed. The most successful problem solvers can choose from many different mental sets and can also judge when to change sets or when to abandon them entirely.

One type of mental set that can seriously hinder problem solving is called functional fixedness. Consider Figure 7–5. Do you see a way to mount the candle on the

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Figure 7–5 To test the effects of functional fixedness, par- ticipants might be given the items shown on the table and asked to mount a candle on the wall. See Figure 7–12 for a solution.

mental set The tendency to perceive and to approach problems in certain ways.

working backward A heuristic strategy in which one works backward from the desired goal to the given conditions.

functional fixedness The tendency to perceive only a limited number of uses for an object, thus interfering with the process of problem solving.


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wall? If not, you are probably stymied by func- tional fixedness. (The solution to this problem appears at the end of the chapter.) The more you use an object in only one way, the harder it is to see new uses for it and to realize that an object can be used for an entirely different purpose. See “Applying Psychology: Becoming a More Skillful Problem Solver” for techniques that will improve your problem-solving skills.

Because creative problem solving requires gen- erating original ideas, deliberate strategies don’t always help. Solutions to many problems rely on insight, often a seemingly arbitrary flash “out of the blue.” (See Chapter 5, “Learning.”) Psychologists have only recently begun to investigate such sponta- neous problem-solving processes as insight and intu- ition (Gilhooly & Murphy, 2005; Sinclair & Ashkanasy, 2005), but research indicates that such “mental breakthroughs” are likely to occur only when we widen our scope of atten- tion from a few obvious but incorrect alternatives to more diverse possible solutions (B. Bower, 2008). This conclusion is supported by neuroimaging, which reveals that insight is generally preceded by periods of increased electrical activity in the frontal regions of the brain involved in suppressing unwanted thoughts (Kounios et al., 2008; Qiu, Li, Jou, Wu, & Zhang, 2008).

The value of looking for new ways to represent a difficult problem cannot be overstressed. Be open to potential solutions that at first seem unproductive. The solution may turn out to be more effective, or it may suggest related solutions that will work. This is the rationale behind the technique called brainstorming: When solving a problem, generate a lot of ideas before you review and evaluate them (Baruah & Paulus, 2008; McGlynn, McGurk, Effland, Johll, & Harding, 2004; Paulus & Brown, 2007).

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brainstorming A problem-solving strategy in which an individual or a group produces numerous ideas and evaluates them only after all ideas have been collected.

Becoming a More Skillful Problem Solver

Even the best problem solvers occa-sionally get stumped, but you can dosome things that will help you find a solution. These tactics encourage you to discard unproductive approaches and find strategies that are more effective.

1. Eliminate poor choices. When we are surer of what won’t work than what will, the tactic of elimination can be very helpful. After listing all the pos- sible solutions you can think of, dis- card all the solutions that seem to lead in the wrong direction. Now, examine the list more closely. Some

solutions that seem to be ineffective may turn out to be good on closer examination.

2. Visualize a solution. If you are stumped by a problem, try using visual images. For example, in the Hobbit and Orc problems draw a pic- ture of the river, and show the Hob- bits and Orcs at each stage of the solution as they are ferried across. Drawing a diagram might help you grasp what a problem calls for, but you also can visualize mentally.

3. Develop expertise. We get stumped on problems because we lack the

knowledge to find a quick solution. Experts not only know more about a particular subject but also organize their information in larger “chunks” that are extensively interconnected, much like a cross-referencing system in a library.

4. Think flexibly. Striving to be more flexible and creative is an excellent tactic for becoming a better problem solver. This will help you avoid functional fixedness or prevent a mental set from standing in the way of solving a problem.

Solving Problems

Think for a moment of the last time you were confronted with a difficult problem. 1. What types of thinking or reasoning did you use to deal with that problem? 2. Having read this portion of the chapter, would you respond differently if you

were faced with a similar problem? If so, what would you do differently? 3. You are headed for Mount Rushmore, and you can see it from a distance.

You have no map. What is the best problem-solving strategy you can use to get there, and why?


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1. Match each problem-solving strategy with the appropriate definition. ___ algorithm a. rule-of-thumb approach that helps in simplifying and

solving problems, although it doesn’t guarantee a correct solution

___ heuristic b. strategy in which each step moves you closer to a solution

___ hill climbing c. step-by-step method that guarantees a solution ___ means-end analysis d. strategy in which one moves from the goal to the

starting point ___ working backward e. strategy that aims to reduce the discrepancy between

the current situation and the desired goal at a number of intermediate points

___ subgoal creation f. breaking down the solution to a larger problem into a set of smaller, more manageable steps

2. Match each form of thinking with its definition and the kind of problems to which it is suited. ___ divergent thinking ___ convergent thinking

a. suited to problems for which there is one correct solution or a limited number of solutions

b. thinking that involves generating many different ideas c. suited to problems that have no one right solution and require an inventive

approach d. thinking that limits its focus to a particular direction

Answers:1. Algorithm—c. heuristic—a. hill climbing—b. means-end analysis—e. working backward—d. subgoal creation—f.2. divergent thinking—b. and c. convergent thinking—a. and d.

Answers:1. a.2. d.


1. Your car is not operating correctly. The mechanic opens the hood and says, “We’ve been seeing lots of cars recently with fouled plugs or dirty fuel filters. Let’s start there and see if that’s your problem, too.” The mechanic is using a(n)

a. heuristic. b. algorithm. c. compensatory decision model. d. noncompensatory decision model.

2. You are at a football game when it begins to rain heavily. As you get soaked, you see the people next to you pull folded plastic garbage bags out of their pockets to use as a temporary “raincoat.” Your failure to realize that the garbage bag might also be used as rain protection is an example of

a. an algorithm. b. a heuristic. c. means-end analysis. d. functional fixedness.

DECISION MAKING How does decision making differ from problem solving?

Decision making is a special kind of problem solving in which we already know all the pos- sible solutions or choices. The task is not to come up with new solutions, but rather to iden- tify the best available one. This process might sound fairly simple, but sometimes we have to juggle a large and complex set of criteria as well as many possible options. For example,

L E A R N I N G O B J E C T I V E • Explain how decision making differs

from problem solving. Describe the process of compensatory decision making and the use of decision-making heuristics. Explain how framing can affect decisions, and how hindsight bias and counterfactual thinking affect the way we view our decisions after the fact.

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suppose that you are looking for an apartment among hundreds available. A reasonable rent is important to you, but so are good neighbors, a good location, a low noise level, and cleanliness. If you find an inexpensive, noisy apartment with undesirable neighbors, should you take it? Is it a better choice than a more expensive, less noisy apartment in a better loca- tion? How can you make the best choice?

Compensatory Decision Making How would you go about making a truly logical decision?

The logical way to make a decision is to rate each of the available choices on all the crite- ria you are using, arriving at some overall measure of the extent to which each choice matches your criteria. For each choice, the attractive features can offset or compensate for the unattractive features. This approach to decision making is therefore called a compensatory model.

Table 7–1 illustrates one of the most useful compensatory models applied to a car-buying decision. The buyer’s three criteria are weighted in terms of importance: price (not weighted heavily), gas mileage, and service record (both weighted more heavily). Next, each car is rated from 1 (poor) to 5 (excellent) on each of the criteria. Car 1 has an excellent price (5) but rela- tively poor gas mileage (2) and service record (1); and Car 2 has a less desirable price but fairly good mileage and service record. Each rating is then multiplied by the weight for that criterion (e.g., for Car 1, the price rating of 5 is multiplied by the weight of 4, and the result is put in parentheses next to the rating). Finally, ratings are totaled for each car. Clearly, Car 2 is the bet- ter choice: It is more expensive, but that disadvantage is offset by its better mileage and service record and these two criteria are more important than price to this particular buyer.

Although most people would agree that using such a table is a good way to decide which car to buy, at times people will abandon the compensatory decision-making process in the face of more vivid anecdotal information. For example, if a friend had previously bought Car 2 and found it to be a lemon, many people will choose Car 1 despite Car 2’s well-thought out advantages. Moreover, as we will see in the next section, it is often not possible or desirable to rate every choice on all criteria. In such situations people typically use heuristics that have worked well in the past to simplify decision making, even though they may lead to less-than-optimal decision making (Dhami, 2003).

Decision-Making Heuristics How can heuristic approaches lead us to make bad decisions?

Research has identified a number of common heuristics that people use to make decisions. We use the representativeness heuristic whenever we make a decision on the basis of cer- tain information that matches our model of the typical member of a category. For example, if every time you went shopping you bought the least expensive items and if all of these items turned out to be poorly made, you might eventually decide not to buy anything that seems typical of the category “very cheap.”

Another common heuristic is availability (E. Greene & Ellis, 2008; Schwarz & Vaughn, 2002). In the absence of full and accurate information, we often base decisions on

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Price (weight = 4) Gas mileage (weight = 8) Service record (weight = 10) Weighted Total

Car 1 5 (20) 2 (16) 1 (10) (46) Car 2 1 (4) 4 (32) 4 (40) (76)

Ratings: 5 = excellent; 1 = poor

compensatory model A rational decision- making model in which choices are systematically evaluated on various criteria.

representativeness A heuristic by which a new situation is judged on the basis of its resemblance to a stereotypical model.

availability A heuristic by which a judgment or decision is based on information that is most easily retrieved from memory.


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whatever information is most readily available, even though this information may not be accurate or complete. A familiar example of the availability heuristic is the so-called subway effect (Gilovich, 1991; Gilovich, Griffin, & Kahneman, 2002). It seems to be a law of nature that if you are waiting at a subway station, one train after another will come along headed in the opposite direction from the direction that you want to go. The problem here is that by the time a subway train does come along, we have already left the scene, so we never get to see the opposite situation: several subway trains going in our direction before one comes the other way. As a result, we tend to assume that those situations seldom or never occur, and so we make our decisions accordingly.

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