The Developing Learner

Psychological Constructivism: Piaget’s Theories

Piaget believed that when we are faced with new information that we experience a cognitive disequilibrium. In response, we are continuously trying to regain cognitive homeostasis through adaptation. Piaget also proposed that, through maturation, we progress through four stages of cognitive development.


When it comes to maintaining cognitive equilibrium, novices have much more of a challenge because they are continually being confronted with new situations. All of this new information needs to be organized. The framework for organizing information is referred to as a schema. We develop schemata through the processes of adaptation. Adaptation can occur through assimilation and accommodation.

Video 3.6.1 Semantic Networks and Spreading Activation explains the creation and use of schemas.

Sometimes when we are faced with new information, we can simply fit it into our current schema; this is called assimilation. For example, a student is given a new math problem in class. They use previously learned strategies to try to solve the problem. While the problem is new, the process of solving the problem is something familiar to the student. The new problem fits into their current understanding of the math concept.

Not all new situations fit into our current framework and understanding of the world. In these cases, we may need accommodation, which is expanding the framework of knowledge to accommodate the new situation. If the student solving the math problem could not solve it because they were missing the strategies necessary to find the answer, they would first need to learn these strategies, and then they could solve the problem.

Figure 3.6.1 Model of Piaget’s adaptation theory.

Video 3.6.2. Schemas, Assimilation, and Accommodation explains Piaget’s theory of constructing schemas through adaptation.

Piaget’s Stages of Cognitive Development

After observing children closely, Piaget proposed that cognition developed through distinct stages from birth through the end of adolescence. By stages he meant a sequence of thinking patterns with four key features:

  1. They 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.

Piaget proposed four major stages of cognitive development: (1) sensorimotor intelligence, (2) preoperational thinking, (3) concrete operational thinking, and (4) formal operational thinking. Each stage is correlated with an age period of childhood, but only approximately.

Video 3.6.3. Piaget’s Stages of Cognitive Development explains the structure of the four stages and major cognitive developments associated with each stage.

The Sensorimotor Stage (0-2 years)

A toddler building a tower out of colorful blocksIn Piaget’s theory, the sensorimotor stage is first, and is defined as the period when infants’ think’ by means of their senses and motor actions. As every new parent will attest, infants continually touch, manipulate, look, listen to, and even bite and chew objects. According to Piaget, these actions allow them to learn about the world and are crucial to their early cognitive development.

At birth, the beginning of the sensorimotor stage, children have only a few simple reflexes (sucking, grasping, looking) to help them satisfy biological needs, such as hunger. By the end of this stage, children can move about on their own, solve simple problems in their heads, search for and find objects that are hidden from view, and even communicate some of their thoughts. Between 4 and 8 months of age, infants learn that they can make things move by banging and shaking them, which is why babies of this age love to play with rattles. Sometime between the eighth and twelfth months, they figure out how to get one thing (like a bottle) by using another (for instance, by knocking a pillow away). Between 12 and 18 months, children can represent hidden objects in their minds. They search for what they want, even when they cannot see it. At the end of this period, children are beginning to use images to stand for objects. For example, a 2-year-old places her doll inside a dollhouse and imaginatively reconstructs her doll’s view of the miniature rooms and furniture. This ability, called mediation, is a significant achievement because it frees the child from the need to think about only those objects she can see around her. A child who can mediate can think about the whole world.

Let us examine the transition that infants make from responding to the external world reflexively as newborns, to solving problems using mental strategies as two-year-olds by examining the various substages that children move through from birth to their second birthday.

Table 3.6.1. Sensorimotor substages.
Stage Age
Stage 1 – Reflexes Birth to 6 weeks
Stage 2 – Primary Circular Reactions 6 weeks to 4 months
Stage 3 – Secondary Circular Reactions 4 months to 8 months
Stage 4 – Coordination of Secondary Circular Reactions 8 months to 12 months
Stage 5 – Tertiary Circular Reactions 12 months to 18 months
Stage 6 – Mental Representation 18 months to 24 months

Substages of Sensorimotor Intelligence

For an overview of the substages of sensorimotor thought, it helps to group the six substages into pairs. The first two substages involve the infant’s responses to its own body, call primary circular reactions. During the first month first (substage one), the infant’s senses, as well as motor reflexes, are the foundation of thought.

Substage One: Reflexive Action (0-1month)

This active learning begins with automatic movements or reflexes (sucking, grasping, staring, listening). A ball comes into contact with an infant’s cheek and is automatically sucked on and licked. This reflexive response is also what happens with a sour lemon, much to the infant’s surprise! The baby’s first challenge is to learn to adapt the sucking reflex to bottles or breasts, pacifiers or fingers, each acquiring specific types of tongue movements to latch, suck, breath, and repeat. This adaptation demonstrates that infants have begun to make sense of sensations. Eventually, the use of these reflexes becomes more deliberate and purposeful as they move onto substage two.

Substage Two: First Adaptations to the Environment (1-4 months)

Fortunately, within a few days or 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 initially occurred by chance. The behavior is identified as circular and primary because it centers on the infant’s own body. At first, most actions have to do with the body, but in months to come, it will be directed more toward objects. For example, the infant may have different sucking motions for hunger and others for comfort (i.e., sucking a pacifier differently from a nipple or attempting to hold a bottle to suck it).

The next two substages (3 and 4), involve the infant’s responses to objects and people, called secondary circular reactions. Reactions are no longer confined to the infant’s body and are now interactions between the baby and something else.

Substage Three: Repetition (4-8 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 by responding to people and objects. Babies try to continue any pleasing event. Repeated motion brings particular interest as the infant can bang two lids together or shake a rattle and laugh. Another example might be to clap their hands when a caregiver says, “patty-cake.” Any sight of something delightful will trigger efforts for interaction.

Substage Four: New Adaptations and Goal-Directed Behavior (8-12 months)

Now the infant becomes more deliberate and purposeful in responding to people and objects and can engage in behaviors that others perform and anticipate upcoming events. Babies may ask for help by fussing, pointing, or reaching up to accomplish tasks, and work hard to get what they want. Perhaps because of continued maturation of the prefrontal cortex, the infant becomes capable of having a thought and carrying out a planned, goal-directed activity such as seeking a toy that has rolled under the couch or indicating that they are hungry. The infant is coordinating both internal and external activities to achieve a planned goal and begins to get a sense of social understanding. Piaget believed that at about 8 months (during substage 4), babies first understood the concept of object permanence, which is the realization that objects or people continue to exist when they are no longer in sight.

The last two stages (5 and 6), called tertiary circular reactions, consist of actions (stage 5) and ideas (stage 6) where infants become more creative in their thinking.

Substage Five: Active Experimentation of “Little Scientists” (12-18 months)

The toddler is considered a “little scientist” and begins exploring the world in a trial-and-error manner, using motor skills and planning abilities. For example, the child might throw their ball down the stairs to see what happens, or delight in squeezing all of the toothpaste out of the tube. The toddler’s active engagement in experimentation helps them learn about their world. Gravity is learned by pouring water from a cup or pushing bowls from high chairs. 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 appreciate how much learning is going on at this time and how many things we come to take for granted must actually be learned. This time is a wonderful and messy time of experimentation, and most learning occurs by trial and error.

Substage Six: Mental Representations (18-24 months)

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 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. Part of this stage also involves learning to use language. 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 thinking.

Current Research

Piaget lacked today’s sophisticated research techniques and scientific equipment for studying early cognition. Today researchers can study the preferences of infants by tracking their eye movements. They can also use sophisticated techniques to teach infants how to manipulate their environments (for example, suck on a bottle more vigorously to see or hear more interesting sights and sounds). This research has shown that infants gain a sense of the stability of objects (called object permanence) much earlier than Piaget estimated—at about 4 months (Baillargeon, 1987). Meltzoff (1988) showed 9- month-old infants a video of an adult playing with toys unfamiliar to the infants. A day later, the infants imitated the adult’s actions they had seen. This behavior suggests that deferred imitation (a form of mediation) is present almost a year earlier than Piaget expected it to occur. Although Piaget appears to have underestimated the ability of infants to take in information, store, organize, remember, and imitate it, he appears to have described correctly the sequences by which these skills develop. Furthermore, his view of the infant as a “mini-scientist” who acts on the world and builds theories about it is very much consistent with current research findings.

The Preoperational Stage (2 to 7 years)

A young girl writing with her father at a tableThe preoperational stage builds on the accomplishments of the sensorimotor stage. Piaget postulated that a radical or qualitative change occurs at this time: the emergence of symbolic thought. In the preoperational stage, children use their new ability to represent objects in a wide variety of activities; however, they do not yet do it in ways that are organized or entirely logical.

Pretend Play

One of the most obvious examples of this kind of cognition is pretend play, the improvised make-believe of preschool children. For example, during the preoperational period, children can make a horse out of a broom, a daddy out of a doll, or a truck or train out of a block of wood. Later (between 3 and 4 years), they play parts or roles: doctor and patient, mommy and daddy, good guys and bad guys, bus driver and passengers. In a way, children immersed in make-believe seem not to think realistically. However, at some level, these children know that it is just pretend and that they are merely representing objects. They are thinking on two levels at once—one imaginative and the other realistic. This dual processing of experience makes dramatic play an early example of metacognition, or reflecting on and monitoring of thinking itself. Metacognition is a highly desirable skill for success in school, one that teachers often encourage (Bredekamp & Copple, 1997; Paley, 2005). Partly for this reason, teachers of young children (preschool, kindergarten, and even first or second grade) often make time and space in their classrooms for dramatic play, and sometimes even participate in it themselves to help develop the play further.

Piaget believed that children’s pretend play and experimentation helped them solidify the new schemas they were developing cognitively. This process 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 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 merely modeling adult speech patterns?


Video 3.6.4. Egocentrism is a demonstration of a Piagetian task assessing a child’s ability to take another’s perspective. The first child in the video is a preschool-aged child. Despite just being in the same position as the adult, the child cannot imagine what the adult sees from their perspective and assumes that the adult sees what he sees. The second child, a school-aged child, after already being in the adult’s seat, can take her perspective and name the items that she likely sees from where she is sitting. Why is it that the first child cannot take the adult’s perspective and the second child can?

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 how preoperational children use their 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?

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.

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. They believe that the taller container holds the greater quantity (centration), without taking into consideration the fact that both beakers were previously noted to contain the same amount of liquid.

beakers of different dimensions showing beakers with various dimensions.

Figure 3.6.2. A demonstration of the conservation 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.


Video 3.6.5. Conservation Task is a demonstration of a few Piagetian tasks to assess children’s ability to understand various types of conservation. The first child is a preschooler and is not able to understand conservation. The second child is in elementary school. She does the same task and clearly understands conservation, although she does have some difficulty explicitly articulating her reasoning. A few additional conservation tasks are demonstrated by preschool children.

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 error 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.”

Theory of Mind

How do we come to understand how our mind works? The theory of mind is the understanding that the mind holds people’s beliefs, desires, emotions, and intentions. One component of this is understanding that the mind can be tricked or that the mind is not always accurate.

A two-year-old child does not understand very much about how their mind works. They can learn by imitating others, they are starting to understand that people do not always agree on things they like, and they have a rudimentary understanding of cause and effect (although they often fall prey to transitive reasoning). By the time a child is four, their theory of the mind allows them to understand that people think differently, have different preferences, and even mask their true feelings by putting on a different face that differs from how they truly feel inside.

To think about what this might look like in the real world, imagine showing a three-year-old child a bandaid box and asking the child what is in the box. Chances are, the child will reply, “bandaids.” Now imagine that you open the box and pour out crayons. If you now ask the child what they thought was in the box before it was opened, they may respond, “crayons.” If you ask what a friend would have thought was in the box, the response would still be “crayons.” Why?

Before about four years of age, a child does not recognize that the mind can hold ideas that are not accurate, so this three-year-old changes their response once shown that the box contains crayons. The child’s response can also be explained in terms of egocentrism and irreversibility. The child’s response is based on their current view rather than seeing the situation from another person’s perspective (egocentrism) or thinking about how they arrived at their conclusion (irreversibility). At around age four, the child would likely reply, “bandaids” when asked after seeing the crayons because by this age a child is beginning to understand that thoughts and realities do not always match.

Theory of Mind

Video 3.6.6. The Theory of Mind Test demonstrates various false belief tests to assess the theory of mind in young children.

Theory of Mind and Social Intelligence

This awareness of the existence of mind is part of social intelligence and the ability to recognize that others can think differently about situations. It helps us to be self-conscious or aware that others can think of us in different ways, and it helps us to be able to be understanding or empathic toward others. This developing social intelligence helps us to anticipate and predict the actions of others (even though these predictions are sometimes inaccurate). The awareness of the mental states of others is important for communication and social skills. A child who demonstrates this skill is able to anticipate the needs of others.

Impaired Theory of Mind in Individuals with Autism

People with autism or an autism spectrum disorder (ASD) typically show an impaired ability to recognize other people’s minds. Under the DSM-5, autism is characterized by persistent deficits in social communication and interaction across multiple contexts, as well as restricted, repetitive patterns of behavior, interests, or activities. These deficits are present in early childhood, typically before age three, and lead to clinically significant functional impairment. Symptoms may include lack of social or emotional reciprocity, stereotyped and repetitive use of language or idiosyncratic language, and persistent preoccupation with unusual objects.

About half of parents of children with ASD notice their child’s unusual behaviors by age 18 months, and about four-fifths notice by age 24 months, but often a diagnosis comes later, and individual cases vary significantly. Typical early signs of autism include:

  • No babbling by 12 months.
  • No gesturing (pointing, waving, etc.) by 12 months.
  • No single words by 16 months.
  • No two-word (spontaneous, not just echolalic) phrases by 24 months.
  • Loss of any language or social skills, at any age.

Children with ASD experience difficulties with explaining and predicting other people’s behavior, which leads to problems in social communication and interaction. Children who are diagnosed with an autistic spectrum disorder usually develop the theory of mind more slowly than other children and continue to have difficulties with it throughout their lives.

For testing whether someone lacks the theory of mind, the Sally-Anne test is performed. The child sees the following story: Sally and Anne are playing. Sally puts her ball into a basket and leaves the room. While Sally is gone, Anne moves the ball from the basket to the box. Now Sally returns. The question is: where will Sally look for her ball? The test is passed if the child correctly assumes that Sally will look in the basket. The test is failed if the child thinks that Sally will look in the box. Children younger than four and older children with autism will generally say that Sally will look in the box.

Ally-Anne Test

Video 3.6.7. Sally-Anne test demonstration with a young child.

Current Research

As with the sensorimotor stage, researchers are discovering that preoperational children are more cognitively capable than Piaget proposed. Donaldson (1978), Bower and Wishart (1972), Chandler, Fritz, and Hala (1989), and Gelman and Ebeling (1989) all concluded that children around the ages of 3 and 4 are not as egocentric as Piaget suggested. Researchers have shown that the difficulties children have with some of Piaget’s classic experiments largely result from a lack of understanding of the researcher’s questions. When researchers take pains to ensure that children understand these tasks, preoperational learners show that they can take the perspective of another; that is, they can begin to imagine another’s viewpoint. Researchers such as Gelman (1972) and Bijstra, van Geert, and Jackson (1989) have shown that operations such as conservation of liquids can be performed by preoperational children. Waxman and Gelman (1986) report that children as young as 4 can understand class inclusion.

Current research on children’s cognitive abilities during the preoperational period suggests two conclusions: (1) Piaget may have underestimated what some children can do during the preoperational stage; and (2) in order to exhibit more and varied abilities at this stage, researchers must first eliminate distractions, give clues, and ensure that children understand their directions. While children’s thinking is still largely dominated by what they see at this time, they can be taught to be less egocentric (Bee, 1995).

The Concrete Operational Stage (7-11 years)

A boy shown deep in thoughtThose who intend to teach at the kindergarten or first-grade level will work with learners just as they enter the concrete operational stage. According to Piaget, this is the time when children become less dominated by appearances and acquire the schemata to understand arithmetic, think in symbols, classify objects (like animal, vegetable, or mineral, or by color and shape), and understand the relationships between uppercase and lower- case letters. It is no wonder that formal education begins in so many societies around the world at this age. The critical accomplishments at this stage involve the learner’s ability to perform operations or rules that involve the mediation of words and images and to modify these mediators to reach a logical conclusion.

As children continue through elementary school, they become able to represent ideas and events more flexibly and logically. Their rules of thinking still seem very basic by adult standards, and usually operate unconsciously. However, these rules allow children to solve problems more systematically than before, and therefore, to be successful with many academic tasks. In the concrete operational stage, for example, a child may unconsciously follow the rule: “If nothing is added or taken away, then the amount of something stays the same,” but may struggle to make these processes explicit.

This simple principle helps children to understand some arithmetic tasks, such as in adding or subtracting zero from a number, as well as to do certain classroom science experiments, such as ones involving judgments of the amounts of liquids when mixed. Piaget called this period the concrete operational stage because children mentally “operate” on concrete objects and events. They are not yet able, however, to operate (or think) systematically about representations of objects or events. Manipulating representations is a more abstract skill that develops later, during adolescence.


Concrete operational thinking differs from preoperational thinking in two ways, each of which renders children more skilled as students. One difference is reversibility, or the ability to think about the steps of a process in any order. Imagine a simple science experiment, for example, such as one that explores why objects sink or float by having a child place an assortment of objects in a basin of water. Both the preoperational and concrete operational child can recall and describe the steps in this experiment, but only the concrete operational child can recall them in any order. This skill is beneficial on any task involving multiple steps—a common feature of tasks in the classroom. In teaching new vocabulary from a story, for another example, a teacher might tell students: “First make a list of words in the story that you do not know, then find and write down their definitions, and finally get a friend to test you on your list.” These directions involve repeatedly remembering to move back and forth between a second step and a first—a task that concrete operational students—and most adults—find easy, but that preoperational children often forget to do or find confusing. If the younger children are to do this task reliably, they may need external prompts, such as having the teacher remind them periodically to go back to the story to look for more unknown words.


The other new feature of thinking during the concrete operational stage is the child’s ability to decenter or focus on more than one feature of a problem at a time. There are hints of decentration in preschool children’s dramatic play, which requires being aware on two levels at once—for example, knowing that a banana can be both a banana and a ‘telephone.’ However, the decentration of the concrete operational stage is more deliberate and conscious than preschoolers’ make-believe. Now the child can attend to two things at once quite purposely. Suppose you give students a sheet with an assortment of subtraction problems on it, and ask them to do this: “Find all of the problems that involve two-digit subtraction and that involve borrowing from the next column. Circle and solve only those problems.” Following these instructions is quite possible for a concrete operational student (as long as they have been listening!) because the student can attend to the two subtasks simultaneously—finding the two-digit problems and identifying which actually involve borrowing. (Whether the student knows how to “borrow” however, is a separate question.)

Implications for Teachers

Elementary school learners are far better problem solvers than preschoolers. They can arrange objects in order; sequence numbers properly; classify objects by color, size, or shape; understand rules for both mathematics and classroom behavior; think about both the past and the future. Nevertheless, concrete operational learners cannot perform these operations with things they cannot see or touch. In other words, their logic works only in concrete situations. Their mental operations are not yet ready for the realm of abstract ideas. One way to illustrate this is to show an 8-year-old three dolls of ascending height whose names are Elleni, Carlos, and Aster. Show the child that Aster is taller than Carlos, and that Carlos is taller than Elleni, and the child will easily figure out that Aster is taller than Elleni. However, present only a verbal description of the three dolls, and the child will have great difficulty determining the height of the first doll relative to the third doll. Thus K through 4 teachers should teach using concrete, hands-on activities that provide examples of more general rules and concepts. The accompanying box, Teaching Concrete Operational Learners, gives some specific examples.

In real classroom tasks, reversibility and decentration often happen together. A well-known example of joint presence is Piaget’s experiments with conservation, the belief that an amount or quantity stays the same even if it changes apparent size or shape (Piaget, 2001; Matthews, 1998). Imagine two identical balls made of clay. Any child, whether preoperational or concrete operational, will agree that the two indeed have the same amount of clay in them simply because they look the same. However, if you squish one ball into a long, thin ‘hot dog,’ the preoperational child is likely to say that the amount of that ball has changed—either because it is longer or because it is thinner, but at any rate, because it now looks different. The concrete operational child will not make this mistake, thanks to new cognitive skills of reversibility and decentration. For them, the amount is the same because “you could squish it back into a ball again” (reversibility) and because “it may be longer, but it is also thinner” (decentration). Piaget would say the concrete operational child “has conservation of quantity.”

The classroom examples described above also involve reversibility and decentration. As already mentioned, the vocabulary activity described earlier requires reversibility (going back and forth between identifying words and looking up their meanings), but it can also be construed as an example of decentration (keeping in mind two tasks at once—word identification and dictionary search). Moreover, as mentioned, the arithmetic activity requires decentration (looking for problems that meet two criteria and also solving them), but it can also be construed as an example of reversibility (going back and forth between subtasks, as with the vocabulary activity). Either way, the development of concrete operational skills supports students in doing many basic academic tasks; in a sense, they make ordinary schoolwork possible

Current Research

Researchers have confirmed Piaget’s conclusions about the sequence and timing at which children acquire the various concrete operations and have shown that children between the ages of 7 and 11 rarely exhibit deductive logic but are adept at inductive reasoning (Tomlinson-Keasey, Eisert, Kalle, Hardy-Brown, & Keasey, 1978). However, there is much debate about what causes these changes. Piaget emphasized that children, particularly at this stage, act as amateur scientists and discover the rules of operations largely on their own, using the functions of organization and adaptation. He said little about the contributions of social influences, such as peers and culture, to cognitive development. We will explore this perspective shortly when we present the social nature of learning as formulated by Lev Vygotsky, an influential Russian developmentalist.

The Formal Operational Stage (11+ years)

Group of teens looking at and reading off of scenario cards as part of a training programIn the fourth (and last) of the Piagetian stages, an adolescent becomes able to reason not only about tangible objects and events, as younger children do, but also about hypothetical or abstract ones. Hence this stage is named the formal operational stage—the period when the individual can “operate” on “forms” or representations.

During the formal operational stage, adolescents can understand abstract principles which have no physical reference. They can now contemplate such abstract constructs as beauty, love, freedom, and morality. The adolescent is no longer limited by what can be directly seen or heard. Additionally, while younger children solve problems through trial and error, adolescents demonstrate hypothetical-deductive reasoning, which is developing hypotheses based on what might logically occur. They can think about all the possibilities in a situation beforehand, and then test them systematically (Crain, 2005). Now they can engage in true scientific thinking. Formal operational thinking also involves accepting hypothetical situations. Adolescents understand the concept of transitivity, which means that a relationship between two elements is carried over to other elements logically related to the first two, such as if A<B and B<C, then A<C (Thomas, 1979). For example, when asked: If Maria is shorter than Alicia and Alicia is shorter than Caitlyn, who is the shortest? Adolescents can answer the question correctly as they understand the transitivity involved.

Video 3.6.8. Formal Operational Stage explains some of the cognitive development consistent with formal operational thought.

Abstract and Hypothetical thinking

One of the major premises of formal operational thought is the capacity to think of possibility, not just reality. Adolescents’ thinking is less bound to concrete events than that of children; they can contemplate possibilities outside the realm of what currently exists. One manifestation of the adolescent’s increased facility with thinking about possibilities is the improvement of skill in deductive reasoning (also called top-down reasoning), which leads to the development of hypothetical thinking. This development provides the ability to plan ahead, see the future consequences of an action, and provide alternative explanations of events. It also makes adolescents more skilled debaters, as they can reason against a friend’s or parent’s assumptions. Adolescents also develop a more sophisticated understanding of probability.

This appearance of more systematic, abstract thinking allows adolescents to comprehend the sorts of higher-order abstract logic inherent in puns, proverbs, metaphors, and analogies. Their increased facility permits them to appreciate how language can be used to convey multiple messages, such as satire, metaphor, and sarcasm (children younger than age nine often cannot comprehend sarcasm at all). This change also permits the application of advanced reasoning and logical processes to social and ideological matters such as interpersonal relationships, politics, philosophy, religion, morality, friendship, faith, fairness, and honesty.

Deductive Reasoning

Video 3.6.9. Deductive Reasoning demonstrates a Piagetian task that presents the child with a hypothetical situation and asks that they deduce what happens given this scenario. The first child is an elementary school-aged child. The second is an adolescent. You can see how these two are able to use hypothetical information differently to make predictions about what will happen next.

Intuitive and Analytic Thinking

Piaget emphasized the sequence of thought throughout four stages. Others suggest that thinking does not develop in sequence, but instead, that advanced logic in adolescence may be influenced by intuition. Cognitive psychologists often refer to intuitive and analytic thought as the dual-process model, the notion that humans have two distinct networks for processing information (Kuhn, 2013.) Intuitive thought is automatic, unconscious, and fast, and it is more experiential and emotional.

In contrast, analytic thought is deliberate, conscious, and rational (logical). While these systems interact, they are distinct (Kuhn, 2013). Intuitive thought is easier, quicker, and more commonly used in everyday life. As discussed in the adolescent brain development section, the discrepancy between the maturation of the limbic system and the prefrontal cortex may make teens more prone to emotional, intuitive thinking than adults. As adolescents develop, they gain in logic/analytic thinking ability and sometimes regress, with social context, education, and experiences becoming significant influences. Simply put, being ‘smarter’ as measured by an intelligence test does not advance cognition as much as having more experience, in school and life (Klaczynski & Felmban, 2014).

Relativistic Thinking

Adolescents are more likely to engage in relativistic thinking—in other words, they are more likely to question others’ assertions and less likely to accept information as absolute truth. Through experience outside the family circle, they learn that rules they were taught as absolute are actually relativistic. They begin to differentiate between rules crafted from common sense (don’t touch a hot stove) and those that are based on culturally relative standards (codes of etiquette). This understanding can lead to a period of questioning authority in all domains.


Because most injuries sustained by adolescents are related to risky behavior (alcohol consumption and drug use, reckless or distracted driving, and unprotected sex), a great deal of research has been done on the cognitive and emotional processes underlying adolescent risk-taking. In addressing this question, it is important to distinguish whether adolescents are more likely to engage in risky behaviors (prevalence), whether they make risk-related decisions similarly or differently than adults (cognitive processing perspective), or whether they use the same processes but value different things and thus arrive at different conclusions. The behavioral decision-making theory proposes that adolescents and adults both weigh the potential rewards and consequences of an action. However, research has shown that adolescents seem to give more weight to rewards, particularly social rewards, than do adults. Adolescents value social warmth and friendship, and their hormones and brains are more attuned to those values than to long-term consequences (Crone & Dahl, 2012).

Some have argued that there may be evolutionary benefits to an increased propensity for risk-taking in adolescence. For example, without a willingness to take risks, teenagers would not have the motivation or confidence necessary to leave their family of origin. In addition, from a population perspective, there is an advantage to having a group of individuals willing to take more risks and try new methods, counterbalancing the more conservative elements more typical of the received knowledge held by older adults.

 Implications for Teachers

School is the main contributor to guiding students towards formal operational thought. With students at this level, the teacher can pose hypothetical (or contrary-to-fact) problems: “What if the world had never discovered oil?” or “What if the first European explorers had settled first in California instead of on the East Coast of the United States?” To answer such questions, students must use hypothetical reasoning, meaning that they must manipulate ideas that vary in several ways at once and do so entirely in their minds.

The hypothetical reasoning that concerned Piaget primarily involved scientific problems. His studies of formal operational thinking, therefore, often look like problems that middle or high school teachers pose in science classes. In one problem, for example, a young person is presented with a simple pendulum, to which different amounts of weight can be hung (Inhelder & Piaget, 1958). The experimenter asks: “What determines how fast the pendulum swings: the length of the string holding it, the weight attached to it, or the distance that it is pulled to the side?” The young person is not allowed to solve this problem by trial-and-error with the materials themselves but must reason a way to the solution mentally. To do so systematically, he or she must imagine varying each factor separately, while also imagining the other factors that are held constant. This kind of thinking requires the facility to manipulate mental representations of the relevant objects and actions—precisely the skill that defines formal operations.

As you might suspect, students with an ability to think hypothetically have an advantage in many kinds of schoolwork: by definition, they require relatively few “props” to solve problems. In this sense, they can, in principle, be more self-directed than students who rely only on concrete operations—certainly a desirable quality in the opinion of most teachers. Note, though, that formal operational thinking is desirable but not sufficient for school success, and that it is far from being the only way that students achieve educational success. Formal thinking skills do not ensure that a student is motivated or well-behaved, for example, nor does it guarantee other desirable skills. The fourth stage in Piaget’s theory is really about a particular kind of formal thinking, the kind needed to solve scientific problems and devise scientific experiments. Since many people do not usually deal with such problems in the ordinary course of their lives, it should be no surprise that research finds that many people never achieve or use formal thinking fully or consistently, or that they use it only in selected areas with which they are very familiar (Case & Okomato, 1996). For teachers, the limitations of Piaget’s ideas suggest a need for additional theories about development—ones that focus more directly on the social and interpersonal issues of childhood and adolescence.

Current Research

Most current research in formal operations focuses on three questions: (1) Do all children reach formal operations? (2) Are young children capable of abstract reasoning? and (3) Are there any higher stages of intellectual development? (Bee, 1995; Berk, 1993; Shaffer, 1993). Do all children reach formal operations?

Try giving the following test to some of your friends:

Premise 1: If there is a knife, then there is a fork.

Premise 2: There is not a knife. Question: Is there a fork?

The correct answer to this question is “maybe.” The wrong answer is “no.” However, 40 to 60 percent of college students fail formal operational problems, such as this one (Keating, 1979). Why? It appears that much of formal operational thought is situation-specific. In other words, although college students and adults are capable of hypothetico-deductive reasoning, they tend to be better at it in the fields with which they are familiar. Thus physics majors are better able to demonstrate formal operations when dealing with physics problems than are psychology majors, who, in turn, are better at abstract reasoning in their discipline than are English majors, and so on (DeLisi & Staudt, 1980). Are young children capable of abstract reasoning? Research indicates that concrete operational children can be taught abstract reasoning. For example, they can be taught how to solve propositions, such as the knife-and-fork task. Furthermore, training improves such performance (Hawkins, Pea, Glick, & Scribner, 1984). These training effects, however, are transitory. Specific training in propositional thinking lasts longer and generalizes more readily to new tasks when the trainees are in the formal operational stage (Greenbowe et al., 1981). Are there higher stages of intellectual development?

Beyond Formal Operational Thought: Postformal Thought

Although Piaget asserts that the formal operations stage represents the apex of cognitive thought, Patricia Arlin (1975, 1977) disagrees. She believes that great thinkers like Einstein, Freud, and Piaget operate in a higher cognitive dimension in which they reconceptualize existing knowledge and reformulate it to come up with unique ways of thinking about the world. She calls this the problem-finding stage of cognitive development.

The hallmark of this type of thinking is the ability to think abstractly or to consider possibilities and ideas about circumstances never directly experienced. Thinking abstractly is only one characteristic of adult thought, however, if you compare a 15-year-old with someone in their late 30s, you would probably find that the latter considers not only what is possible but also what is likely. Why the change? The adult has gained experience and understands why possibilities do not always become realities. They learn to base decisions on what is realistic and practical, not idealistic, and can make adaptive choices. Adults are also not as influenced by what others think. This advanced type of thinking is referred to as postformal thought (Sinnott, 1998).

In addition to moving toward more practical considerations, thinking in early adulthood may also become more flexible and balanced. Abstract ideas that the adolescent believes in firmly may become standards by which the adult evaluates reality. Adolescents tend to think in dichotomies; ideas are true or false; good or bad; there is no middle ground. However, with experience, the adult comes to recognize that there are some right and some wrong in each position, some good or some bad in a policy or approach, some truth and some falsity in a particular idea. This ability to bring together salient aspects of two opposing viewpoints or positions is referred to as dialectical thought and is considered one of the most advanced aspects of postformal thinking (Basseches, 1984). Such thinking is more realistic because very few positions, ideas, situations, or people are entirely right or wrong. So, for example, parents who were considered angels or devils by the adolescent eventually become just people with strengths and weaknesses, endearing qualities, and faults to the adult.

Video 3.6.10. Perry’s Stages of Intellectual Development explains post-formal stages of cognitive development in adulthood.

Does Everyone Reach Formal Operational or Postformal Thought?

Formal operational thought is influenced by experience and education. Most people attain some degree of formal operational thinking but use formal operations primarily in the areas of their strongest interest (Crain, 2005).  Even those that can use formal or postformal thought, do not regularly demonstrate it. Moreover, in small villages and tribal communities, it is barely used at all. A possible explanation is that an individual’s thinking has not been sufficiently challenged to demonstrate formal operational thought in all areas.

Some adults lead lives in which they are not challenged to think abstractly about their world. Many adults do not receive any formal education and are not taught to think abstractly about situations they have never experienced. Further, they are also not exposed to conceptual tools used to analyze hypothetical situations formally. Those who do think abstractly, in fact, may be able to do so more easily in some subjects than others. For example, psychology majors may be able to think abstractly about psychology, but be unable to use abstract reasoning in physics or chemistry. Abstract reasoning in a particular field requires a knowledge base that we might not have in all areas. Consequently, our ability to think abstractly depends to a large extent on our experiences.


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