Piaget identifies four major stages of cognitive development. These are stages in the sense that all human beings who develop to maturity exhibit patterns of thinking that follow the orderly and predictable sequence that Piaget describes. These stages are described in Table 4.2. It is important to note (1) that Table 4.2 is an oversimplification of human cognitive development and (2) that the ages listed in the table are merely approximations. Development is a gradual process; children do not suddenly "graduate" to a new stage at any specific time. Table 4.3 estimates the proportion of learners at various ages who fall into each of these stages of development.
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Table 4.2. Piaget's Stages. |
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Sensorimotor |
Integrating senses with motor functions. Specifically goal directed behavior. Develops object permanence and other basic skills. |
0-2 years |
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Preoperational |
Cannot yet perform mental operations. Rapid increase in language ability. Engage in symbolic thought, but dominated by perception. |
2-7 years |
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Concrete Operational |
Can perform operations on objects that are immediately present or easily imagined. Cannot handle abstractions of abstractions. |
7-11 years |
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Formal Operational |
Can perform operations on abstract concepts. Capable of performing abstract and hypothetical thinking, but may still prefer concrete thinking (because it is easier). |
11 years - adulthood |
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Table 4.3. Percentage of Students at Each Grade Level Who Have Begun Each Piagetian Stage (Students are assumed to begin next level as soon as they finish previous. Formal Operational 2 refers to "solid competence at formal operational thinking.") |
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Grade |
Sensorimotor |
Preoperational |
Concrete Operational |
Formal Operational |
Formal Operational 2 |
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K |
100% |
100% |
5% |
0% |
0% |
|
1 |
100% |
100% |
25% |
0% |
0% |
|
2 |
100% |
100% |
80% |
0% |
0% |
|
3 |
100% |
100% |
90% |
0% |
0% |
|
4 |
100% |
100% |
100% |
0% |
0% |
|
5 |
100% |
100% |
100% |
0% |
0% |
|
6 |
100% |
100% |
100% |
0% |
0% |
|
7 |
100% |
100% |
100% |
5% |
0% |
|
8 |
100% |
100% |
100% |
10% |
0% |
|
1 HS |
100% |
100% |
100% |
50% |
0% |
|
2 HS |
100% |
100% |
100% |
75% |
25% |
|
3 HS |
100% |
100% |
100% |
100% |
50% |
|
4 HS |
100% |
100% |
100% |
100% |
60% |
|
1 Col |
100% |
100% |
100% |
100% |
80% |
|
2 Col |
100% |
100% |
100% |
100% |
85% |
|
3 Col |
100% |
100% |
100% |
100% |
90% |
|
4 Col |
100% |
100% |
100% |
100% |
95% |
|
Grad |
100% |
100% |
100% |
100% |
100% |
{Note: These estimates are pretty much guesses. If anyone can give me a citation on a good source, I would certainly appreciate it.}
Learners think in distinctly different ways at different stages of cognitive development. The major importance of Piaget's description of these stages is that he has identified specific ways in which learners change and develop as they progress toward maturity. By taking into consideration the ways in which learners think, teachers and instructional designers can understand learners better and prepare instructional materials or units of instruction that will more likely lead to mastery of educational goals.
Piaget's earliest stage of cognitive development is the sensorimotor stage (ages 0 to about 2 years). Until they are about two years old, children spend most of their intellectual efforts integrating their senses with their psychomotor abilities - hence the term sensorimotor. These children constantly assimilate new persons, objects, and ideas through their existing structures and modify these structures while they progress from a bundle of reflexes to the more sophisticated thinkers of the next stage. Because they are relatively predictable, interesting, and uncomplicated creatures, children in this stage offer ideal exhibits for the study of Piaget's ideas; and Piaget and others have developed very detailed descriptions of children during this stage. However, nearly all readers of this book will be primarily interested in older learners; and therefore detailed treatment will not be given to this initial stage. Parents who have children under two years of age will understand both their children and Piaget more fully by reading such sources as Flavell (1963), Phillips (1975), Ginsburg & Opper (1979), and Wadsworth (1989).
Note that people continue to develop their sensorimotor skills throughout their entire lives. They don't stop when they reach the next stage of development. The sensorimotor period receives its name because the integration of the senses with motor abilities is the primary activity during this time. During subsequent stages other activities will become more important.
The next three stages all contain the word operation. By merely looking at the labels for the stages, we can guess that preoperational children do not yet do operations, that concrete operational children can perform operations on concrete objects or ideas, and that formal operational learners can perform operations on abstract concepts. Therefore, if we can understand what an operation is, we can understand what Piaget meant by these three labels.
An operation is the mental manipulation of an object or idea. (Specific names for these operations, such as transformations, conservation, and reversals will not be discussed in detail in this book.) Figure 4.6 gives an example of an operation. Preoperational children (from about age 2 to about age 7) are not yet able to mentally manipulate objects or ideas. They are stuck with what they can directly perceive through their senses; therefore, they are overwhelmed and confused by the task shown in Figure 4.6 When they are presented with some sort of information that confuses their senses, like the optical illusion shown in Figure 4.6, they are unable to think it through and to realize that reality must be different from what they see. Note that even more mature learners (including readers of this book) could be confused by the optical illusion shown in Figure 4.6 and think that one line is longer than the other. However, even if the additional lines are drawn right in front of a preoperational child who is watching the process, that child is likely to be confused by the obvious perception that one line has "become" longer than the other. More mature learners would easily let their reasoning overrule their sensory input and realize that nothing has happened to the original lines. Table 4.4 lists some of the activities that children become capable of during the preoperational stage of development.
Figure 4.6. A simple operation. {A person who can perform concrete operations will recognize that the lines have remained the same size, because nothing has been added or taken away.}
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Table 4.4. Guidelines for Teaching Preoperational Children. |
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Use concrete props and visual aids. |
They cannot manipulate ideas mentally. |
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Make instruction sessions short. |
They have a short attention span, especially when they themselves do not initiate the activity. |
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Use actions as well as words. |
Actions are more concrete than words. |
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Give them a wide range of experiences. |
Lay the foundation for concept acquisition. |
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Give abundant hands-on experience. |
Lay the foundation for concept acquisition. |
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Be aware that they are likely to be deficient or inconsistent in seeing things from others' point of view. |
They have an egocentric perspective. |
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They may have unique viewpoints and parts of their language that you may be unaware of. |
They have an egocentric perspective. |
Concrete operational children (from about age 7 to about age 12), on the other hand, can mentally manipulate objects or ideas - as long as these are concretely present or at least directly recalled from memory. For example, when presented with a problem like that shown in Figure 4.6, a concrete operational child would be able to solve the problem by reversing the process - that is, by reasoning like this: "The two lines must still be the same. If the additional lines would be erased, we would be able to see that the original lines have not changed." The child could also apply the principle of identity: "Nothing has been added to or taken away from the original lines, and so they must still be equal." This mental manipulation enables the concrete operational child to go beyond simple sensory input. In different language, the concrete operational child is engaging in a low level of abstraction. What this child cannot do is perform abstractions on abstractions. For example, the concrete operational child would be stumped by this problem: "John is taller than Fred and Fred is shorter than Bill. Who is the tallest of them all? Who is the shortest of them all? Explain your answers." The answer is that Fred is the shortest of the three; but it is impossible to tell who is tallest, because all we know is that both John and Bill are taller than Fred. The concrete operational child could solve this problem - but only by first making it more concrete, perhaps by drawing diagrams.
The formal operational learner (beginning around age 12 but not fully developed until age 18 or 20), however, could solve this problem by simply inventing the imaginary people and moving them around mentally. Note that if these were real persons whom the child actually knew, this would become a simple concrete operational problem, since it would involve the mental manipulation of directly recalled persons rather than abstractions. Table 4.5 lists some things that learners become capable of during the stage of concrete operations.
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Table 4.5. Guidelines for Teaching Concrete Operational Children. |
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Use concrete props and visual aids. |
They can manipulate ideas mentally, but they need props as the ideas presented to them continue to become more abstract. |
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Make instruction sessions short. |
Their attention span is longer than for preoperational children, but they often want to focus on something new. |
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Give them opportunities to classify objects and ideas into increasingly complex groupings. |
This is what these children are good at &emdash; and they get better as they get older. Without doing this, they would never become formal operational. |
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Give them a wide range of experiences. |
These continue to lay the foundation for concept acquisition. These experiences also give them an opportunity to follow the preceding guidelines. |
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Give abundant hands-on experience. |
These continue to lay the foundation for concept acquisition. These experiences also give them an opportunity to classify and to develop their logical skills. |
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Present problems that require logical thinking of a relatively non-abstract level. |
They need practice dealing with abstractions. What they cannot do is abstractions on abstractions. |
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Use familiar objects and ideas to explain more complex concepts. |
They need practice at logical thinking as well as a push toward beginning really abstract thinking. |
As the previous paragraph indicated, formal operational learners can perform mental manipulations on abstractions as well as concrete objects. Table 4.6 lists some things that learners become capable of during this stage.
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Table 4.6. Guidelines for Teaching Formal Operational Children. |
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Continue to use strategies that were effective with concrete operational thinkers. |
Even though they are capable of abstract thinking, concrete thinking is still easier. Most people don't get really good at formal operational thinking and use it habitually until they are 21-23 years old. Even then, most sensible people check their abstract reasoning with concrete diagrams, etc. |
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Build abstractions upon solidly understood concrete concepts. |
Abstractions are essential for complex ideas, but these require that concrete ideas on which these are built be overlearned. |
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Give them opportunities to explore hypothetical questions. |
This is what these students are good at &emdash; and they get better as they get older. Without opportunities and encouragement, they would have no inducement to go beyond concrete operational thought. |
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Give them opportunities to solve problems that seem impossible to solve. |
Students take pride and build self-efficacy when they are able to solve problems that they could not have solved when they were less mature. |
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Promote scientific thinking. |
Scientific thinking is by its very nature supportive of abstract thinking. |
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Integrate concrete concepts with broad concepts, and encourage them to apply concepts in numerous settings. |
They need to generalize their abstract thinking abilities to numerous settings, many of which they will not encounter until they leave school. |
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Respect and encourage apparently off-the-wall thinking that involves insightful hypothetical reasoning. |
Even when they are incorrect, their attempt at hypothetical thinking may be a productive step in the right direction. |
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Model effective formal operational thinking to them. |
You are probably capable of formal operational thinking yourselves, and students can use you as a productive model while developing their own skills. If necessary, use deliberate scaffolded instruction (chapter 12). |
Teaching the Classics
Does it make sense to teach the "classics" to children at early ages? Should fifth graders read Julius Caesar? Should high school juniors read The Scarlet Letter and Red Badge of Courage? Should high school seniors read Macbeth? In Piaget's terms, reading will be productive to the extent that readers are able to assimilate what they read and accommodate their cognitive structures when necessary. The classics have achieved their enduring prominence because they have much to say that is worth assimilating; readers of great books develop cognitive structures that will serve them well throughout their lives. Therefore, exposure to the classics can be valuable - but only if the readers have the prerequisite cognitive structures and the developmental abilities to assimilate what the classics have to say and to make appropriate accommodations.
The problem with many of the classics is that they are written for adults. This is natural, since a culture would not develop very far if its literature were written only for children. Therefore, the classics often deal with complex emotions that children and adolescents are not likely to have experienced. Indeed, sometimes their major value lies in the fact that they deal with emotions that even adults are not likely to experience in their own lives. A major value of these books is that they often enable readers to identify with characters and vicariously experience situations and emotions that would otherwise be beyond their experience.
These vicarious experiences can be valuable - provided the readers are capable of benefiting from the vicarious experiences. But can learners identify with characters in novels before they are proficient at formal operational thinking? Certainly, even very young children do identify with characters in books in movies. I even remember identifying with Lassie, when I was younger. However, what very young children do is project themselves directly into the shoes of the characters in a story. When I identified with Lassie, I simply imagined myself (a fairly heroic person) facing tasks and overcoming problems similar to those encountered by Lassie (a heroic dog). The fact that a female dog had characteristics that made her distinctly different from myself never occurred to me.
What concrete operational children cannot do is project themselves into the shoes of a person who is distinctly different from themselves. This was driven home to me when I was discussing with my concrete operational son a newscast about a terrorist hostage situation. I asked him how he thought the hostages felt, and his answer was very realistic. I then asked him how he thought the family of the hostages felt, and again his answer was realistic. Finally, I asked him how he thought the hostage takers felt, and he replied, "Dirty and rotten." I clarified the question to make sure he was focusing on their feelings, and he was sincerely convinced that the hostage takers felt dirty and rotten. He was incapable of creating in his mind people whose ways and ideas were very different from his (one abstraction) and mentally projecting himself into their frame of reference (another abstraction). With the hostages and their families however, he simply assumed that they were very much like himself (a realistic assumption in this case) and projected himself into their frame of reference.
Similar problems arise when concrete operational children read Macbeth. Ask concrete operational children what the play is about, and they'll almost always reply, "It's about a bad man and a bad lady who got what was coming to them." Is that the play that Shakespeare wrote? When I first read Red Badge of Courage as a high school junior, I was convinced that it was a very boring war story. Johnny Tremain had been a lot more exciting. I was fortunate enough to reread Crane's novel fifteen years later, and I discovered that it was actually a fascinating psychological study. The main difference was that on the second occasion I possessed a more sophisticated set of cognitive structures and was fully formal operational.
It is distinctly possible that we are wasting students' time by ramming the classics down their throats at an age when they are not capable of understanding them. In many schools the main impact of reading Shakespeare in high school is to guarantee that they will never read Shakespeare as an adult, because they are certain that he is incomprehensible. Had they been exposed to Shakespeare when they were capable of the level of abstraction needed to understand the plays, their reaction may have been completely different.
The solution may be to have learners read good books that are not themselves classics but promote active and intelligent interaction that will enable them to develop cognitive structures and levels of thinking that will help them read these classics at a later time. The shelves of libraries are full of good books for concrete operational readers. The English Journal publishes a topical list in nearly every issue. The ideal book for adolescents and pre-adolescents may be one that can be understood sensibly at both the concrete operational and formal operational levels. For example, in Treasure Island, Jim can be almost completely understood by concrete operational readers; but Long John Silver can be more completely understood by more abstract levels of thinking. Such novels are useful, because they enable readers to make gradual accommodations, which will make it easier for them to make the transition to formal operational thinking.
With regard to Shakespeare, it should be very obvious that the plays - if they are to be studied at all by most pre-college students - should be viewed rather than read. Reading injects an additional level of abstraction that makes them more difficult to understand. In addition, the plays vary in their level of abstraction. For example, many adolescents would easily identify with the characters in Romeo and Juliet, especially if the plot is related to West Side Story, Titanic, or All My Children.
Note that the label for each stage describes the highest level of cognitive activity or the skill that the learner will predominantly be developing during that period. Learners can always go back and think at earlier stages; but during each stage they become increasingly free of constraints that would have been imposed on them at the previous stage. Thus, at the beginning of the concrete operational stage children are not completely competent in performing mental operations on concrete objects; they develop concrete reasoning skills while they progress through this stage. By the end of the stage they have thoroughly mastered the mental manipulation of concrete objects and are ready to mentally manipulate abstractions. Note also that simply because learners are capable of the type of thinking described by a higher stage this does not mean that they will find it easy or want to do so. For example, all intellectually mature adults are capable of formal operational thinking, but many of them tend to approach problems (such as the national economy, a marital argument, or an automotive malfunction) at a concrete operational level. However, if they are properly motivated and have access to appropriate background knowledge and opportunities, formal operational thinkers can solve problems that require abstract thinking.
One of the factors that enable learners to progress from one stage to the next is the fact that many concepts can be dealt with at more than one level of thinking. For example, not everything is either purely concrete or purely abstract. A specific dog is a very concrete notion, and the theory of relativity is very abstract. The concepts friend and democracy lie somewhere in between, and each of these concepts can be approached at various levels of abstraction. As Box 4.4 suggests, learners may move to higher levels of abstraction by dealing with information that they understand fully at a low level of abstraction, while they stretch a little to understand it less completely at a slightly higher level of abstraction.
It is important to note that Piaget classifies learners at various stages not based on what or how much they know, but rather on the basis of how they think. For this reason, followers of Piaget do not put much stock in traditional IQ tests to obtain information about a child's mental processes. They consider it much more important to know how a child arrived at an answer than to know how the number of correct answers given by a child compares to the number of correct answers given by similar children of the same age. Piagetians would never simply show children a series of problems like that shown in Figure 4.6 and classify as "smarter" those who gave correct answers. Rather, they would ask the children to explain their answers, and they would make inferences about the children's thought processes on the basis of these explanations. Careful observation and perceptive interviews are an important part of Piaget's studies; and educators who wish to understand children more fully and tailor instruction to their needs will be well advised to follow Piaget's example.
Although this chapter has discussed Piaget's theory of intellectual functioning and his stages of human development separately, the two topics actually overlap. The stages are merely broad categories that describe the ways in which learners assimilate and accommodate information and the level of abstraction that is likely to be typified by their structures. Another way to say this is to state that as children grow older, they develop not only structures related to specific objects, persons, and events, but also structures related to general problem solving strategies. Initially, children have a very primitive problem solving structure, consisting mostly of reflexes. As they try to assimilate information through this primitive structure, they find it necessary to expand this structure. After innumerable adaptations of this type, the initial problem solving structure (or set of structures) has changed enough that it makes sense to relabel it as preoperational rather than sensorimotor. Then the preoperational child continues to assimilate information through the current revision of the problem solving structures, and again accommodations become necessary. After numerous assimilations and accommodations as a result of active interaction with the environment, the problem solving structures evolve to the formal operational capacity of mature adulthood.
Some Piagetian Experiments
Imagine you are interviewing a second grader who can complete worksheets on double digit addition that involves carrying (e.g., 16+17=33). If you showed this child a card with "16" written on it and asked the child to show you how many chips the "1" stood for, what would the child say? Ten? Wrong! Almost all second graders (and many fourth graders) have no real concept that the 1 in 16 represents "10."
To prove this, conduct a detailed analysis of a group of children's understanding of the concept of place value. The children should be in primary grades (1-4) and should be expected to be familiar with the concept of tens.
Interview 1: Place in front of the child a large number of chips or pennies (70-80 for first graders, 100-120 for older children) and ask the child to guess how many there are. (The only purpose of this step is to get the child motivated to count the chips.) Then ask the child to verify his/her guess by counting the chips. If the child counted by ones, when he/she finishes, suggest counting by tens. Most bright second graders (and even many older children) will do silly things indicating a lack of understanding of the concept of place value.
Interview 2: Put 20 or more pennies or chips in front of the child. Show the child an index card with a large number 16 written on it. Ask the child to read the number. Ask the child to show you the number of chips the number represents. Move the extra chips aside, so that only the 16 chips are in front of the child. Then circle the 6 on the index card. Ask the child how many chips this number stands for. (Most children will have no trouble with this.) Then circle the "1" in 16. Ask the child how many chips this number stands for. Almost all bright second graders and many older children will show you one penny. (Some will even take this one penny from the six represented by the 6.) To probe, say, "If this 6 stands for these six pennies, and this 1 stands for this penny, then what about these? (Point to the remaining pennies.) Most children will say something like, "Those are nine more." Others will see no problem. Even those who see a problem are unlikely to reply that the "1" in 16 really stands for 10 chips.
For good background information and for information on the interview and observation methodology, refer to Kamii (1986, 1987).
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