by Morton Hunt
Piaget once recounted the story of a mathematician friend that nicely illustrates how the assimilation of new information leads to accommodation and new thinking. The friend, as a small child, was counting pebbles one day. He lined them up, counted from left to right, and got ten. Then, to see what he would get by counting in the other direction, he recounted them from right to left—and was amazed: he still got ten. Inventively, he then arranged them in a circle and counted them: ten, of course. He recounted, going around the circle the other way: ten! “He discovered here,” Piaget commented, “what is known in mathematics as commutativity; that is, the sum is independent of the order.”11
Such mental development does not take place smoothly and continuously. From time to time, the accumulation of small changes such as the discovery of commutativity brings about a relatively abrupt shift to a different stage of thinking. The notion that the human psyche develops stage by stage was not original with Piaget—it had been suggested earlier by other psychologists—but Piaget was the first to identify and describe the stages on the basis of a wealth of observational and experimental evidence. The four major stages in Piaget’s theory (there are many substages) are:
—sensorimotor (birth to 18–24 months),
—preoperational (18–24 months to 7 years),
—concrete operations (7 years to 12 years), and
—formal operations (12 years and up).
The ages are only averages; Piaget was well aware that there are individual differences. But he said that the sequence was invariant; each stage is the necessary foundation of the succeeding one.
This is what takes place in each (some of the following findings have been modified by later research, as we will shortly see):12
Sensorimotor (birth to 18–24 months): At first infants are aware only of their sensations and do not connect them with external objects. They do not even connect the images of their hands with the sensations of their hands moving, and only gradually, through trial and error, discover how to make their reaching for a toy coincide with what they see.
Even when their movements become more purposeful and accurate, they have no sense of what the objects around them are like or how those things will respond to their actions. So they experiment: they suck, shake, bang, hit, or throw objects, thereby acquiring new knowledge that leads to more intelligent and purposeful actions.
From such experiences, and with the help of the growing power of memory (in part due to continuing maturation of the brain), children begin to have a store of mental images. This is why they realize, in the latter quarter of the first year, that a hidden object still exists, even though the perception of it is gone. Piaget called this the attainment of “object permanence.”
Toward the end of this stage, children begin to use their stored images and information to solve problems involving physical objects; they think about what might happen, instead of relying solely on manipulating things. Piaget, as a young father, proudly reported an episode of such thinking by his daughter Lucienne, who was sixteen months old. While playing with her, he put a watch chain in an empty matchbox, which he carefully left slightly open. He handed the matchbox to Lucienne, who had not been aware of his opening and closing it and had not seen him put the watch chain in it. She had only two “schemes” (learned ways of dealing with the situation): turning the box upside down to dump out its contents, and pushing her fingers in the slit to bring out the chain. She tried the second procedure first, groping to reach the chain, but was unable to. Then came a pause, during which Lucienne did something odd and noteworthy; as Piaget later reported the event:
She looks at the slit with great attention; then, several times in succession, she opens and shuts her mouth, at first slightly, then wider and wider… [then] unhesitatingly puts her finger in the slit, and instead of trying as before to reach the chain, she pulls so as to enlarge the opening. She succeeds and grasps the chain.13
Children also begin, at this time, to think about how to effect desired social consequences. Again Piaget reports his observation of one of his children:
At one year, four months, twelve days, Jacqueline has just been wrested from a game she wants to continue and placed in her playpen, from which she wants to get out. She calls, but in vain. Then she clearly expresses a certain need [i.e., to go to the bathroom], although the events of the last ten minutes [attest that] she no longer needs to. No sooner has she left the playpen than she indicates the game she wishes to resume!14
The child is acquiring a rudimentary ability to imagine or predict the results of certain simple actions and to conduct trial-and-error experiments in the mind. Henceforth, says Piaget, intellectual development proceeds “in the conceptual-symbolic rather than purely sensorimotor arena.”15
Preoperational (18–24 months to 7 years): Now the child rapidly acquires images, concepts, and words and becomes better able to talk and think about external objects and events in symbolic terms. The two-year-old shoves a wooden block around the floor and makes the sounds of a truck; the three-year-old pretends to drink out of an empty toy cup. At first, the child learning to talk regards things and their names as one and the same (the two-year-old sees a bird and says “Bird!” and if an adult uses the word “bird” the child says, “Where bird?”), but eventually learns that the word is a symbol, detachable from what it stands for. From then on, he or she is able to talk and think about absent things and past or future events.16
But the child’s internal representation of the world is still primitive, lacking such organizing concepts as causality, quantity, time, reversibility, comparison, and perspective. The child cannot perform mental operations involving these ideas; hence it is the “preoperational” stage. (By “operation” Piaget meant any mental routine that transforms information for some purpose. Classifying, subdividing, recognizing the parts in a whole, and counting are typical operations.) This is why the five-year-old thinks that six buttons spread out are more than six closely bunched, and water transferred to a tall thin glass is more than it was in a wide shallow glass. Even when children learn to count, for some time they do not grasp that 2×3 has to equal 3×2. Shown a bunch of flowers, most of which are yellow, and asked, “Are there more flowers or more yellow flowers?” they answer “Yellow.”
The preoperational child is also “egocentric” (as was the sensorimotor child), a term Piaget defined as incapable of imagining how things look from another perspective. Piaget would show four- to six-year-olds a model of three mountains, put a little doll in a particular place amidst the mountains, display a set of photographs of the mountains taken from different positions, and ask the children which one showed what the doll was now seeing. The children always chose the view they themselves saw. Similarly, he reported, preoperational children have trouble imagining what other people are thinking, and often speak without realizing that the other person is unfamiliar with what they are talking about.
Concrete operations (7 to 12 years): By seven or thereabouts, children shift to a distinctly new and more competent level of thinking. Now they can perform such operations as counting and classifying, and can understand and think about relationships. Where the preoperational child knows the word “brother” but cannot say what a brother is and knows what “big” is but cannot say which is the bigger of two big things, the operational child can deal with both.17 Mentally reversing a procedure is another operation. When a child can imagine pouring water back from the tall thin container into the original one, he acquires the concept of reversibility and with it that of “conservation,” the recognition that quantity does not change when shape does.
Children in this stage also become aware that events outside themselves have causes outside themselves. Preoperational children will say it gets dark at night because we go to sleep; concrete-operational children say it is because the sun sets. They are also better able to imagine how things look from another perspective, and how other people think and feel. They can thus mentally manipulate symbols as if they w
ere the things they refer to—but only symbols of physical objects and actions, not abstract ideas or logical processes. Deductive reasoning eludes them. Give them the first two propositions of a syllogism and they are not consistently able, if able at all, to draw the right conclusion.
Nor can they proceed systematically when tackling a problem with several variables. One of Piaget’s most productive tests was his pendulum problem. He would show a child a weight hanging from a string and demonstrate how to vary the length of the string, the amount of weight suspended by it, how to release the weight from different heights, and how to push it with different degrees of force. Then he would ask the child to figure out what factor or factors (length, weight, height, and force, singly or together) affected the pendulum’s rate of swinging. Pre-operational children made no plan of action; they tried different things at random, often varying several factors at once, making many incorrect observations, and reaching wrong conclusions. Operational children, though more systematic and accurate, still made frequent mistakes owing to illogical thinking. One ten-year-old boy tried changing the length of the string and concluded correctly that a pendulum swings slower when the string is longer. Then he compared the effect of a hundred-gram weight on a long string against that of a fifty-gram weight on a short string and concluded incorrectly that the pendulum also swings slower when the weight is greater.18
Formal operations (12 and up): In the final stage of development, children become capable of thinking about abstract relationships, like ratio and probability. They grasp syllogistic reasoning, cope with algebra, and begin to comprehend the elements of scientific thought and methodology. They can formulate hypotheses, concoct theories, and systematically examine the possibilities in a puzzle, mystery, or scientific problem. They play a game like Twenty Questions methodically, starting with broad questions and narrowing down the field of possibilities; until this stage their questions skipped from broad areas to narrow ones and back to broad ones, or overlapped, or were repetitive.
More important, they can now think not only about the concrete world but about possibilities, probabilities, and improbabilities, about the future, about justice, and values. As Piaget and his longtime collaborator, Bärbel Inhelder, say:
The great novelty of this stage is that by means of a differentiation of form and content the subject becomes capable of reasoning correctly about propositions he does not believe, or at least not yet; that is, propositions he considers pure hypotheses. He becomes capable of drawing the necessary conclusions from truths which are merely possible.19
Jerome Kagan has called Piaget’s analysis of the fundamentally new cognitive powers of adolescence “one of the most original ideas in any theory of human nature” and the source of “insights about adolescent behavior that challenge traditional explanations.” For one thing, it helps us understand the rise in the suicide rate in the teen years: the ability to think about hypothetical situations and know when one has exhausted all solution possibilities enables the adolescent to tell himself (rightly or wrongly) that he has tried or examined all ways of solving some personal problem and that none will work. For another, the ability to perceive inconsistencies within his own beliefs or those he is told to believe helps explain the rebelliousness, anger, and anxiety of the adolescent. Among the common and deeply troubling inconsistencies: conflicting values about teenage sex (it is immoral and risky, yet to abstain may seem “hung up” and abnormal); conflicting perceptions of the teenager’s relation to his parents (he wants and needs their support but also wants to be independent); and so on.*20
As opposed to admiration like Kagan’s, for several decades there has been a rising tide of revision and modification of Piaget’s ideas and findings; thousands of neo-, post-, and anti-Piagetian papers have been published or delivered at seminars. While much of this work has value, most of it is small stuff compared with the work of the giant himself. Isaac Newton once said, with false modesty, “If I have seen farther, it is by standing on the shoulders of giants”; the swarm of psychologists who have been correcting and revising Piaget’s theory could say in all truth that they see farther than he because they stand on his shoulders.
Cognitive Development
In the 1920s, Piaget’s early publications launched the modern study of cognitive development in Europe and America. But in the United States interest soon waned; behaviorism was becoming supreme and its adherents saw little value in what they considered new wine in the old bottle of mentalism. However, in the 1960s, when cognitivism began to regain favor, Piaget was rediscovered, and intellectual development research in his mode became a booming field.
But the tidy outlines of Piaget’s theory became blurred as swarms of doctoral candidates and psychologists, performing hundreds of Piaget-inspired studies, produced findings that often modified and sometimes challenged various aspects of the original. In the course of the past four decades, the field of cognitive development, though still much influenced by Piaget, has become an overgrown and unweeded garden. Outside it, moreover, researchers in two relatively new and burgeoning fields, cultural psychology and evolutionary psychology, have been vigorously raising a crop of studies that broaden and modify developmental psychology in distinctly non-Piagetian ways. But we will defer looking into these two specialties until we have seen what has been happening in Piagetian-based studies, some of which are sure to enlighten, delight, and occasionally astonish the viewer. Here, with no pretense to completeness or even representativeness, is a small gathering of the flowers and fruits of several decades of this genre of research.
Memory: How is one to investigate the memory of an infant who cannot speak, or, in the case of a newborn, indicate recognition even by facial expressions or hand movements? Researchers have thought up ingenious approaches to the problem. In an experiment conducted in 1959, infants less than a month old were conditioned to turn their heads at a particular sound (they turned them in response to a touch on the cheek and were rewarded by a bottle); a day later they still turned their heads when they heard the sound.21 The method, used with infants of different ages, yielded data on the growth of memory.
With infants a few months old, the method most frequently used has been the observation of their eye movements. The baby lies on his back looking up; above him is a display area where the experimenter puts two large cards, each containing a design such as a circle, a bull’s-eye, or a sketch of a face. The researcher times how long the baby’s eyes are directed at one pattern or the other. Since infants look at a new image longer than at a familiar one, the method yields a direct indication of what the infant remembers having seen.
Another technique, used in a 1979 experiment, called for a mobile to be suspended over the crib of an infant; subjects ranged from two to four months. When the baby kicked his legs, the researcher made the mobile move, and the infant soon learned to kick in order to see it move. Then he did not see the mobile again for a week, but when he did, he immediately started kicking. However, if two weeks went by, he did not. Again, the growth of memory was precisely measured.22
Such memory (recognition) is different from the more actively employed memory involved in a baby’s looking for an object that he has seen being hidden from view. If a baby of eight or nine months has twice retrieved a toy from under one of two similar covers, and if the researcher then puts it under the other cover—while the baby watches—the baby, unless allowed to look for the toy within a few seconds, will look where he previously found the toy. His memory functions at a primitive level. But a few months later he no longer makes that mistake. The advance is due to maturation of certain brain circuits. Monkeys in whom a particular region of prefrontal cortex is surgically destroyed never learn to look under the correct cover.23
By five, children effortlessly remember thousands of words, but the longest number they can repeat after hearing it read slowly is four digits long. By six or seven they can remember five digits, and by nine to twelve, six. This increase, however, comes about less from m
aturation than from the knowledge of how to remember. Before going to school children do not “rehearse” (repeat or review) information or use associative strategies; parents of a first-grader are often puzzled that their child can’t remember what went on at school that day. But in school children gradually learn memory strategies and soon know how, for instance, to visualize themselves in class at the beginning of the school day and so recall what happened first, and next, and next.24
Sense of self, sense of competence: The young child’s explorations of its world are a measure of his sharpening sense of self and growing sense of competence. At nine months, children still mouth and bang objects or aimlessly turn them over and over, but toward the end of their first year they begin to explore actual uses of those objects: they try drinking from a toy cup, “talking” into a toy phone, and so on. They become interested in investigating new territory and will momentarily crawl out of the mother’s sight; they turn whatever knobs and dials they can reach; they open closet and cupboard doors and take everything out. Such activities show what many developmentalists call “the attainment of competence.” Exploratory behavior, contrary to behaviorist theory, is not the consequence of rewarded acts but is spontaneous and self-initiated; the human infant and child has a need to investigate his own capacity for acting on objects, intervening in events, and widening his horizons.25
Another indication of the growth of the sense of competence is the smile of a child nearing two, even if no one is present, on successfully building a tower, putting a final piece in a puzzle, or fitting a dress on a doll. At the same time the child is becoming aware of failure and its meaning about the self. Jerome Kagan and his colleagues have noted that between fifteen and twenty-four months, children show anxiety if an adult demonstrates a form of advanced play and then tells them it is their turn. The play may consist of making a doll cook food in a pan and then have two dolls eat dinner, or making three animals take a walk and then hide under a cloth to avoid getting wet. Faced with the challenge of following such a relatively complicated scenario, children will fuss, cry, or cling to their mother. Kagan has interpreted this as evidence of the child’s fear of being unable to remember or to carry out the play in front of the adult, since if no onlooker is present, the child will often try out the modeled act or some part of it.26