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Assignment Piaget’s three-mountains problem.

Assignment: Piaget’s three-mountains problem.

Each mountain is distinguished by its color and by its summit. One has a red cross, another a small house, and the third a snow-capped peak. Children at the preoperational stage respond egocentrically. They cannot select a picture that shows the mountains from the doll’s perspective. Instead, they simply choose the photo that reflects their own vantage point.

FIGURE 7.6 Some Piagetian conservation tasks.
Children at the preoperational stage cannot yet conserve. These tasks are mastered gradually over the concrete operational stage. Children in Western nations typically acquire conservation of number, mass, and liquid sometime between 6 and 7 years and of weight between 8 and 10 years.

Inability to Conserve.
Piaget’s famous conservation tasks reveal a variety of deficiencies of preoperational thinking. Conservation refers to the idea that certain physical characteristics of objects remain the same, even when their outward appearance changes. At snack time, Priti and Sammy had identical boxes of raisins, but when Priti spread her raisins out on the table, Sammy was convinced that she had more. Piaget’s three-mountains problem.

In another conservation task involving liquid, the child is shown two identical tall glasses of water and asked if they contain equal amounts. Once the child agrees, the water in one glass is poured into a short, wide container, changing its appearance but not its amount. Then the child is asked whether the amount of water has changed. Preoperational children think the quantity has changed. They explain, “There is less now because the water is way down here” (that is, its level is so low) or, “There is more now because it is all spread out.” Figure 7.6 illustrates other conservation tasks that you can try with children.

The inability to conserve highlights several related aspects of preoperational children’s thinking. First, their understanding is centered, or characterized by centration . They focus on one aspect of a situation, neglecting other important features. In conservation of liquid, the child centers on the height of the water, failing to realize that changes in width compensate for changes in height. Second, children are easily distracted by the perceptual appearance of objects. Third, children treat the initial and final states of the water as unrelated events, ignoring the dynamic transformation (pouring of water) between them.Piaget’s three-mountains problem.

The most important illogical feature of preoperational thought is its irreversibility , an inability to mentally go through a series of steps in a problem and then reverse direction, returning to the starting point. Reversibility is part of every logical operation. After Priti spills her raisins, Sammy cannot reverse by thinking, “I know that Priti doesn’t have more raisins than I do. If we put them back in that little box, her raisins and my raisins would look just the same.”

Lack of Hierarchical Classification.
Preoperational children have difficulty with hierarchical classification —the organization of objects into classes and subclasses on the basis of similarities and differences. Piaget’s famous class inclusion problem, illustrated in Figure 7.7 , demonstrates this limitation. Preoperational children center on the overriding feature, red. They do not think reversibly by moving from the whole class (flowers) to the parts (red and blue) and back again.

FIGURE 7.7 A Piagetian class inclusion problem.
Children are shown 16 flowers, 4 of which are blue and 12 of which are red. Asked, “Are there more red flowers or flowers?” the preoperational child responds, “More red flowers,” failing to realize that both red and blue flowers are included in the category “flowers.” Piaget’s three-mountains problem.

Follow-Up Research on Preoperational Thought
Over the past three decades, researchers have challenged Piaget’s view of preschoolers as cognitively deficient. Because many Piagetian problems contain unfamiliar elements or too many pieces of information for young children to handle at once, preschoolers’ responses do not reflect their true abilities. Piaget also missed many naturally occurring instances of effective reasoning by preschoolers.

Egocentric, Animistic, and Magical Thinking.
Do young children really believe that a person standing elsewhere in a room sees exactly what they see? When researchers use simplified tasks with familiar objects, 3-year-olds show clear awareness of others’ vantage points, such as recognizing how something looks to another person who is looking at it through a color filter (Moll & Meltzoff, 2011 ). Even 2-year-olds realize that what they see sometimes differs from what another person sees. When asked to help an adult looking for a lost object, 24-month-olds—but not 18-month-olds—handed her a toy resting behind a bucket that was within the child’s line of sight but not visible to the adult (Moll & Tomasello, 2006 ).

Nonegocentric responses also appear in young children’s conversations. For example, preschoolers adapt their speech to fit the needs of their listeners. Four-year-olds use shorter, simpler expressions when talking to 2-year-olds than to agemates or adults (Gelman & Shatz, 1978 ). And in describing objects, children do not use such words as “big” and “little” in a rigid, egocentric fashion. Instead, they adjust their descriptions to allow for context. By age 3, children judge a 2-inch shoe as small when seen by itself (because it is much smaller than most shoes) but as big for a tiny 5-inch-tall doll (Ebeling & Gelman, 1994 ). Piaget’s three-mountains problem.

In Chapter 5 , we saw that toddlers have already begun to infer others’ intentions (see page 157 ). And in his later writings, Piaget ( 1945 / 1951 ) did describe preschoolers’ egocentrism as a tendency rather than an inability. As we revisit the topic of perspective taking, we will see that it develops gradually throughout childhood and adolescence.

Piaget also overestimated preschoolers’ animistic beliefs. Even young infants have begun to distinguish animate from inanimate, as indicated by their developing categorical distinctions between living and nonliving things (see page 166 ). By age 2½, children give psychological explanations (“he likes to” or “she wants to”) for people and occasionally for animals, but rarely for objects (Hickling & Wellman, 2001 ). In addition, preschoolers rarely attribute biological properties (like eating and growing) to robots, indicating that they are well aware that even a self-moving robot with lifelike features is not alive. They often say that robots have perceptual and psychological capacities—for example, seeing, thinking, and remembering (Jipson & Gelman, 2007 ; Subrahmanyam, Gelman, & Lafosse, 2002 ). But these responses result from incomplete knowledge about certain objects, and they decline with age.

Similarly, preschoolers think that magic accounts for events they otherwise cannot explain, as in Sammy’s magical explanation of thunder (Rosengren & Hickling, 2000 ). Consequently, most 3- and 4-year-olds believe in the supernatural powers of fairies, goblins, and other enchanted creatures. Furthermore, older 3-year-olds and 4-year-olds think that violations of physical laws (walking through a wall) and mental laws (turning on the TV just by thinking about it) require magic more than violations of social conventions (taking a bath with shoes on) (Browne & Woolley, 2004 ). These responses indicate that preschoolers’ notions of magic are flexible and appropriate. Piaget’s three-mountains problem.

Between ages 4 and 8, as children gain familiarity with physical events and principles, their magical beliefs decline. They figure out who is really behind Santa Claus and the Tooth Fairy, and they realize that the antics of magicians are due to trickery (Subbotsky, 2004 ). And increasingly, children say that characters and events in fantastical stories aren’t real (Woolley & Cox, 2007 ). Still, because children entertain the possibility that something imaginary might materialize, they may react with anxiety to scary stories, TV shows, and nightmares.

Logical Thought.
Many studies show that when preschoolers are given tasks that are simplified and relevant to their everyday lives, they do not display the illogical characteristics that Piaget saw in the preoperational stage. For example, when a conservation-of-number task is scaled down to include only three items instead of six or seven, 3-year-olds perform well (Gelman, 1972 ). And when asked carefully worded questions about what happens to a substance (such as sugar) after it is dissolved in water, most 3- to 5-year-olds know that the substance is conserved—that it continues to exist, can be tasted, and makes the liquid heavier, even though it is invisible in the water (Au, Sidle, & Rollins, 1993 ; Rosen & Rozin, 1993 ).

Preschoolers’ ability to reason about transformations is evident on other problems. They can engage in impressive reasoning by analogy about physical changes. Presented with the picture-matching problem “Play dough is to cut-up play dough as apple is to …?,” even 3-year-olds choose the correct answer (a cut-up apple) from a set of alternatives, several of which (a bitten apple, a cut-up loaf of bread) share physical features with the right choice (Goswami, 1996 ). These findings indicate that in familiar contexts, preschoolers can overcome appearances and think logically about cause and effect.

Finally, even without detailed biological or mechanical knowledge, preschoolers understand that the insides of animals are responsible for certain cause–effect sequences (such as willing oneself to move) that are impossible for nonliving things, such as machines (Gelman, 2003 ; Keil & Lockhart, 1999 ). Preschoolers seem to use illogical reasoning only when grappling with unfamiliar topics, too much information, or contradictory facts that they cannot reconcile. Piaget’s three-mountains problem.

Despite their difficulty with Piagetian class inclusion tasks, preschoolers organize their everyday knowledge into nested categories at an early age. By the beginning of early childhood, children’s categories include objects that go together because of their common function, behavior, or natural kind (animate versus inanimate), despite varying widely in perceptual features.

These 4-year-olds understand that a category (“dinosaurs”) can be based on underlying characteristics (“cold-blooded”), not just on perceptual features such as upright posture and scaly skin.

Indeed, 2- to 5-year-olds readily draw appropriate inferences about nonobservable characteristics shared by category members (Gopnik & Nazzi, 2003 ). For example, after being told that a bird has warm blood and that a stegosaurus (dinosaur) has cold blood, preschoolers infer that a pterodactyl (labeled a dinosaur) has cold blood, even though it closely resembles a bird.

During the second and third years, and perhaps earlier, children’s categories differentiate. They form many basic-level categories—ones that are at an intermediate level of generality, such as “chairs,” “tables,” and “beds.” By the third year, children easily move back and forth between basic-level categories and general categories, such as “furniture.” And they break down basic-level categories into subcategories, such as “rocking chairs” and “desk chairs.” Piaget’s three-mountains problem.

Assignment Piaget’s three-mountains problem.

Assignment Piaget’s three-mountains problem.

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Preschoolers’ rapidly expanding vocabularies and general knowledge support their impressive skill at categorizing. As they learn more about their world, they devise ideas about underlying characteristics that category members share—for example, that a combination of physical features, internal organs, and behaviors determines an animal’s identity (Gelman & Koenig, 2003 ). Also, adults label and explain categories to children, and picture-book reading is a rich context for doing so (Gelman & Kalish, 2006 ). In conversing about books, parents provide information (“Penguins live at the South Pole, swim, catch fish, and have thick layers of fat and feathers that help them stay warm”) that guides children’s inferences about the structure of categories. Furthermore, as the Social Issues: Education box on page 232 indicates, young children ask many questions about their world and usually get informative answers, which are well-suited to advancing their conceptual understanding.

In sum, although preschoolers’ category systems are less complex than those of older children and adults, they already have the capacity to classify hierarchically and on the basis of nonobvious properties. And they use logical, causal reasoning to identify the interrelated features that form the basis of a category and to classify new members.

TABLE 7.2 Some Cognitive Attainments of Early Childhood


2–4 years


Shows a dramatic increase in representational activity, as reflected in language, make-believe play, drawing, understanding of symbol–real-world relations, and categorization

Takes the perspective of others in simplified, familiar situations and in everyday, face-to-face communication

Distinguishes animate beings from inanimate objects; denies that magic can alter everyday experiences

Grasps conservation, notices transformations, reverses thinking, and understands many cause-and-effect relationships in familiar contexts

Categorizes objects on the basis of common function, behavior, and natural kind, not just perceptual features. Uses logical, causal reasoning to identify interrelated features that form the basis of a category

Sorts familiar objects into hierarchically organized categories

4–7 years


Becomes increasingly aware that make-believe (and other thought processes) are representational activities

Replaces beliefs in magical creatures and events with plausible explanations

Evaluation of the Preoperational Stage
Table 7.2 provides an overview of the cognitive attainments of early childhood. TAKE A MOMENT… Compare them with Piaget’s description of the preoperational child on pages 228 – 229 . The evidence as a whole indicates that Piaget was partly wrong and partly right about young children’s cognitive capacities. When given simplified tasks based on familiar experiences, preschoolers show the beginnings of logical thinking, which suggests that they attain logical operations gradually.

Evidence that preschoolers can be trained to perform well on Piagetian problems also supports the idea that operational thought is not absent at one point in time and present at another (Ping & Goldin-Meadow, 2008 ; Siegler & Svetina, 2006 ). Over time, children rely on increasingly effective mental (as opposed to perceptual) approaches to solving problems. For example, children who cannot use counting to compare two sets of items do not conserve number (Rouselle, Palmers, & Noël, 2004 ; Sophian, 1995 ). Once preschoolers can count, they apply this skill to conservation-of-number tasks involving just a few items. As counting improves, they extend the strategy to problems with more items. By age 6, they understand that number remains the same after a transformation as long as nothing is added or taken away (Halford & Andrews, 2006 ). Consequently, they no longer need to count to verify their answer.

The gradual development of logical operations poses yet another challenge to Piaget’s assumption of abrupt change toward logical reasoning around age 6 or 7. Does a preoperational stage really exist? Some no longer think so. Recall from Chapter 5 that according to the information-processing perspective, children work out their understanding of each type of task separately, and their thought processes are basically the same at all ages—just present to a greater or lesser extent. Piaget’s three-mountains problem.

Social Issues: Education Children’s Questions: Catalyst for Cognitive Development
Dad, what’s that?” asked 4-year-old Emily as her father chopped vegetables for dinner.

“It’s an onion,” her father said.

“Is an onion a fruit?” Emily asked.

“It’s a vegetable,” her father replied. “A root vegetable because it grows underground.”

Emily wrinkled her nose. “Why does it smell yucky?”

“I don’t know,” her father admitted. “But after dinner we can look it up online and find out.”

When young children converse with adults, they ask, on average, more than one question per minute! Do inquisitive children like Emily really want answers to their many questions? Or are they—as their parents sometimes conclude—merely clamoring for attention?

An analysis of diaries that parents diverse in SES and ethnicity kept of their children’s questions and of audio recordings of parent–child interactions revealed that at every age between 1 and 5 years, 70 to 90 percent of children’s questions were information-seeking (“What’s that [pointing to a crawfish]?”) as opposed to non-information-seeking (“Can I have a cookie?”) (Chouinard, 2007 ). And from age 2 on, children increasingly built on their fact-oriented questions with follow-up questions that asked for causes and explanations (“What do crawfish eat?” “Why does it have claws?”). By age 3½, these sets of “building questions” made up about half of children’s questions, confirming that preschoolers ask questions purposefully, to obtain clarifying information about things that puzzle them.

Unlike information obtained in other ways, answers to children’s questions provide them with the precise knowledge they need at the precise moment they need it. And the content of children’s questions is related to their cognitive development. At a time when vocabulary is advancing rapidly, about 60 percent of 1½- to 2-year-olds’ questions ask for names of objects. With age, preschoolers increasingly ask about function (“What’s it do?”), activity (“What’s he doing?”), state (“Is she hungry?”), and theory of mind (“How does the pilot know where to fly?”). Piaget’s three-mountains problem.

The usefulness of children’s questions depends on adults’ answers. Most of the time, parents respond informatively. If they do not, preschoolers are amazingly persistent: They ask again until they get the information they want. Parents adjust the complexity of their answers to fit their children’s maturity (Callanan & Oakes, 1992 ). To a question like “Why does the light come on?” 3-year-olds typically get simpler, “prior cause” explanations (“I turned on the switch”). Slightly older children frequently get “mechanism” explanations (“The switch allows electricity to reach the light bulb”).

Clearly, asking questions is a major means through which children strive to attain adultlike understandings. Children’s questions offer parents and teachers a fascinating window into their factual and conceptual knowledge, along with a wealth of opportunities to help them learn.

Preschoolers’ questions are often purposeful efforts to understand things that puzzle them. Because adults’ answers provide the precise knowledge children need at the precise moment they need it, question-asking is a powerful source of cognitive development.

Other experts think the stage concept is still valid, with modifications. For example, some neo-Piagetian theorists combine Piaget’s stage approach with the information-processing emphasis on task-specific change (Case, 1998 ; Halford & Andrews, 2006 ). They believe that Piaget’s strict stage definition must be transformed into a less tightly knit concept, one in which a related set of competencies develops over an extended period, depending on brain development and specific experiences. These investigators point to evidence that as long as the complexity of tasks and children’s exposure to them are carefully controlled, children approach those tasks in similar, stage-consistent ways (Andrews & Halford, 2002 ; Case & Okamoto, 1996 ). For example, in drawing pictures, preschoolers depict objects separately, ignoring their spatial arrangement. In understanding stories, they grasp a single story line but have trouble with a main plot plus one or more subplots.

This flexible stage notion recognizes the unique qualities of early childhood thinking. At the same time, it provides a better account of why, as Leslie put it, “Preschoolers’ minds are such a blend of logic, fantasy, and faulty reasoning.”

Piaget and Education
· Three educational principles derived from Piaget’s theory continue to have a major impact on both teacher training and classroom practices, especially during early childhood:

· ● Discovery learning. In a Piagetian classroom, children are encouraged to discover for themselves through spontaneous interaction with the environment. Instead of presenting ready-made knowledge verbally, teachers provide a rich variety of activities designed to promote exploration, including art, puzzles, table games, dress-up clothing, building blocks, books, measuring tools, and musical instruments.

· ● Sensitivity to children’s readiness to learn. In a Piagetian classroom, teachers introduce activities that build on children’s current thinking, challenging their incorrect ways of viewing the world. But they do not try to hasten development by imposing new skills before children indicate interest or readiness.

· ● Acceptance of individual differences. Piaget’s theory assumes that all children go through the same sequence of development, but at different rates. Therefore, teachers must plan activities for individual children and small groups, not just for the whole class. In addition, teachers evaluate educational progress in relation to the child’s previous development, rather than on the basis of normative standards, or average performance of same-age peers.

Like his stages, educational applications of Piaget’s theory have met with criticism. Perhaps the greatest challenge has to do with his insistence that young children learn mainly through acting on the environment (Brainerd, 2003 ). In the next section, we will see that young children also rely on language-based routes to knowledge.

REVIEW Select two of the following features of preoperational thought: egocentrism, a focus on perceptual appearances, difficulty reasoning about transformations, and lack of hierarchical classification. Present evidence indicating that preschoolers are more capable thinkers than Piaget assumed.

CONNECT Make-believe play promotes both cognitive and social development (see page 227 ). Explain why this is so.

APPLY Three-year-old Will understands that his tricycle isn’t alive and can’t feel or move on its own. But at the beach, while watching the sun dip below the horizon, Will exclaimed, “The sun is tired. It’s going to sleep!” What explains this apparent contradiction in Will’s reasoning?

REFLECT On the basis of what you have read, do you accept Piaget’s claim for a preoperational stage of cognitive development? Explain.

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