pendulum experiment formal operational stage

Piaget’s Formal Operational Stage: Definition & Examples

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

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The formal operational stage begins at approximately age twelve and lasts into adulthood. As adolescents enter this stage, they can think abstractly by manipulating ideas in their head, without any dependence on concrete manipulation (Inhelder & Piaget, 1958).

In the formal operational stage, children tend to reason more abstractly, systematically, and reflectively. They are more likely to use logic to reason out the possible consequences of each action before carrying it out.

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.

Formal Operational Thought

Hypothetico-deductive reasoning.

Hypothetico-deductive reasoning is the ability to think scientifically through generating predictions, or hypotheses, about the world to answer questions.

The individual will approach problems in a systematic and organized manner rather than through trial-and-error.

A teenager can consider “what if” scenarios, like imagining the future consequences of climate change based on current trends.

Abstract Thought

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

A student understands and manipulates concepts like justice, love, and freedom without needing concrete examples or experiences. For instance, they can comprehend and discuss a statement such as “Justice is not always fair.”

Scientific Reasoning

An example of formal operational thought could be the cognitive ability to plan and test different solutions to a problem systematically, a process often referred to as “scientific thinking.”

The ability to form hypotheses, conduct experiments, analyze results, and use deductive reasoning is an example of formal operational thought.

A student forms a hypothesis about a science experiment, predicts potential outcomes, systematically tests the hypothesis, and then analyzes the results.

For example, they could hypothesize that increasing sunlight exposure will increase a plant’s rate of growth, design an experiment to test this, and then understand and explain the results.

Metacognition

Adolescents can think about their own thought processes, reflecting on how they learn best or understanding why they might have made a mistake in judgment.

For example, they might realize that they rush decisions when they’re feeling stressed and plan to use stress-reducing techniques before making important decisions in the future.

Testing 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 could 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, 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 pendulum task (Inhelder & Piaget, 1958). The method involved a length of string and a set of weights. Participants had to consider three factors (variables) the length of the string, the heaviness of the weight, and the strength of the push.

The task was to work out which factor was most important in determining the speed of swing of the pendulum.

Participants can vary the length of the pendulum string, and vary the weight. They can measure the pendulum speed by counting the number of swings per minute.

To find the correct answer, the participant has to grasp the idea of the experimental method -that is to vary one variable at a time (e.g., trying different lengths with the same weight). A participant who tries different lengths with different weights will likely end up with the wrong answer.

Children in the formal operational stage approached the task systematically, testing one variable (such as varying the string length) at a time to see its effect. However, younger children typically tried out these variations randomly or changed two things simultaneously.

Piaget concluded that the systematic approach indicated that children were thinking logically, in the abstract, and could see the relationships between things. These are the characteristics of the formal operational stage.

Critical Evaluation

Psychologists who have replicated this research, or used a similar problem, have generally found that children cannot complete the task successfully until they are older.

Robert Siegler (1979) gave children a balance beam task in which some discs were placed on either side of the center of balance. The researcher changed the number of discs or moved them along the beam, each time asking the child to predict which way the balance would go.

He studied the answers given by children from five years upwards, concluding that they apply rules which develop in the same sequence as, and thus reflect, Piaget’s findings.

Like Piaget, he 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.

He concluded that children’s cognitive development is based on acquiring and using rules in increasingly more complex situations, rather than in stages.

Learning Check

Which of the following is/are not an indication of an individual being in the formal operational stage?

Mark often struggles with planning for the future. He can’t envision different possible outcomes based on his actions. Which of the following is true about Mark? a. He is in the Formal Operational stage. b. He is in the Preoperational stage. c. He is in the Concrete Operational stage. d. He is in the Sensorimotor stage.

Which of the following actions does NOT indicate that Lucy is in the Formal Operational stage? a. Lucy can think about abstract concepts like justice and fairness. b. Lucy enjoys debates and discussions where she can express her thoughts. c. Lucy can only solve problems that are concrete and immediately present. d. Lucy enjoys conducting experiments to test her hypotheses.

Sam can play with his friends and imagine what they think about him. However, he can’t conceptualize different outcomes of a hypothetical situation. What stage is Sam likely in? a. He is in the Formal Operational stage. b. He is in the Preoperational stage. c. He is in the Concrete Operational stage. d. He is in the Sensorimotor stage.

• (b) He is in the Preoperational stage.
• (c) Lucy can only solve problems that are concrete and immediately present.
• (c) He is in the Concrete Operational stage.

According to Jean Piaget, in what stage do children begin to use abstract thinking processes?

According to Jean Piaget, children begin to use abstract thinking processes in the Formal Operational stage, which typically develops between 12 and adulthood.

In this stage, children develop the capacity for abstract thinking and hypothetical reasoning. They no longer rely solely on concrete experiences or objects in their immediate environment for understanding. Instead, they can imagine realities outside their own and consider various possibilities and perspectives.

They can formulate hypotheses, consider potential outcomes, and plan systematic approaches for problem-solving. Additionally, they can understand and manipulate abstract ideas such as moral reasoning, logic, and theoretical concepts in mathematics or science.

Based on Piaget’s theory, what should a teacher provide in the formal operational stage?

Based on Piaget’s theory, a teacher should provide the following for students in the Formal Operational stage:

Abstract Problems and Hypothetical Tasks : Encourage students to think abstractly and solve complex problems. Provide tasks that require logical reasoning, hypothesizing, and the consideration of multiple variables.

Opportunities for Debate and Discussion : Encourage students to express their thoughts and challenge the views of others. This can help them learn to view problems from multiple perspectives.

Experiments : Design lessons to allow students to develop hypotheses and conduct experiments. The scientific method is a valuable tool at this stage.

Real-world Applications : Connect classroom learning to real-world scenarios. This can help students understand the relevance and application of abstract ideas.

Higher-order Questions : Use questions involving analysis, synthesis, and evaluation to improve students’ critical thinking skills.

Guidance in Self-reflection : Encourage students to reflect on their thoughts, emotions, and behavior, which can help them understand their own cognitive processes better.

Moral and Ethical Discussions : As students in this stage begin to think more about abstract concepts such as justice, fairness, and rights, engage them in discussions around moral and ethical issues.

Piaget’s formal operational stage begins around age 11 or 12 and continues throughout adulthood. Does this suggest that once one reaches this level of cognitive development, they plateau? or are there different levels of formal operations?

According to Piaget’s theory, once individuals reach the Formal Operational stage, they have attained the highest level of cognitive development, as defined by his model. However, this does not suggest a cognitive plateau.

Cognitive development is individual and influenced by a range of factors beyond mere biological maturation.

The nature of human cognition is such that there’s always room for refinement, growth, and development throughout adulthood.

Furthermore, individual competence can vary greatly within the Formal Operational stage. For instance, a person might employ formal operational thinking in one area of life (such as their professional specialization) but not others.

Similarly, skills like problem-solving, logical reasoning, and handling abstract concepts can continue to improve with practice and experience.

Inhelder, B., & Piaget, J. (1958). Adolescent thinking.

Piaget, J. (1970). Science of education and the psychology of the child . Trans. D. Coltman.

Schaffer, H. R. (1988). Child Psychology: the future. In S. Chess & A. Thomas (eds), Annual Progress in Child Psychiatry and Child Development . NY: Brunner/Mazel.

Siegler, R. S. & Richards, D. (1979). Development of time, speed and distance concepts. Developmental Psychology, 15 , 288-298.

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10.2 Piaget’s Concrete Operational and Formal Operational Stages

The Human Development Teaching & Learning Group

Learning Objectives

• Name three major advances in cognitive development that occur with the shift to concrete operational thinking.
• What do these developments allow that thinking during the preoperational stage did not?
• Provide some examples of how concrete operational thought is seen in children’s everyday functioning during middle childhood.
• What are the limitations of concrete operational thought?
• Describe Piaget’s formal operational stage and the characteristics of formal operational thought.
• Identify the advances and limitations of formal operational thought.
• Describe metacognition.
• Explore whether postformal thought exists.

Recall from the last section that during early childhood children are in Piaget’s preoperational stage , and during this stage, children are learning to think symbolically about the world. As children continue into elementary school, they develop the ability to represent ideas and events more flexibly and logically . Their rules of thinking still seem very basic by adult standards and usually operate unconsciously, but they allow children to solve problems more systematically than before, and therefore to be successful with many academic tasks.

Concrete Operational Thought

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. Piaget called this period the concrete operational stage because children mentally “ operate ” on concrete objects and events. 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. A child may unconsciously follow the rule: “If nothing is added or taken away, then the amount of something stays the same.” This simple principle helps children to understand certain 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.

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 as deductive reasoning emerges. We will now explore three of the major capacities that the concrete operational child exhibits.

Thought becomes multidimensional

Concrete operational children no longer focus on only one dimension of any object (such as the height of the glass) and instead can coordinate multiple dimensions simultaneously (such as the width of the glass). (That is, they are no longer limited by centration, which is why this gain is also known by the term “decentration”). Multidimensionality allows children to take multiple perspectives at the same time, to understand part-while relationships, and to cross classify objects using multiple features.

• Multiple perspectives. Recall that when young children in the preoperational stage were asked to describe the Three Mountain display from the perspective of someone sitting across the table form them, they could only report on the view form one perspective– their own. With the emergence of connote operations, children can now understand that people looking from different vantage points, see different features. They can coordinate multiple perspectives. This skill is very useful, and can be practiced, while playing with peers and settling peer disputes.
• Part-whole relationships. Think back to preoperational thought, where if you showing a long child a bouquet of six daisies and 3 roses, and asked them whether there were more daisies or flowers, they would typically answer”daisies”? They could not coordinate the two perspectives of “part” and “whole.” Now in middle childhood, these questions seem silly– of course there are more flowers, flowers include both daisies and roses. At the age, the correct answer is obvious– it’s a logical necessity.
• Classification.  As children’s experiences and vocabularies grow, they build schemata and are able to organize objects in many different ways . They also understand classification hierarchies and can arrange objects into a variety of classes and subclasses.

Thought becomes operational

A second major shift in cognitive development during middle childhood coccus when thought becomes operational , by which Piaget meant that it consists of reversible, organized systems of mental actions.  These systems allow children to mentally undo actions ( reversibility ) and to understand that certain properties of objects (like their number, mass, volume, and so on) remain constant despite transformations in appearance ( conservation ).

• 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.

Thought becomes logical

A third major accomplishment of concrete operational development is that thought becomes logical , and children can reason logically about concrete events.

• Inferring higher-order characteristics. Where young children’s reasoning was focused on perceptual cues, older children can now consider a variety of specific cues and from, use the power of inference, to reach a logical conclusion about  higher-order characteristics. This capacity is seen in children’s understanding of their own and other people’s capacities and personalities. For example, after a child does well on multiple multiple assignments in math, she may conclude that she is high in math ability.
• Identify defining features. Whereas young children’s understanding was dominated by the most perceptually salient features of objects, with concrete operational thought, children in middle childhood focus instead on the defining features of particular objects or states.  They are not distracted by the most salient features; they recognize the underlying defining features. For example, young children might think that bicycles and toasters are alive (a kind of thought called “animism,” remember?) because they move. By middle childhood, however, children understand that even though many mechanical devices (e.g., cars, fireworks) and natural objects move (e.g., the sun, the tides), only plants and animals have a life force, which is the defining feature of being alive.

• Transitive inference.  Being able to understand how objects are related to one another is referred to as transitivity, or transitive inference. This means that if one understands that a dog is a mammal, and that a poodle is a dog, then a poodle must be a mammal.

Limitations of concrete operational thought

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).

Formal Operational Thought

In the last of the Piagetian stages, the young adolescent becomes able to reason not only about tangible objects and events, but also about hypothetical or abstract ones. Hence, it has the name formal operational stage—the period when the individual can “operate” on “forms” or representations. This allows an individual to think and reason with a wider perspective. This stage of cognitive development, which Piaget called  formal operational thought , marks a movement from an ability to think and reason from concrete visible events to an ability to think hypothetically and entertain what-if possibilities about the world. An individual can solve problems through abstract concepts and utilize hypothetical and deductive reasoning. Adolescents initially use trial and error to solve problems, but the ability to systematically solve a problem in a logical and methodical way emerges.

Hypothetical and Abstract Thinking

One of the major advances 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 provides the ability to plan ahead, see the future consequences of an action and to provide alternative explanations of events. It also makes adolescents more skilled debaters, as they can reason against a friend’s or parent’s position. Adolescents also develop a more sophisticated understanding of probability.

This video explains some of the cognitive development consistent with formal operational thought.

You can view the transcript for “Formal operational stage – Intro to Psychology” here (opens in new window) .

Link to Learning: Formal Operational Thinking in the Classroom

School is a main contributor in 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, onto 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 facility at manipulating 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 school work: 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 normally deal with such problems in the normal 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 cognitive developments—ones that focus more directly on the social and interpersonal issues of childhood and adolescence.

Propositional thought

The appearance of more systematic, abstract thinking also allows adolescents to comprehend higher order abstract ideas, such as those inherent in puns, proverbs, metaphors, and analogies. Their increased facility permits them to appreciate the ways in which 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 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. This newfound ability also allows adolescents to take other’s perspectives in more complex ways, and to be able to better think through others’ points of view.

Metacognition

Meta-cognition refers to “thinking about thinking.” This often involves monitoring one’s own cognitive activity during the thinking process. Adolescents are more aware of their own thought processes and can use mnemonic devices and other strategies to think and remember information more efficiently. Metacognition provides the ability to plan ahead, consider the future consequences of an action, and provide alternative explanations of events.

The capacity to consider multiple possibilities and perspectives often leads adolescents to the conclusion that nothing is absolute– everything appears to be relative. As a  result, teens often start questioning everything that they had previously accepted– such as parent and family values, authority figures, religious practices, school rules, and political events. They may even start questioning things that took place when they were younger, like adoption or parental divorce. It is common for parents to feel that adolescents are just being argumentative, but  this behavior signals a normal phase of cognitive development.

Beyond Formal Operational Thought: Post-formal Development?

According to Piagetian theory, formal operational thought emerges during adolescents. The hallmark of this type of thinking is the ability to think abstractly or to consider possibilities and ideas about circumstances not 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 that 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.

In addition to moving toward more practical considerations, thinking in adulthood may also become more relativistic, dialectical, and systemic. These advanced ways of  t hinking are referred to as Postformal Thought (Sinnott, 1998).  Relativistic thinking refers to the appreciation of multiple perspectives, and the understanding that knowledge depends on the perspective of the knower . In later life, adults are able to continue to entertain multiple perspectives simultaneously, and also at the same time, in the face of all those possibilities, to make a decision, commit to a specific course of action, and carry it out. This suggests that such post-formal thought goes beyond cognition to the integration of thought and action.

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; and there is no middle ground . However, with experience, the adult comes to recognize that there is 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 appreciate essential paradox and 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 completely right or wrong. So, for example, parents who were considered angels or devils by their adolescent children, to adult children, eventually become just people with strengths and weaknesses, endearing qualities, and faults.

Does everyone reach postformal or even formal operational thought?

Formal operational thought involves being able to think abstractly; however, this ability does not apply to all situations or all adults. Formal operational thought is influenced by experience and education. 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, many people are not exposed to conceptual tools used to formally analyze hypothetical situations. Those who do think abstractly 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 no one has in all areas. Consequently, our ability to think abstractly also depends on our experiences.

Basseches, M. (1984). Dialectical thinking and adult development . Ablex Pub.

Crain, W. (2005). Theories of development concepts and applications (5th ed.). Pearson

Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence . Basic Books.

Sinnott, J. D. (1998). The development of logic in adulthood . Plenum Press.

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16 Formal Operational Stage Examples

Dave Cornell (PhD)

Dr. Cornell has worked in education for more than 20 years. His work has involved designing teacher certification for Trinity College in London and in-service training for state governments in the United States. He has trained kindergarten teachers in 8 countries and helped businessmen and women open baby centers and kindergartens in 3 countries.

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The formal operational stage is the fourth and final stage in Piaget’s theory of cognitive development. From the ages of 11 and up, children’s cognitive abilities continue to advance and lead to many notable milestones.

As children progress though this stage, their cognitive processing abilities become increasingly advanced. They are no longer limited by centration or the need for a physical representation of concepts.

Piaget’s Stages

Formal Operational Stage Examples

The following are examples of formal operational stage milestones.

1. Abstract thinking

Children in the formal operational stage can think abstractly. They can ponder hypothetical scenarios and understand theoretical perspectives.

They are capable of understanding different philosophical arguments and consider abstract issues such as justice or the role of political systems in society.

2. Scientific reasoning

Children are capable of understanding the basis of the scientific method .

They can consider the causal factors that may lead to specific outcomes and conduct a mental examination of how those various factors may affect different situations.

No longer being limited by centration, they can understand the principle of multi-causality and the notion that one factor may produce multiple outcomes.

3. Moral reasoning

At this stage, children can examine moral dilemmas and various ethical issues .

These matters can be abstract and hypothetical because children are no longer limited by the need to have physical representation of concepts.

They are able to see a given moral scenario from multiple perspectives and analyze the different points of view from the different characters in those scenarios.

4. Critical analysis

The ability to engage in critical-thinking is another attribute of advanced cognitive development.

Now children can recognize bias and easily point out faults in reasoning. 

Children in this stage can question, analyze, interpret and make judgements about what they read, hear, or even say themselves.

Literary works can be critiqued and it is now possible for children to engage in more advanced compare and contrast exercises.

See More: Critical Analysis Examples

5. Perspective-taking

Children are no longer bound by egocentrism. They are able to understand the perspectives of others and feel empathy.

They can identify the reasons behind the actions of others and remove their own biases from that understanding.

Even when at fault, they can see the role of their own actions and how that may affect the actions of classmates and parents.

6. Language development

Language skills in the formal operational stage continue to evolve.

Their vocabulary continues to expand and their ability to express themselves both orally and in writing continues to progress.

Children can engage in rationale and organized discourse regarding the pros and cons of various issues.

They are able to articulate their opinions and engage in organized and reasoned discussions.

Case Studies

The next 10 examples explore case studies of the formal operational stage in real life.

7. Responding to Hypotheticals

In the formal operational stage, being able to think about hypothetical situations is a key characteristic.

Children in the concrete stage are limited to thinking about situations that they can experience directly. However, children in the formal operational stage are able to consider events and issues mentally.

Those situations don’t have to be experienced and can include novel scenarios that are completely imaginary.

Piaget and other researches test for formal operational thinking by presenting unusual hypothetical questions to children of different ages.

The responses are then carefully analyzed for abstract reasoning.

One question that is commonly used is: What if people did not have thumbs?

In the above video you can see very different responses to this hypothetical scenario.

Children in the concrete operational stage give very concrete responses. They identify specific actions that people would no longer be able to perform.

However, the older child in the video, who is in the formal operational stage, gives a much more abstract explanation.

8. Scientific Reasoning

Scientists must be able to consider the possible impact of multiple factors in a given situation.

Those factors may occur simultaneously, sequentially, and/or be interconnected to varying degrees. Moreover, each factor, or in combination with others, will often produce different outcomes.

That’s a lot to think about. Fortunately, as students get older, they develop the ability to engage in scientific reasoning. This leads to the ability to conduct scientific experiments that involve manipulating and controlling variables to assess their effect on other variables.

Scientific reasoning also includes being able to maintain objectivity and not allow one’s personal biases come into play. That requires a degree of self-reflection and introspection that is also part of the formal operational stage.

If that wasn’t enough, scientific reasoning also involves the ability to not be consumed with the obvious. Sometimes the explanation for a given phenomenon is difficult to see, it may even be a bit counterintuitive. This means that the scientist’s thinking cannot be bound by centration.

9. Song Writing

Creating music is a uniquely human ability. Writing lyrics that have deep meaning and touch the souls of listening usually involve a degree of abstraction.

Of course, there is a range, but some of the most popular songs in Western culture have been those that are abstract and but poignant.

Great songs often include metaphors and symbolism that speak to matters of the heart or offer commentary on societal ills. Sometimes the meaning of lyrics can be vague and open to interpretation, which may or may not have been done intentionally.

Perhaps one of the best examples of meaningful lyrics that have inspired considerable interpretation comes from the song American Pie by Don McLean.

Engaging in debate is an example of a skill that requires functioning at the highest level of the formal operational stage. It requires the organization of ideas, the ability to critique arguments, and examine the pros and cons of a wide range of issues.

In addition to the high-level thinking processes required, debate also requires advanced language skills. Debating requires the ability to express one’s views clearly and concisely.

This also means putting oneself in the shoes of an audience to determine if they will be able to understand the arguments presented. That means a bit of perspective-taking and empathy, both formal operational skills.

Debate is an example that utilizes many skills that emerge during the formal operational stage.

11. Innovation

Innovation can be defined as the creation of a new process, product, service or mechanism that results in a significant advance from previous forms.

The end results of innovation can dramatically change technology, medicine, an entire industry, society, or the daily lives of ordinary people.

Typically, innovation results from seeing a situation from a unique angle. It involves the careful examination of a matter that may be complex and include a wide range of interconnecting variables.

The person responsible for the innovation was able to arrange those various factors in a way that produces something never before imagined by others.

If we break down all of those elements, we have the following:

• seeing a situation from a unique angle
• careful examination of interconnecting variables
• arrangement of factors never imagined by others

These elements are the hallmark of formal operational thinking.

12. The Third Eye

To assess formal operational thinking, Piaget devised a set of hypothetical questions. He would present those hypotheticals to children of different ages, and then carefully analyze their response.

One of his questions is commonly referred to as “the third eye.” Piaget would ask: If you had a third eye, where would you put it?

Younger children often say they would put the eye on their forehead or somewhere around their face. Their explanation is usually about being able to see better and includes a lot of concrete concepts and terminology.

However, children in the formal operational stage will often be more inventive. For example, they might say they would put it in their hand so they could see around corners.

The above video shows a typical response of a young child to the third eye question.

13. The Pendulum Test

One way of assessing operational thinking is the pendulum test (Inhelder & Piaget, 1958). This test involves providing a child with 3 strings of varying lengths and a set of light weights. The child is asked what will make the weight swing faster.

Most students will immediately give a response that identified the weight of the object as the main factor. Piaget was more interested in how they went about finding the answer afterwards.

In the Inhelder and Piaget study, children in the formal operational stage often tried to be systematic in their methodology. They tested one variable at a time, such as using different lengths of string for the same weight, then changing the weight.

Younger children just tried variating both string length and weight in a seemingly random manner. Sometimes changing both variables at the same time.

According to Piaget, the systematic approach is representative of scientific thinking and the formal operational stage. They could speculate about the relationship between the variables mentally and then test that thinking experimentally.

14. Board Game Strategy

Many board games require strategy. For example, to win at Monopoly, it is best to not buy just any properties, but to only buy the ones that can garner the most income later. This represents a good use of cash and takes a long-term perspective.

Children in the formal operational stage are more likely to adopt this approach. They are able to make predictions about the future and devise a strategy that increases their chances of winning.

Younger children do have this ability yet. Therefore, their approach will be to buy any and every property that they land on. Or, maybe they choose which properties they buy based on the color of the cards.

Taking a long-term perspective and speculating about future events that may occur represents a more advanced level of thinking that takes place in the formal operational stage.

15. Emotional Intelligence

Emotional intelligence (EI) refers to a person’s ability to understand and manage their emotions and the emotions of others. This means being able to accurately perceive the emotions displayed by others and oneself.

People with a high degree of EI have advanced cognitive skills that allow them to take the perspective of others. They can identify factors that may play a role in their emotional experience, which forms the basis for understanding their actions in an objective manner.

They can then use those insights to manage their reactions and react accordingly.

These skills all require the ability to understand cause and effect , engage in perspective taking, and use critical thinking to assess and evaluate possible motives and response options.

All of which are a function of formal operational thinking.

See More: High Emotional Intelligence Examples

16. Performance Art

Performance art is created by artists or actors engaging in different actions that are either spontaneous or scripted and rehearsed. It is usually acted out in the presence of an audience or casual observers, and can take place just about anywhere, such as a museum, on stage, or on the streets.

The performance is often video recorded or photographed and may include elements of acting, poetry, dance, and music. 

Most performance art produces a commentary on society. That can include pointing out the flaws in the judicial system, political system, civil rights, or gender equality, just to name a few possible subjects.

These are all examples of the kind of abstract thinking and critical analysis that can be found in the formal operational stage .

Performance art has been around for nearly a century and can take many different forms of expression.

The formal operational stage is characterized by highest level of cognitive development. It is in this stage that children develop the capacity to think abstractly and engage in critical analysis.

This gives them the ability to participate in debate, write a song with deep meaning, or engage in performance art.

Piaget devised several tests to determine if a child was in the formal operational stage. For example, he might present a hypothetical scenario and then carefully examine the thinking processes exhibited in the child’s response.

In another test, he might present the material necessary to conduct a simple scientific experiment and observe the child’s approach. Older more advanced children may be methodical, while younger children will just explore different possibilities in a random manner.

Formal operational thinking lays the foundation for emotional intelligence, innovations of all manner, and successful board game strategizing.

Babakr, Z. H., Mohamedamin, P., & Kakamad, K. (2019), Piaget’s cognitive developmental theory: Critical review. Education Quarterly Reviews, 2 (3), 517-524.

Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence: An essay on the construction of formal operational structures. New York: Basic Books. https://doi.org/10.1037/10034-000

Piaget, J. (1959). The language and thought of the child: Selected works vol. 5. Routledge, London.

Piaget, J. (1968). Quantification, conservation, and nativism. Science , 162, 976-979.

Piaget, J. (1970). Science of education and the psychology of the child . Trans. D. Coltman.

Schaffer, H. R. (1988). Child Psychology: the future. In S. Chess & A. Thomas (eds), Annual Progress in Child Psychiatry and Child Development . NY: Brunner/Mazel.

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Formal Operational Stage – Piaget’s 4th Stage (Examples)

Would you say that you think abstractly? Do you think about the “bigger picture?” I don’t mean thinking about your life 10 years in the future. I mean thinking about the purpose of existence and why humans have evolved as we have. We’re not tackling all of these questions today, but we will talk about how we came to ask them and how we answer them.

Children in elementary or middle school typically do not possess these skills. Until children reach the formal operational stage in Jean Piaget's Theory of Cognitive Development, they go through three concrete development stages that only allow them to think concretely. They can follow the rules of how the world works but are limited by these concrete concepts.

What Is the Formal Operational Stage?

Once children reach adolescence, they enter the Formal Operational Stage. This is the last stage in Piaget’s Theory of Cognitive Development. The Formal Operational Stage doesn’t end - there are ways that you can heighten your abstract problem-solving skills from age 12 to age 112! 

The formal operational stage begins between around 11-12. Children are usually in grade school around this time. They can take on more responsibilities than they did in earlier stages of development, but they are still considered young children. Health organizations still categorize ages 11 and 12 as "middle childhood."

Entering the Formal Operational Stage

Children ages 11 and 12 have just finished the concrete operational stage. This stage lasts from ages 6-11. By the time a child enters the formal operational stage, they should be able to:

• Arrange items in a logical order
• Build friendships based on empathy
• Understand that 5mL of water in one glass is the same amount as 5mL of water in a separate glass
• Recognize that a ball of pizza dough is the same as flattened pizza dough

Playing games and doing science experiments with children is much more fun at this age. They understand so much more!

During this stage, individuals develop the ability to think abstractly, reason logically, and solve problems in a systematic manner. Here are 14 examples of behaviors and thought processes that are characteristic of the formal operational stage:

• Hypothetical Thinking : The ability to consider hypothetical situations and possibilities. For instance, a teenager might ponder, "What would happen if the sun never rose?"
• Abstract Thought : Thinking about concepts not directly tied to concrete experiences, such as justice, love, or morality.
• Systematic Problem Solving : When faced with a problem, individuals can systematically test potential solutions. For example, if a science experiment doesn't produce the expected result, a student might change one variable at a time to determine which one is responsible.
• Metacognition : The ability to think about one's own thought processes. Students might reflect on how they study best or recognize when they do not understand a concept.
• Moral Reasoning : Moving beyond black-and-white thinking to consider the nuances of moral dilemmas. For instance, understanding that stealing is generally wrong but pondering whether it's justified if someone is stealing food to feed their starving family.
• Scientific Reasoning : Formulating hypotheses and conducting experiments in a methodical manner to test them.
• Understanding Sarcasm and Metaphors : Recognizing that the phrase "It's raining cats and dogs" doesn't mean animals are falling from the sky.
• Planning for the Future : Considering future possibilities and making plans based on them, such as choosing college courses based on a desired future career.
• Evaluating the Quality of Information : Recognizing the difference between opinion and fact or understanding that just because something is on the internet doesn't make it true.
• Logical Thought : Thinking logically and methodically, even about abstract concepts. For example, if all roses are flowers and some flowers fade quickly, then some roses fade quickly.
• Considering Multiple Perspectives : Understanding that others might have a different point of view and trying to see things from their perspective.
• Propositional Thought : Understanding that a statement can be logical based solely on the information provided, even if it's untrue. For instance, "If all dogs can fly and Fido is a dog, then Fido can fly" is logically sound, even though we know dogs can't fly.
• Complex Classification : Classifying objects based on multiple characteristics. For example, organizing books by both genre and author.
• Understanding Abstract Relationships : Recognizing relationships like "If A is greater than B, and B is greater than C, then A is greater than C."

What Characterizes the Formal Operational Stage?

Four specific skills are signs that a child is in the formal operational stage:

Deductive Reasoning

Abstract thought, problem-solving.

• Metacognition

The child learns to apply logic to certain situations during the Concrete Operational Stage . But they are limited to inductive reasoning. In the Formal Operational Stage, they start to learn (and learn the limits of) deductive reasoning.

Inductive reasoning uses observations to make a conclusion. Say a student has six teachers throughout their life, all strict. They are likely to conclude that all teachers are strict. They may find that later in life, they will change their conclusion, but until they observe a teacher who is not strict, this is the conclusion they will come to.

Deductive reasoning works differently. It uses facts and lessons to create a conclusion. The child will be presented with two facts:

“All teachers are strict.”

“Mr. Johnson is a teacher.”

Using deductive reasoning, the child can conclude that Mr. Johnson is strict.

Throughout the child’s development, they start to expand their world. In the sensorimotor stage, their world consists of only what is directly in front of them. If something is out of sight or earshot, it no longer exists.

As they develop object permanence, they understand that the world exists beyond what they can physically see, hear, or touch. In the concrete operational stage, children begin to apply the rules of logic to things and rules they know exist.

In this final stage, they begin to expand their worldview further. They begin to develop abstract thought. They can apply logic to situations that don’t follow the rules of the physical world.

Piaget's Third Eye Question: The Difference Between Concrete Operational and Formal Operational Stages

One of the ways that Piaget tested this skill was to ask the children questions. Here’s an example of a question that Piaget asked children:

“If you had a third eye, where would you put it?” 

Children in the Concrete Operational Stage were limited to answering that they would put the eye on their forehead or face. They were typically only exposed to animals and humans with eyes on their faces. But children in the Formal Operational Stage were likelier to branch out and think of more useful and abstract answers. They considered putting the eye on their hand, back, or elsewhere where it would serve a greater purpose.

These skills make solving problems a whole lot easier. Children can only solve problems through trial and error in the Concrete Operational Stage and earlier stages. As they enter the Formal Operational Stage, they can look back at the problem, use past experience and reasoning to form a hypothesis, and test out what they believe will happen. This can save them a lot of time.

To determine when children had developed these skills, Piaget used another testing method. He gave them a scale with a set of weights and asked them to balance the scale with the weights. But simply putting the same amount of weight on each side wasn’t enough. The children had to determine that the distance between the weights and the scale's center also impacted the balance.

Children under the age of 10 heavily struggled with the task because they could not understand the concept of balance (if they were in the Preoperational Stage) or could not grasp that the center of balance is also important. (These children were in the early stages of the Concrete Operational Stage.) At age 10, the children could solve the problem, but at a much slower pace due to their process of trial and error.

It wasn’t until age 11 or 12 that children could look at the problem from a distance and use logic to use both the distance and size of the weights to balance the scale.

MetaCognition

Not all of these thought processes are perfect the first time around. You know that I know that, and children in the Formal Operational Stage are just starting to discover that. By using MetaCognition, they are more likely to assess their thinking and transform it into a more effective form of problem-solving.

MetaCognition is simply “thinking about thinking.” It is the ability to run through your own thought process, figure out how you developed that process, and maybe unwind some things that aren’t logical or can be disproven. This can help you “rebuild” your thought process as if it were building blocks, creating a more solid structure for you to solve problems.

Piaget did not actually coin this term while developing his theory on the Formal Operational Stage. John Flavell, an American psychologist, actually proposed the theory on MetaCognition in the late 1970s.

We’ve seen throughout these videos that the Theory of Cognitive Development has continued to grow and change with additional input and studies. Our minds can also change their thought processes and begin to notice imperfections and flawed logic as they come up. But this often requires going back and asking yourself how you built certain thought processes and where you could have made flawed conclusions.

How to Support a Child in the Formal Operational Stage

Children in the formal operational stage (typically 12 years and older) begin thinking more abstractly and logically, engaging in hypothetical reasoning and considering multiple variables in problem-solving. To best support and nurture their cognitive development outside of school, consider these activity suggestions:

• Play Strategic Board Games: Introduce games that require planning, strategizing, and critical thinking. Games like chess, Risk, Settlers of Catan, and Ticket to Ride can enhance their deductive reasoning and promote patience. These games also often require players to predict opponents' moves, honing their skills in understanding perspectives.
• Engage in Thought Experiments: Stimulate abstract thinking by posing hypothetical questions. Asking imaginative yet thought-provoking questions like, "If you could invent a new school subject, what would it be and why?" or "How would our lives change if we had no electricity for a year?" can spark interesting discussions and foster creativity.
• Encourage Scientific Experiments: Let them set up a mini-lab at home. Whether it's a simple vinegar and baking soda reaction or a more complex examination of plant growth under different conditions, hands-on experiments can solidify their understanding of cause and effect.
• Delve into Philosophy and Ethics: Discuss moral dilemmas or philosophical conundrums suitable for their age. Questions like, "Is it ever okay to lie?" or "What makes something 'right' or 'wrong'?" can challenge them to consider multiple viewpoints and refine their moral reasoning.
• Read and Analyze Stories Together: Choose books or movies with deeper themes or complex characters. Discuss the motives, the plot's implications, or any symbolism. This improves their comprehension skills and teaches them to think critically about media.
• Involve Them in Real-Life Problem-Solving: Whether planning a family trip, budgeting for a big purchase, or deciding on the best route for a journey, including them in the process can provide practical applications for their developing logical reasoning skills.
• Respect and Respond to Their Queries: Children at this stage are brimming with questions, many of which can be profound or reflective. When they approach you with a query, respond with patience and logic. If you don't know the answer, consider researching it together. This collaborative approach provides them with information and models a proactive attitude toward learning.

By actively engaging with children in these ways, parents and caregivers can provide invaluable support as they navigate the challenges and opportunities of the formal operational stage.

Formal Operational Stage vs. Other Stages of Development

Jean Piaget is not the only psychologist to create stages of development. Other psychologists have offered their theories on how a child develops social skills and how their experiences during each stage impact their relationships and behavior. Some theories, like Erikson's stages of psychosocial development, last for the span of the person's life. Other theories, like Piaget's, only cover childhood and early adolescence. When we compare Piaget's theory to other theories, we see some overlap and other perspectives on what makes a child the person they grow up to be.

Erikson's Stages of Psychosocial Development

At ages 11-12, a child exits the Industry vs. Inferiority stage and enters the Identity vs. Role Confusion stage. The child should be aware that they are responsible for their own decisions and how they affect others. They also start to see that they are different from other children. They will successfully exit these stages if they feel confident that they can advocate for themselves and live the way they want. Otherwise, they may develop insecurities. Erikson coined the term "identity crisis." This crisis could take place in the identity vs. role confusion stage!

Freud's Stages of Psychosexual Development

During the ages of 11-12, a child is in the latent stage of psychosexual development and may be entering the genital stage. The change in stages all depends on when the child goes through puberty. Freud's controversial stages focused on a child's erogenous zones and sexual interests. As the child discovers sexual interests in the latent stage, they must learn to channel their energy into intellectual activities. The child can form healthy relationships by letting the superego tame the id. In the genital stage, teenagers and adults learn to explore their maturing sexual interests.

Which Theory is "Right?"

All these theories can play out simultaneously, but remember, these are just theories. Some ideas, like Freud's Oedipal Complex that occurred in earlier stages of development, have been discredited and largely rejected by today's psychologists. We continue to learn about Jean Piaget, Erik Erikson, and other psychologists to understand how psychology developed into the field we know today.

Thanks for checking out these pages on the Theory of Cognitive Development! I hope these will allow you to look at your own thinking and build a stronger foundation for solving problems and understanding the world around you - no matter how old you are!

Piaget's Influence on Modern Educational Practices

Jean Piaget's groundbreaking theories on cognitive development have left an indelible mark on the realm of education. Even today, educators worldwide employ strategies rooted in Piaget's insights. Here's how Piaget’s theories continue to shape contemporary educational practices:

• Active Learning: Piaget emphasized the importance of active learning. He believed children learn best when interacting with their environment and manipulating objects. This belief has shifted from passive rote memorization to hands-on, experiential learning. Schools often incorporate field trips, lab experiments, and interactive activities to facilitate this.
• Developmentally Appropriate Practices: Recognizing that children progress through specific stages of cognitive development, educators design curricula tailored to these stages. For instance, in the pre-operational stage (2-7 years), children benefit from using concrete objects and visuals. Meanwhile, older children in the formal operational stage (12 years and up) are more equipped for abstract thinking and can engage in more complex problem-solving tasks.
• Focus on the Process, Not Just the Outcome: Piaget believed that the process of thinking and the journey of arriving at an answer are just as necessary as the answer itself. This philosophy has encouraged educators to value and assess how students approach problems, not just the correctness of their answers.
• Peer Interaction: Piaget felt that peer interaction is crucial for cognitive development. He observed that children often learn best when discussing, debating, and collaborating with classmates. Group work, cooperative learning, and classroom discussions are now staples in many classrooms, promoting social interaction as a valuable learning tool.
• Incorporating Real-life Situations: To make learning meaningful, Piaget suggested relating it to real-life situations. This has led to problem-based learning and the inclusion of real-world issues in the curriculum, ensuring that students see the relevance and applicability of their learning.
• Role of the Teacher: In line with Piaget's theories, the teacher's role has evolved from the traditional "sage on the stage" to more of a "guide on the side." Teachers now often act as facilitators, providing resources, posing guiding questions, and helping students make their discoveries.
• Assessment Practices: Piaget's emphasis on stages of cognitive development has led to more nuanced and stage-sensitive assessment methods. Teachers are more attuned to the developmental readiness of their students, ensuring that assessments are appropriate for their cognitive level.
• Constructivist Classrooms: Stemming from Piaget's idea that learners construct knowledge based on their experiences, many modern classrooms adopt a constructivist approach. Here, students are encouraged to construct their understanding and knowledge of the world by experiencing and reflecting on those experiences.

While educational practices have evolved and integrated various theories, Piaget's influence is unmistakably prevalent. His focus on the child as an active learner, the stages of cognitive development, and the significance of hands-on, relevant learning continues to shape how education is delivered in the 21st century.

Related posts:

• Concrete Operational Stage (3rd Cognitive Development)
• Piaget's Theory of Moral Development (4 Stages + Examples)
• Jean Piaget’s Theory of Cognitive Development
• Havighurst’s Developmental Task Theory
• The Psychology of Long Distance Relationships

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Trust vs Mistrust

Autonomy vs Shame

Initiative vs Guilt

Industry vs inferiority

Identity vs Confusion

Intimacy vs Isolation

Generativity vs Stagnation

Integrity vs Despair

Attachment Styles

Avoidant Attachment

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Lawrence Kohlberg's Stages of Moral Development

Piaget's Cognitive Development

Sensorimotor Stage

Object Permanence

Preoperational Stage

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• The formal operational stage: age 11 and beyond

In the last of the Piagetian stages, the child becomes able to reason not only about tangible objects and events, but also about hypothetical or abstract ones. Hence it has the name formal operational stage the period when the individual can “operate” on “forms” or representations. 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 facility at manipulating 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 school work: 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 insure that a student is motivated or well-behaved, for example, nor does it guarantee other desirable skills, such as ability at sports, music, or art. 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 normally deal with such problems in the normal 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. The next sections describe some of these.

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The Formal Operational Stage of Cognitive Development

• Conceptualizing Balance
• Abstraction of Ideas
• Next in Stages of Cognitive Development Guide Support and Criticism of Piaget's Stage Theory

The formal operational stage is the fourth and final stage of Jean Piaget's theory of cognitive development . It begins at approximately age 12 and lasts into adulthood.

In the formal operational stage, children's thinking becomes much more sophisticated and advanced. Kids can think about abstract and theoretical concepts and use logic to come up with creative solutions to problems. Skills such as logical thought, deductive reasoning, and systematic planning also emerge during this stage.

Piaget tested formal operational thought in a few different ways. Two of the better-known tests explored physical conceptualization and the abstraction of thought.

Balance in the Formal Operational Stage

One task involved having children of different ages balance a scale by hooking weights on each end. To balance the scale, the children needed to understand that both the heaviness of the weights and the distance from the center played a role.

• Younger children around the ages of 3 and 5 were unable to complete the task because they did not understand the concept of balance.
• Seven-year-olds knew that they could adjust the scale by placing weights on each end, but failed to understand that where they put the weights was also important.
• By age 10, the kids considered location as well as weight but had to arrive at the correct answer using trial and error.

It wasn't until around age 13 that children could use logic to form a hypothesis about where to place the weights to balance the scale and then complete the task.

Abstraction in the Formal Operational Stage

In another experiment on formal operational thought, Piaget asked children to imagine where they would want to place a third eye if they had one.

Younger children said that they would put the imagined third eye in the middle of their forehead. Older children, however, were able to come up with a variety of creative ideas about where to place this hypothetical eye and various ways the eye could be used.

For example, an eye in the middle of one's hand would be useful for looking around corners. An eye at the back of one's head could be helpful for seeing what is happening in the background.

Creative ideas represent the use of abstract and hypothetical thinking, both important indicators of formal operational thought.

Formal Operational Stage Skills

Important skills that emerge during the formal operational stage include the following:

Deductive Logic

Piaget believed that deductive reasoning becomes necessary during the formal operational stage. Deductive logic requires the ability to use a general principle to determine a particular outcome. Science and mathematics often require this type of thinking about hypothetical situations and concepts.

Abstract Thought

While children tend to think very concretely and specifically in earlier stages, the ability to think about abstract concepts emerges during the formal operational stage. Instead of relying solely on previous experiences, children begin to consider possible outcomes and consequences of actions. This type of thinking is important in long-term planning.

Problem-Solving

In earlier stages, children used trial-and-error to solve problems . During the formal operational stage, the ability to systematically solve a problem in a logical and methodical way emerges. Children at the formal operational stage of cognitive development are often able to plan quickly an organized approach to solving a problem.

Hypothetical-Deductive Reasoning

Piaget believed that what he referred to as "hypothetical-deductive reasoning" was essential at this stage of intellectual development. At this point, teens become capable of thinking about abstract and hypothetical ideas. They often ponder "what-if" type situations and questions and can think about multiple solutions or possible outcomes.

While kids in the previous stage ( concrete operations ) are very particular in their thoughts, kids in the formal operational stage become increasingly abstract in their thinking.

As children gain greater awareness and understanding of their own thought processes, they develop what is known as metacognition, or the ability to think about their thoughts as well as the ideas of others.

Criticisms of the Formal Operational Stage

Some researchers have noted that while Piaget's theory indicates there are four stages of cognitive development, there is also evidence that indicates that not all adolescents reach the formal operational stage.

The formal operational stage hinges on the emergence of critical thinking skills. Depending on factors such as education, parenting, and cultural influences, some children do not necessarily develop the requisite thinking skills to fully approach this stage.

It has also been noted that formal operational thought may, in some cases, be domain specific. A trained engineer may be able to engage in formal operational thought with regard to their profession, but they may lack the ability to apply similar skills in domains such as economics, politics, or social science.

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Piaget’s pendulum

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For those who want to calculate what is going on, the period of oscillation of a simple pendulum is:

T = 2π√(l / g) where:

T = time period for one oscillation (s) l = length of pendulum (m) g = acceleration due to gravity (m/s-2)

But why does the mass have no effect on the pendulum period? Because all materials accelerate towards Earth at the same rate!

Sources of error

• Defining when the pendulum period ends
• Did the mass get ‘released’ or ‘pushed’?
• The initial height of the pendulum mass needs to be consistent

Application

This simple science experiment was used by the psychologist Piaget in 1958 to determine if children could isolate and test variables one at a time to experimentally test an idea (also called formal operational thinking ). Children who struggled with this experiment were found to change more than one variable at a time whilst running the pendulum experiment and as such produce the incorrect answer that it is the mass at the end of the string that influences the speed of the pendulum. It’s all about variable testing!

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• Newton’s cradle used to demonstrate transfer of forces

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• DOI: 10.1111/J.2044-8279.1974.TB00780.X
• Corpus ID: 145143752

THE PENDULUM PROBLEM: PATTERNS OF PERFORMANCE DEFINING DEVELOPMENTAL STAGES

• S. Somerville
• Published 1 November 1974
• Psychology, Education
• British Journal of Educational Psychology

30 Citations

What the pendulum can tell educators about children’s scientific reasoning, language skills and formal operations., solving three‐term series problems: a comparison of two stages of cognitive development, content variations and performance on formal operational tasks by gender, social class and ability, formal operational thinking in young adults as a function of education and sex, durin'g- concrete and formal operations, levels of availability of a formal operational strategy., the pendulum: its place in science, culture and pedagogy, the future of formal thought research: the study of analogy and metaphor, study of formal reasoning patterns by means of three piagetian tasks: implications for science education, related papers.

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What the Pendulum Can Tell Educators about Children’s Scientific Reasoning

• Published: November 2004
• Volume 13 , pages 757–790, ( 2004 )

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• Erin Stafford 1  

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Inhelder and Piaget (1958) studied schoolchildren’s understanding of a simplependulum as a means of investigating the development of the control of variablesscheme and the ceteris paribus principle central to scientific experimentation.The time-consuming nature of the individual interview technique used by Inhelderhas led to the development of a whole range of group test techniques aimed attesting the empirical validity and increasing the practical utility of Piaget’s work.The Rasch measurement techniques utilized in this study reveal that the Piagetian Reasoning Task III — Pendulum and the méthode clinique interview revealthe same underlying ability. Of particular interest to classroom teachers is theevidence that some individuals produced rather disparate performances across thetwo testing situations. The implications of the commonalities and individualdifferences in performance for interpreting children’s scientific understanding arediscussed.

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