16 Formal Operational Stage Examples & Case Studies

formal operational stage examples definition

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

Piaget Stages of Development
StageAge RangeDescription
Sensorimotor0-2 yearsChild develops object permanence (realizing that objects out of sight still exist), goal-directed action (learning to act intentionally to achieve a goal), and deferred imitation (continuing to imitate others after the event).
Preoperational stage2-7 yearsChild develops symbolic thought (using language and signs to represent their thoughts) but remains egocentric.
Concrete operational stage7-12 yearsChild develops logical thought and conservation (discovers that changes in appearance do not correspond with changes in weight, volume, etc.)
Formal operational stage12-18 yearsAdolescent develops inductive and deductive reasoning. They can use abstract thought and general principles to develop increasingly complex hypotheses.

6 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.

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.

Formal Operational Stage Examples

1. 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.

2. 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.

3. 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.

4. Debate

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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

Conclusion

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.

References

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

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.

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.

Dave Cornell (PhD)
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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.

Chris Drew (PhD)
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This article was peer-reviewed and edited by Chris Drew (PhD). The review process on Helpful Professor involves having a PhD level expert fact check, edit, and contribute to articles. Reviewers ensure all content reflects expert academic consensus and is backed up with reference to academic studies. Dr. Drew has published over 20 academic articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education and holds a PhD in Education from ACU.

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