Jean Piaget’s Theory of Cognitive Development

Cognition refers to thinking and memory processes, and cognitive development refers to long-term changes in these processes. One of the most widely known perspectives about cognitive development is the cognitive stage theory of Swiss psychologist Jean Piaget, who studied how infants and children gradually become able to think logically and scientifically.^[1]

Piaget was a psychological constructivist, which means that Piaget believed that a person learns by mentally organizing and reorganizing new information.  In addition, Piaget also believed that learning was not simply modeling or imitation, but rather an active process and interchange between individuals and their environment^[2] Piaget used the concept of equilibrium or equilibration to describe one of four critical factors in cognitive development, the others being maturation, physical environment, and social interaction. Piaget conceived equilibration as an ongoing process that refines and transforms mental structures, constituting the basis of cognitive development. More equilibration tends to occur as an individual is transitioning from one major developmental stage to the next.

Equilibration also explains an individual’s motivation for development. Individuals naturally seek equilibrium because disequilibrium, or disequilibration, which is a mismatch between one’s way of thinking and one’s environment, is inherently dissatisfying. When individuals encounter new discrepant information, they enter into a state of disequilibrium. In order to return to a state of equilibrium, individuals can ignore the information or attempt to manage it. One option for managing discrepant information is called assimilation, and the other option is called accommodation.^[3] The to-and-fro of these two processes, caused by cognitive disequilibration, leads not only to short-term learning, but also to long-term developmental change.^[4]

After observing children closely, Piaget proposed that cognition developed through four distinct stages from birth through the end of adolescence.

1. Sensorimotor Stage (Birth through 2 years old)
2. Preoperational Stage (2-7 years old)
3. Concrete Operational Stage (7-11 years old)
4. Formal Operational (12 years old- adulthood)

By stages Piaget meant a sequence of thinking patterns with the following four key features:

1. Stages always happen in the same order.
2. No stage is ever skipped.
3. Each stage is a significant transformation of the stage before it.
4. Each later stage incorporated the earlier stages into itself.^[5]

Schema, Assimilation, and Accommodation: Piaget believed that we are continuously trying to maintain cognitive equilibrium, or a balance, in what we see and what we know (Piaget, 1954). Children have much more of a challenge in maintaining this balance because they are constantly being confronted with new situations, new words, new objects, etc. All this new information needs to be organized, and a framework for organizing information is referred to as a schema. Children develop schemata through the processes of assimilation and accommodation. ^[6]

When faced with something new, a child may demonstrate assimilation, which is fitting the new information into an existing schema, such as calling all animals with four legs “doggies” because he or she knows the word doggie. Instead of assimilating the information, the child may demonstrate accommodation, which is expanding the framework of knowledge to accommodate the new situation and thus learning a new word to more accurately name the animal. For example, recognizing that a horse is different than a zebra means the child has accommodated, and now the child has both a zebra schema and a horse schema. Even as adults we continue to try and “make sense” of new situations by determining whether they fit into our old way of thinking (assimilation) or whether we need to modify our thoughts (accommodation).

Sensorimotor Stage

According to the Piagetian perspective, infants learn about the world during the primarily through their senses and motor abilities (Harris, 2005). These basic motor and sensory abilities provide the foundation for the cognitive skills that will emerge during the subsequent stages of cognitive development. Piaget called this first stage of cognitive development the sensorimotor stage and it occurs through the following six substages. ^[7]

Piaget’s Six Substages of Sensorimotor Development^[8]

Substage One: Simple Reflexes (Birth through 1st month)

This active learning begins with automatic movements or reflexes. For example, the nipple of a bottle comes into contact with an infant’s cheek and the infant will orient toward the object and automatically begin to suck on and lick the object.  However, this is also what happens with a sour lemon, much to the infant’s surprise!

Substage Two: First habits and primary circular reactions (1st through 4th month)

Fortunately, within a couple of weeks, the infant begins to discriminate between objects and adjust responses accordingly as reflexes are replaced with voluntary movements. An infant may accidentally engage in a behavior and find it interesting such as making a vocalization. This interest motivates trying to do it again and helps the infant learn a new behavior that originally occurred by chance. At first, most actions have to do with the body, but in months to come, will be directed more toward objects.

Substage Three: Secondary circular reactions (4th through 8th months)

During the next few months, the infant becomes more and more actively engaged in the outside world and takes delight in being able to make things happen. Repeated motion brings particular interest as the infant is able to bang two lids together from the cupboard when seated on the kitchen floor.

Substage Four: Coordination of circular reactions (8th through 12th months)

Now the infant can engage in behaviors that others perform and anticipate upcoming events. Perhaps because of continued maturation of the prefrontal cortex, the infant become capable of having a thought and carrying out a planned, goal-directed activity such as seeking a toy that has rolled under the couch. The object continues to exist in the infant’s mind even when out of sight and the infant now can make attempts to retrieve it. This ability is called object permanence.

Substage Five: Tertiary Circular Reactions (12th through 18th months)

Infants from one year to 18 months of age more actively engage in experimentation to learn about the physical world. Gravity is learned by pouring water from a cup or pushing bowls from highchairs. The caregiver tries to help the child by picking it up again and placing it on the tray. And what happens?  Another experiment! The child pushes it off the tray again causing it to fall and the caregiver to pick it up again! A closer examination of this stage causes us to really appreciate how much learning is going on at this time and how many things we come to take for granted must actually be learned. A mom tells the story of handing her daughters (who are close in age) a small container of candy and watching as they struggled to move the pieces up and out of the small box becoming more frustrated as their fingers would lose their grip on the treats before they made it up and out of top of the boxes.  The reason for their frustration is because these children had not yet learned to simply use gravity and turn the box over in their hands. This is a wonderful and messy time of experimentation, and most learning occurs by trial and error.

Substage Six: Internalization of Schemes and Early Representational thought (18th month to 2 years of age)

The child is now able to solve problems using mental strategies, to remember something heard days before and repeat it, to engage in pretend play, and to find objects that have been moved even when out of sight. Take for instance, the child      who is upstairs in a room with the door closed, supposedly taking a nap. The doorknob has a safety device on it that makes it impossible for the child to turn the knob. After trying several times in vain to push the door or turn the doorknob, the child carries out a mental strategy to get the door opened-he knocks on the door! Obviously, this is a technique learned from the past experience of hearing a knock on the door and observing someone opening the door. The child is now better equipped with mental strategies for problem-solving. This initial movement from the “hands-on” approach to knowing about the world to the more mental world of stage six marked the transition to preoperational intelligence that we will discuss in the next lesson. Part of this stage involves learning to use language.^[9]

Critical Evaluation Object Permanence

The main development during the sensorimotor stage is the understanding that objects exist and events occur in the world independently of one’s own actions (‘the object or ‘object permanence’).

Object permanence means knowing that an object still exists, even if it is   hidden. It requires the ability to form a mental representation (i.e. a schema) of the object. For example, if you place a toy under a blanket, the child who has achieved object permanence knows it is there and can actively seek it. At the beginning of this stage the child behaves as if the toy had simply disappeared.

The attainment of object permanence generally signals the transition from the sensorimotor stage to the preoperational stage of development.

Blanket and Ball Study

Aim: Piaget (1963) wanted to investigate at what age children acquire object permanence.

Method: Piaget hid a toy under a blanket, while the child was watching, and observed whether or not the child searched for the hidden toy.

Searching for the hidden toy was evidence of object permanence. Piaget   assumed that the child could only search for a hidden toy if s/he had a mental representation of it.

Results: Piaget found that infants searched for the hidden toy when they   were around 8-months-old.

Conclusion: Children around 8 months have object permanence because they are able to form a mental representation of the object in their minds.

Evaluation: Piaget assumed the results of his study occur because the children under 8 months did not understand that the object still existed underneath the blanket (and therefore did not reach for it). However, there are alternative reasons why a child may not search for an object:

The child could become distracted or lose interest in the object and therefore lack the motivation to search for it, or simply may not have the physical coordination to carry out the motor movements necessary for the retrieval of the object (Mehler & Dupoux, 1994).

There is evidence that object permanence occurs earlier than Piaget claimed. Bower and Wishart (1972) used a lab experiment to study infants aged between 1 – 4 months old.

Instead of using a Piaget’s blanket technique they waited for the infant to reach for an object, and then turned out the lights so that the object was no longer visible. They then filmed the infant using an infrared camera. They found that the infant continued to reach for the object for up to 90 seconds after it became invisible.

Again, just like Piaget’s study there are also criticisms of Bower’s “reaching in the dark” findings. Each child had up to 3 minutes to complete the task and reach for the object. Within this time period, it is plausible they may have successfully completed the task by accident.  For example, randomly reaching out and finding the object or even reaching out due to the distress of the lights going out (rather than reaching out with the intention of searching for an object).

Violation of Expectation Research

A further challenge to Piaget’s claims comes from a series of studies designed by Renee Baillargeon. She used a technique that has come to be known as the violation of expectation (VOE) paradigm. This technique exploits the fact that infants tend to look longer at situations or things they have not encountered before.

In a VOE experiment, an infant is first introduced to a novel situation. They are repeatedly shown this stimulus until they habituate to the stimulus, which is indicated, by the infant looking away. In Baillargeon’s  (1985, 1987) study, the habituation stimulus was a ‘drawbridge’ that repeatedly moved through 180 degrees (see image below).

The infants are then shown two new stimuli, each of which is a variation on the habituation stimulus. In Baillargeon’s experiments, one of these test stimuli is a possible event (i.e. one which could physically happen) and the other is an impossible event (i.e. one that could not physically happen in the way it appears).

In the ‘drawbridge’ study, a colored box was placed in the path of the drawbridge and infants were shown a “possible” event and an “impossible” event. In the possible event, the drawbridge stopped at the point where its path would be blocked by the box. In the impossible event, the drawbridge appeared to pass through the box and ended up lying flat, the box apparently having disappeared.

Baillargeon found that infants spent much longer looking at the impossible event. She concluded that this indicated surprise on the infants’ part and that the infants were surprised because they had expectations about the behavior of physical objects that the impossible event had violated.  That is a solid object cannot pass through another solid object.

In other words, the infants knew that the box still existed behind the drawbridge and, furthermore, also knew that one solid object cannot just pass through another. The infants in this study were five months old, an age at which Piaget would say that such knowledge is quite beyond them.^[10]

Renee Baillargeon Violation of Expectation Experiment: Possible versus Impossible Event

The A-not-B Error

The data does not always support Piaget’s claim that certain processes are crucial in transitions from one stage to the next. For example, in Piaget’s theory, an important feature in the progression into substage 4, coordination of   secondary circular reactions, is an infant’s inclination to search for a hidden object in a familiar location rather than to look for the object I in a new location. Thus, if a toy is hidden twice, initially at location A and subsequently at location B, 8- to 12-month-old infants search correctly at location A initially. But when the toy is subsequently hidden at location B, they make the mistake of continuing to search for it at location A. The A-not-B error is the term used to describe this common mistake. Older infants are less likely to make the A-not-B error because their concept of object permanence is more complete.^[11]

Preoperational Stage

 Remember that Piaget believed that we are continuously trying to maintain balance in how we understand the world. With rapid increases in motor skill and language development, young children are constantly encountering new experiences, objects, and words. In the module covering main developmental theories, you learned that when faced with something new, a child may either assimilate it into an existing schema by matching it with something they already know or expand their knowledge structure to accommodate the new situation. During the preoperational stage, many of the child’s existing schemas will be challenged, expanded, and rearranged. Their whole view of the world may shift.

Piaget’s second stage of cognitive development is called the preoperational stage and coincides with ages 2-7 (following the sensorimotor stage). The word operation refers to the use of logical rules, so sometimes this stage is misinterpreted as implying that children are illogical. While it is true that children at the beginning of the preoperational stage tend to answer questions intuitively as opposed to logically, children in this stage are learning to use language and how to think about the world symbolically. These skills help children develop the foundations they will need to consistently use operations in the next stage. Let’s examine some of Piaget’s assertions about children’s cognitive abilities at this age.

Pretend Play

Pretending is a favorite activity at this time. For a child in the preoperational stage, a toy has qualities beyond the way it was designed to function and can now be used to stand for a character or object unlike anything originally intended. A teddy bear, for example, can be a baby or the queen of a faraway land!

Piaget believed that children’s pretend play and experimentation helped them solidify the new schemas they were developing cognitively. This involves both assimilation and accommodation, which results in changes in their conceptions or thoughts. As children progress through the preoperational stage, they are developing the knowledge they will need to begin to use logical operations in the next stage.

Egocentrism

Egocentrism in early childhood refers to the tendency of young children to think that everyone sees things in the same way as the child. Piaget’s classic experiment on egocentrism involved showing children a three-dimensional model of a mountain and asking them to describe what a doll that is looking at the mountain from a different angle might see. Children tend to choose a picture that represents their own, rather than the doll’s view. However, when children are speaking to others, they tend to use different sentence structures and vocabulary when addressing a younger child or an older adult. Consider why this difference might be observed. Do you think this indicates some awareness of the views of others? Or do you think they are simply modeling adult speech patterns?^[12]

Testing for Egocentrism: Piaget’s Three Mountain Task^[13]

Martin Hughes (1975) argued that the three mountain task did not make sense to children and was made more difficult because the children had to match the doll’s view with a photograph.

Hughes devised a task which made sense to the child. He showed children a model comprising two intersecting walls, a ‘boy’ doll and a ‘policeman’ doll. He then placed the policeman doll in various positions and asked the child to hide the boy doll from the policeman.

Hughes did this to make sure that the child understood what was being asked of him, so if s/he made mistakes they were explained and the child tried again.   Interestingly, very few mistakes were made.

Hughes (1975) Police Doll Experiment^[14]

The experiment then began. Hughes brought in a second policeman doll, and placed both dolls at the end of two walls, as shown in the illustration  above. The child was asked to hide the boy from both policemen, in other words he had to take account of two different points of view.

Hughes’ sample comprised children between three and a half and five years of age, of whom 90 percent gave correct answers. Even when he devised a more complex situation, with more walls and a third policeman, 90 percent of four-year-old’s were successful.

This experiment showed that children have largely lost their egocentric thinking by four years  of age, because they are able to take the view of another. Hughes’ experiment allowed them to demonstrate this because the task made sense to the child, whereas Piaget’s did not.

In Borke’s (1975) test of egocentrism the child is given two identical models of a three-dimensional scene (several different scenes were used including different arrangements of toy people and animals and a mountain model similar to Piaget and Inhelder’s). One of the models is mounted on a turntable so it can easily be turned by the child.

After a practice session where the child is familiarized with the materials and the idea of looking at things from another person’s point of view, a doll is introduced (in Borke’s study it was the character Grover from ‘Sesame Street’, a program the children were familiar with).

The Grover doll was placed so it was ‘looking’ at the model from a particular vantage point and the child was invited to turn the other model around until its view of the model matched what Grover would be able to see.

Using the “mountains” model, Borke (1975) found that three-year-old’s selected a correct view 42% of the time and four-year-old’s selected the right view 67% of the time. With other displays, the three-years-old’s accuracy increased to 80% and the four-year old’s’ to 93%.^[15]

Precausal Thinking

Similar to preoperational children’s egocentric thinking is their structuring of cause-and-effect relationships based on their limited view of the world. Piaget coined the term “precausal thinking” to describe the way in which preoperational children use their own existing ideas or views, like in egocentrism, to explain cause-and-effect relationships. Three main concepts of causality, as displayed by children in the preoperational stage, include animism, artificialism, and transductive reasoning.

Animism is the belief that inanimate objects are capable of actions and have lifelike qualities. An example could be a child believing that the sidewalk was mad and made them fall down, or that the stars twinkle in the sky because they are happy. To an imaginative child, the cup may be alive, the chair that falls down and hits the child’s ankle is mean, and the toys need to stay home because they are tired. Young children do seem to think that objects that move may be alive, but after age three, they seldom refer to objects as being alive (Berk, 2007). Many children’s stories and movies capitalize on animistic thinking. Do you remember some of the classic stories that make use of the idea of objects being alive and engaging in lifelike actions?

Piaget identified four stages of animism beginning up to the ages of 4 or 5, Piaget noted that the child believes that almost everything is alive and has a purpose.  In the next stage (5-7 years), children begin to think that only objects that move have a purpose.  During the third stage (7-9 years), children believe that only objects that move spontaneously are thought to be alive, and finally in the fourth stage (9-12 years) the child understand that only plants and animals are alive.

Artificialism refers to the belief that environmental characteristics can be attributed to human actions or interventions. For example, a child might say that it is windy outside because someone is blowing very hard, or the clouds are white because someone painted them that color.

Finally, precausal thinking is categorized by transductive reasoning. Transductive reasoning is when a child fails to understand the true relationships between cause and effect. Unlike deductive or inductive reasoning (general to specific, or specific to general), transductive reasoning refers to when a child reasons from specific to specific, drawing a relationship between two separate events that are otherwise unrelated. For example, if a child hears a dog bark and then a balloon pop, the child would conclude that because the dog barked, the balloon popped. Related to this is syncretism, which refers to a tendency to think that if two events occur simultaneously, one caused the other. An example of this might be a child asking the question, “if I put on my bathing suit will it turn to summer?”

Cognition Errors

Between about the ages of four and seven, children tend to become very curious and ask many questions, beginning the use of primitive reasoning. There is an increase in curiosity in the interest of reasoning and wanting to know why things are the way they are. Piaget called it the intuitive substage because children realize they have a vast amount of knowledge, but they are unaware of how they acquired it.

Centration and conservation are characteristic of preoperative thought. Centration is the act of focusing all attention on one characteristic or dimension of a situation while disregarding all others. An example of centration is a child focusing on the number of pieces of cake that each person has, regardless of the size of the pieces. Centration is one of the reasons that young children have difficulty understanding the concept of conservation. Conservation is the awareness that altering a substance’s appearance does not change its basic properties. Children at this stage are unaware of conservation and exhibit centration. Imagine a 2-year-old and 4-year-old eating lunch. The 4-year-old has a whole peanut butter and jelly sandwich. He notices, however, that his younger sister’s sandwich is cut in half and protests, “She has more!” He is exhibiting centration by focusing on the number of pieces, which results in a conservation error.

Conservation of Liquid

In Piaget’s famous conservation task, a child is presented with two identical beakers containing the same amount of liquid. The child usually notes that the beakers do contain the same amount of liquid. When one of the beakers is poured into a taller and thinner container, children who are younger than seven or eight years old typically say that the two beakers no longer contain the same amount of liquid, and that the taller container holds the larger quantity (centration), without taking into consideration the fact that both beakers were previously noted to contain the same amount of liquid.

Irreversibility is also demonstrated during this stage and is closely related to the ideas of centration and conservation. Irreversibility refers to the young child’s difficulty mentally reversing a sequence of events. In the same beaker situation, the child does not realize that, if the sequence of events was reversed and the water from the tall beaker was poured back into its original beaker, then the same amount of water would exist.

Centration, conservation errors, and irreversibility are indications that young children are reliant on visual representations. Another example of children’s reliance on visual representations is their misunderstanding of “less than” or “more than”. When two rows containing equal amounts of blocks are placed in front of a child with one row spread farther apart than the other, the child will think that the row spread farther contains more blocks.

Class inclusion refers to a kind of conceptual thinking that children in the preoperational stage cannot yet grasp. Children’s inability to focus on two aspects of a situation at once (centration) inhibits them from understanding the principle that one category or class can contain several different subcategories or classes. Preoperational children also have difficulty understanding that an object can be classified in more than one way. For example, a four-year-old girl may be shown a picture of eight dogs and three cats. The girl knows what cats and dogs are, and she is aware that they are both animals. However, when asked, “Are there more dogs or more animals?” she is likely to answer “more dogs.” This is due to her difficulty focusing on the two subclasses and the larger class all at the same time. She may have been able to view the dogs as dogs or animals, but struggled when trying to classify them as both, simultaneously. Similar to this is a concept relating to intuitive thought, known as transitive inference.

Transitive inference is using previous knowledge to determine the missing piece, using basic logic. Children in the preoperational stage lack this logic. An example of transitive inference would be when a child is presented with the information “A” is greater than “B” and “B” is greater than “C.” The young child may have difficulty understanding that “A” is also greater than “C.”

As the child’s vocabulary improves and more schemes are developed, they are more able to think logically, demonstrate an understanding of conservation, and classify objects.^[16]

Limitations in the Child’s Thinking

Piaget focused most of the description of this stage on limitations in the child’s thinking, identifying a number of mental tasks which children seem unable to do.

These include the inability to decenter, conserve, understand seriation (the inability to understand that objects can be organized into a logical series or order) and to carry out inclusion tasks.

Children in the preoperational stage are able to focus on only one aspect or dimension of problems (i.e. centration). For example, suppose you arrange two rows of blocks in such a way that a row of 5 blocks is longer than a row of 7 blocks.

Preoperational children can generally count the blocks in each row and tell you The number contained in each. However, if you ask which row has more, they will likely say that it is the one that makes the longer line, because they cannot simultaneously focus on both the length and the number. This inability to decenter contributes to the preoperational child’s egocentrism.

Conservation is the understanding that something stays the same in quantity even though its appearance changes. To be more technical, conservation is the ability to understand that redistributing material does not affect its mass, number or volume. The ability to solve this and other “conservation” problems signals the transition to the next stage. So, what do these tasks tell us about the limitations of preoperational thought in general?  Piaget drew a number of related conclusions:

1) Understanding of these situations is ‘perception bound’. The child is drawn by changes in the appearance of the materials to conclude that a change has occurred.

2) Thinking is ‘centered’ on one aspect of the situation. Children notice changes in the level of water or in the length of clay without noticing that other aspects of the situation have changed simultaneously.

3) Thinking is focused on states rather than on transformations. Children fail to track what has happened to materials and simply make an intuitive judgment based on how they appear ‘now’.

4) Thinking is ‘irreversible’ in that the child cannot appreciate that a reverse transformation would return the material to its original state. Reversibility is a crucial aspect of the logical (operational) thought of later stages.^[17]

Concrete Operational Stage

From ages 7 to 11, children are in what Piaget referred to as the concrete operational stage of cognitive development (Crain, 2005). This involves mastering the use of logic in concrete ways. The word concrete refers to that which is tangible; that which can be seen, touched, or experienced directly.  The concrete operational child is able to make use of logical principles in solving problems involving the physical world. For example, the child can understand principles of cause and effect, size, and distance. The child can use logic to solve problems tied to their own direct experience, but has trouble solving hypothetical problems or considering more abstract problems. The child uses inductive reasoning, which is a logical process in which multiple premises believed to be true are combined to obtain a specific conclusion. For example, a child has one friend who is rude, another friend who is also rude, and the same is true for a third friend. The child may conclude that friends are rude. We will see that this way of thinking tends to change during adolescence being replaced with deductive reasoning.

Children Studying^[18]

We will now explore some of the major abilities that the concrete child exhibits.

Classification: As children’s experiences and vocabularies grow, they build schemata and are able to organize objects in many different ways. They also classification hierarchies and can arrange objects into a variety of classes and subclasses. Identity: One feature of concrete operational thought is the understanding that objects have qualities that do not change even if the object is altered in some way. For instance, mass of an object does not change by rearranging it. A piece of chalk is still chalk even when the piece is broken in two.

Reversibility: The child learns that some things that have been changed can be returned to their original state. Water can be frozen and then thawed to become liquid again, but eggs cannot be unscrambled. Arithmetic operations are reversible as well: 2 3 = 5 and 5 – 3 = 2. Many of these cognitive skills are incorporated into the school’s curriculum through mathematical problems and in worksheets about which situations are reversible or irreversible.

Conservation: Remember the example in our last chapter of preoperational children thinking that a tall beaker filled with 8 ounces of water was “more” than a      short, wide bowl filled with 8 ounces of water? Concrete operational children can understand the concept of conservation which means that changing one quality (in this example, height or water level) can be compensated for by changes in another quality (width). Consequently, there is the same amount of water in each container, although one is taller and narrower and the other is shorter and wider.

Decentration: Concrete operational children no longer focus on only one dimension of any object (such as the height of the glass) and instead consider the changes in other dimensions too (such as the width of the glass). This allows           for conservation to occur.

Seriation: Arranging items along a quantitative dimension, such as length or weight, in a methodical way is now demonstrated by the concrete operational child. For example, they can methodically arrange a series of different-sized sticks in order by length, while younger children approach a similar task in a haphazard way. ^[19]

Example of a Seriation Task that Involves Sorting by Shape and Size[15]

These new cognitive skills increase the child’s understanding of the physical world, however according to Piaget, they still cannot think in abstract ways. Additionally, they do not think in systematic scientific ways. For example, when asked which variables influence the period that a pendulum takes to complete its arc and given weights they can attach to strings in order to do experiments, most children younger than 12 perform biased experiments from which no conclusions can be drawn (Inhelder & Piaget, 1958).)^[20]

Horizontal Decalage

Piaget used the term horizontal décalage refers to fact that once a child learns a certain function, he or she does not have the capability to immediately apply the learned function to all problems. In other words, “a horizontal décalage arises when a cognitive structure that can be successfully applied to task X cannot, though it is composed of the same organization of logical operations, be extended to task Y.” Horizontal décalage is frequently used in reference to a child’s ability to solve different conservation tasks. This concept recognizes that an individual child will not necessarily be on the same level of functioning in all possible areas of performance. Rather, “concepts and schemas develop through operation on and manipulation of objects in a specific manner.”

An example of horizontal décalage is the invariance of quantity, which is typically mastered around the age of 6 or 7 when matter is concerned, at the age of 9 or 10 when weight is concerned, and around 11 or 12 years old when the invariant is volume. A 7-year-old child understands that when one of two equivalent balls of clay is transformed into a sausage-shape, the two lumps still consist of equal amounts of clay. The child, however, fails to correctly comprehend that the differently shaped clumps of clay weigh the same. Both tasks are similar, but the child is clearly unable to apply his understanding about the first situation to the second situation. A comparable phenomenon can be seen in a child’s increasing ability to perform seriation tasks, which consists of ordering objects according to increasing or decreasing size. The ability to arrange rods in order of decreasing/increasing size is always acquired prior to the capacity to seriate according to weight.[17]

 Formal Operational Stage

The formal operational stage begins at approximately age twelve and lasts into adulthood. As adolescents enter this stage, they gain the ability to think in an abstract manner by manipulating ideas in their head, without any dependence on concrete manipulation (Inhelder & Piaget, 1958). He/she can do mathematical calculations, think creatively, use abstract reasoning, and imagine the outcome of particular actions. An example of the distinction between concrete and formal operational stages is the answer to the question “If Kelly is taller than Ali and Ali is taller than Jo, who is tallest?” This is an example of inferential reasoning, which is the ability to think about things which the child has not actually experienced and to draw conclusions from its thinking. The child who needs to draw a picture or use objects is still in the concrete operational stage, whereas children who can reason the answer in their heads are using formal operational thinking.

Hypothetico-deductive reasoning:  The ability to think scientifically through generating predictions, or hypotheses, about the world to answer questions is hypothetico-deductive reasoning. The individual will approach problems in a systematic and organized manner, rather than through trial-and-error.

Abstract Thought : Concrete operations are carried out on things whereas formal operations are carried out on ideas. The individual can think about hypothetical and abstract concepts they have yet to experience. Abstract thought is important for planning regarding the future.

How Did Piaget Test Formal Operations?

Piaget (1970) devised several tests of formal operational thought. One of the simplest was the ‘third eye problem’. Children were asked where they would put an extra eye, if they were able to have a third one, and why. Schaffer (1988) reported that when asked this question, 9-year-olds all suggested that the third eye should be on the forehead. However, 11-year-olds were more inventive, for example suggesting that a third eye placed on the hand would be useful for seeing round corners.

Formal operational thinking has also been tested experimentally using the balance scale task (Inhelder & Piaget, 1958).  The balance-scale task (Inhelder and Piaget, 1958) is a logicomathematical problem-solving task. The scale consists of two arms in the form of a unitary beam, centrally attached to a fulcrum. On each arm, there are pegs placed at equally spaced distance from the fulcrum which are used to place unit weights. The child’s task is to predict whether the left or the right arm will tilt down, or whether the unitary beam will remain in balance. Children’s understanding of the weight-distance relationship with force (i.e., the torque applied to the arms) is examined according to their responses.

In line with the general idea of sequential stages of development Piaget (2002), believed that children go through three stages of development in order to solve the task (Inhelder and Piaget, 1958). It was argued that around 5–8 years of age, children acquire an understanding that their actions can impact those of an object, and consequently, children begin to understand the impact of weight and distance on the scale. However, 5–8-year-olds do not seem to be able to successfully combine the values of weight and distance together. This coordination of information would be understood around adolescence (Inhelder and Piaget, 1958).

The mathematical solution to solve the balance-scale task is to calculate torque. The torque, product of weight and distance (the amount of weight multipied by the distance from the fulcrum or center of the balance scale, represents the force applied to one side of the scale (Inhelder and Piaget, 1958; Ferretti and Butterfield, 1992; Shultz et al., 1994). The arm with the largest torque will be the one that tilts down. When torques are equal, the beam remains balanced.

Using Hypothetical Deductive Reasoning to Solve a Problem^[21]

According to Piaget, most people attain some degree of formal operational thinking, but use formal operations primarily in the areas of their strongest interest (Crain, 2005). In fact, most adults do not regularly demonstrate formal operational thought. A possible explanation is that an individual’s thinking has not been sufficiently challenged to demonstrate formal operational thought in all areas.

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Critical Evaluation

While Piaget used the balance scale task to test his stage theory, Siegler (2016) suggested that development is more of a continuum and  differentiated between a series of rules that children might use to solve balance-scale items. A child using Rule I will only consider the number of blocks in the prediction of the movement and disregards the distances—the number of blocks is more dominant than the distance. A child using Rule II does include the distance dimension in the prediction, but only when the number of blocks on each side of the fulcrum is equal. A child using Rule III does know that both the number-of-blocks and the distance dimension are relevant but does not know how to integrate both dimensions. A child using this rule will guess or ‘muddle through’ when both dimensions are in conflict. A child using Rule IV compares the torques on each side resulting in correct responses on all problems.^[22]

Like Piaget, Siegler found that eventually the children were able to take into account the interaction between the weight of the discs and the distance from the center, and so successfully predict balance. However, this did not happen until participants were between 13 and 17 years of age. Consequently, Siegler concluded that children’s cognitive development is based on acquiring and using rules in increasingly more complex situations, rather than in stages.^[23]

Criticisms of Piaget’s Theory

As with other major contributors of theories of development, several of Piaget’s ideas have come under criticism based on the results of further research. For example, several contemporary studies support a model of development that is more continuous than Piaget’s discrete stages (Courage & Howe, 2002; Siegler, 2005, 2006). Many others suggest that children reach cognitive milestones earlier than Piaget describes (Baillargeon, 2004; de Hevia & Spelke, 2010).

According to Piaget, the highest level of cognitive development is formal operational thought, which develops between 11 and 20 years old. However, many developmental psychologists disagree with Piaget, suggesting a fifth stage of cognitive development, known as the postformal stage (Basseches, 1984; Commons & Bresette, 2006; Sinnott, 1998). In postformal thinking, decisions are made based on situations and circumstances, and logic is integrated with emotion as adults develop principles that depend on contexts. One way that we can see the difference between an adult in postformal thought and an adolescent in formal operations is in terms of how they handle emotionally charged issues.

It seems that once we reach adulthood our problem-solving abilities change: As we attempt to solve problems, we tend to think more deeply about many areas of our lives, such as relationships, work, and politics (Labouvie-Vief & Diehl, 1999). Because of this, postformal thinkers can draw on past experiences to help them solve new problems. Problem-solving strategies using postformal thought vary, depending on the situation. What does this mean? Adults can recognize, for example, that what seems to be an ideal solution to a problem at work involving a disagreement with a colleague may not be the best solution to a disagreement with a significant other.^[24]

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Vygotsky’s Sociocultural Theory of Cognitive Development

While Vygotsky and Piaget are contemporaries, and both agreed that children were active learners in their own development, each also differed in their thinking when it came to how one’s cognition develops.  Unlike Piaget, Vygotsky argued that learning preceded cognitive development, and that culture directly affected cognitive development. Recall that for Piaget, egocentric speech, or disappears at the end of the preoperational stage, and was no longer necessary.  For Vygotsky, egocentric speech does not disappear, but rather begins to partner with the child as they take part in cognitive tasks.  According to Vissers, Tomas, and Law (2020), the first stage of language development defined by Vygotsky occurs during early childhood language acquisition when children master the fundamentals of an external dialogue.  This early form of speech focuses on connecting with others – on communication and regulation of one another’s behavior and was referred to by Vygotsky as external speech.  Then around the age of 3-4 years, as children’s linguistic experience increases, they begin to start talking to themselves.  Vygotsky referred to this type of speech as “private speech,” or speech for oneself.  At this stage, the main function of private speech is self-regulation or self-guidance.  For example, during this stage, you may observe a 4-year-old, “whisper” to themselves while planning their next step or commenting on their current activity.  A distinguishing feature of private speech compared to external speech is the absence of an interlocutor, which allows for the child to simplify the compositional and syntactic conventions that are required in a dialogue with another person. The flexibility in using speech covertly, what Vygotsky called “inner speech,” or thought develops after the age of 6 or 7, when children fully internalize their thought during various cognitive tasks, such as silent remembering, reading, and writing. ^[25]

According to Vygotsky, learning is a process of acquiring knowledge, beliefs, and problem solving strategies through interactions with what he termed “more knowledgeable others”. It is through our interactions with others that we make sense of the information we encounter. It is an inherently social process, one in which we depend on others to help us understand the world. Social learning thus precedes individual development and is unique to the individual.

The Zone of Proximal Development, or ZPD, explains the ability of a learner to extend beyond their own innate ability through interaction with others in their environment. It is the difference between one’s level of actual development, or what a learner can achieve independently, and the individuals level of potential development, or what they can learn with the guidance and support of what Vygotsky referred to as “more knowledgeable others.”  More knowledgeable others, or MKOs, are central to the ZPD learning process. Simply put, an MKO is someone with higher level knowledge or skill than the learner. As such, they serve as a source of sociocultural learning. MKOs are often thought of as older individuals, but they can be peers or younger persons provided they have a body of knowledge and experience that the learner doesn’t yet possess.^[26]

The Zone of Proximal Development

The sociocultural theory of learning emphasizes the need for scaffolding of information. That is, teaching is done to build knowledge and skill in incremental stages. For example, a teacher may demonstrate a technique, have the learner practice it under supervision, and provide guidance for skill improvement. Cycles of this may occur until the learner is able to practice the skill in its entirety independently. Cooperative learning opportunities are also important in this model. In this approach, more knowledgeable others (MKOs), or skilled peers are allowed to interact with the learner within the ZPD. Through these types of interactions, the learner grows and develops without direct intervention from the teacher. Composing groups with a mixture of high and lower performing students helps foster collaborative development. Reciprocal teaching is also a methodology under this model. With reciprocal teaching, teachers and learners use summarizing, questioning, clarifying, and predicting to improve the student’s ability to learn from text. As with other sociocultural methodologies, the teacher’s involvement is reduced over time until the learner is functioning independently.^[27] Scaffolding is effective when:

• The task is broken down into manageable steps.
• Direction is provided to keep the child focused.
• The child’s interest in the task is motivated by the teacher.
• Factors that cause frustration are reduced.
• The expectation of the activity are defined and modeled.
• Using open-ended questions like, “What do you think will happen if we…?

Vygotsky vs. Piaget

Vygotsky and Piaget were two influential theorists who focused on children’s cognitive development. While they share some similarities in their perspectives, there are also some significant differences between their theories. Who is correct? Both theories certainly contribute to our understanding of how children learn.  Overall, Vygotsky’s theory emphasizes the role of social and cultural factors in cognitive development, while Piaget’s theory focuses on individual exploration and experience with the physical world. ^[28]

Comparison of Vygotsky and Piaget’s Theories

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