The Formal Operational Stage

Jean Piaget was a Swiss developmental psychologist (1896–1980). He gained such worldwide renown that a recent analysis by Haggbloom, Warnick, Warnick, and Jones (2002) found that his work ranked second in professional journal citations (first position going to Sigmund Freud) and fourth in citations within introductory psychology textbooks (after Sigmund Freud, B. F. Skinner, and Albert Bandura).

The formal operational stage is the fourth and final stage in Piaget’s theory of cognitive development, which he began discussing in the 1950s and continued to develop over the next few decades. According to this theory, each child goes through the following stages at roughly the same age:

  • The sensorimotor stage: birth to age 2.
  • The preoperational stage: age 2 to age 7.
  • The concrete operational stage: age 7 to age 11.
  • The formal operational stage: age 11 to adulthood.

The key component of the formal operation stage is the ability to develop abstract thought and hypothetical reasoning. However there is more to it than that.

How does the Formal Stage differ from the other stages?

You may have noticed that both the concrete and the formal stages are classed as “operational”. In this context operational is defined as “a means for mentally transforming data about the real world so that they can be organised and used selectively in the solution of problems” (Inhelder and Piaget, 1958). Prior to the operational stages, children can only execute simple actions to achieve their goals.

At roughly age 7, the concrete operational stage begins and children start to develop more complex and logical thought patterns in order to complete their goals. To do this they perform “operations” to organise information around them by understanding relationships between categories.

For instance children will begin to understand that their dalmatian can be categorised as a dog, a pet, and an animal whereas their kitten can also be categorised as a pet and an animal, but not as a dog. While these cognitive developments are huge, during the concrete stage the operations are based on logic and are fairly inflexible, hence the label “concrete”.

However during the formal operational stage children begin to perform mental operations which are much more complex and not necessarily based on simple logic. Forming categories becomes more important and also more complex. Piaget stated: 

“Everyone knows that at the age of 11-12, children have a marked impulse to form themselves into groups and that the respect paid to the rules and regulations of their play constitutes an important feature of this social life.”

In other words, children no longer form simple categories based on objects and animals around them; they also form social categories with complex, shifting rules for membership, constituting their own mini-society.

Children entering adolescence can use more abstract patterns of thought and deductive reasoning to problem solve creatively. However it is more complicated that simply a development in verbal reasoning. It is the ability to perform multiple mental operations including, among others: 

  • Metacognition. Metacognition refers to our ability to think about our own thought processes, allowing us to monitor and reason with them. 
  • Hypothetical-deductive reasoning. In the four earlier stages, children’s thought process revolves around previous experiences or concrete situations. In the formal operational stage, these thoughts evolve into the ability to ponder hypothetical situations.
  • Proportional reasoning. This refers to the ability to compare a range of numbers or ratios such as comparing different common fractions or percentages. For instance, children in earlier stages of cognitive development would view a chocolate bar cut into 4 equal pieces as larger than the same bar cut into two pieces because they do not have the ability to mentally manipulate the concepts of one half vs two quarters. 
  • Probabilistic reasoning. This is the ability to use probabilities to make predictions of likely outcomes. It starts to develop at an early age but by the formal operational stage, it is very well developed.
  • Correlations. Piaget stated that children in the formal operational stage can recognize and understand relationships to the level that they understand correlations. For instance the positive correlation of height and weight; taller people tend to be heavier.
  • Combinatorial analysis. Following on from an elevated understanding of categories, the formal operational stage enables children to manipulate and combine different categories systematically to solve problems. For example, when given piles of different colored

    buttons and asked to make as many different combinations as possible (red/blue, green/yellow, etc), young children stumble across different combinations through trial and error. It is only in the later developmental stages that the older children develop a systematic method for finding all possible combinations (Piaget and Inhelder, 1951).

Although these processes seem quite different, linked only by the fact that they are complex thought processes, research has confirmed that they all develop simultaneously (Eckstein and Smemesh, 1992).

How do we know whether a child has reached the Formal Stage?

Piaget performed many different tests to assess the various developmental stages and most of them have been repeated in different countries under different conditions to see just how reliable the findings are. One of the most well-known is the test of balance.

Children of different ages are given scales and a set of weights. The experimenter places a weight on one side of the scales and the child is asked to make the scales balance. In order to achieve this efficiently the children need to know that both the heaviness of the weights and their placement on the scales will affect the balance.

child has reached the Formal Stage?
child has reached the Formal Stage?

Young children in the sensorimotor stage and the beginnings of the preoperational stage are completely unable to complete the task. Towards the end of the preoperational stage children can understand the affect of the different weights and children in the concrete operational stage also understand that the weight’s position on the scale also affects balance.

However in the concrete stage the children are still generally achieving the task through trial and error. It is only once the children reach the formal operational stage that they develop an organised, systematic approach to solving the problem using their knowledge of weight and distance.

In a very different style of experiment, children were asked to imagine they could have a third eye and where on their body they would place it. Young children up to around age 9 generally said they would put it on their forehead, suggesting they still lack in abstract thought.

By the age of 11 and the onset of the formal operational stage, the children were given a variety of answers suggestive of more creative, abstract, and hypothetical thinking. For instance, saying they would place a third eye on their hand so they could look around corners or under objects.

A final example involves asking children questions that require some mental manipulation to work out, for example “Sarah is taller than Adam and Adam is taller than Jo. Who is the tallest?”. 

If the children were allowed a pen and paper to help them work it out then those still in the concrete operational stage may be able to do it. However, without these tools and only the ability to mentally manipulate the information, only children who had reached the formal operational stage could successfully calculate the answer.


Piaget has been widely criticised for using small samples of children, often his own or his friends’ children, often without even saying how many children there were. In fact, one very influential book of his (The Origins of Intelligence in Children, 1952), contained conclusions based on findings involving only three children-his own.

He claimed that all children go through these stages at roughly the same time but because all the children he tested were well educated and from a high-socioeconomic household, additional testing was important to determine the importance of environmental factors.

Eckstein and Smemesh (1992) found that the formal operational stage is reached at the same age in the USA and in Israel, suggesting culture does not have a significant impact and that development would be similar in other countries around the world.

On the contrary, Badakar and colleagues (2017) conducted a number of tests on 120 orphaned children and 120 parented children aged 4-7. They found that cognitive development of the parented children was significantly greater than that of the orphaned children, demonstrating that Piaget was wrong to discount the role of environmental factors, at least in the earlier stages.

Furthermore, Piaget’s procedures were often as relaxed as his recruitment methods, meaning he did not always objectively define his variables or analysis methods, etc. This has sometimes made it difficult for researchers to replicate his findings.

Another criticism of the cognitive development theory in general is that it underestimates children’s abilities. For instance, it states that children are completely egocentric (only able to see things from their own point of view) until at least the concrete operational stage at age 7.

However, a large body of research demonstrates that theory of mind, the ability to understand that other people have different perspectives and mental states, is present t a much younger age (Baron-Cohen, 1991). This shows that the ability to recognize the thought processes and points of view of other people is present at a much earlier stage than Piaget suggested.

However the formal operational stage has often garnered the opposite criticism, with many researchers saying these complex thought operations are not possible for many adolescents until much later than Piaget stated.

For instance, Siegler and Richards (1979) found that 12-year-olds could not complete the scales task and some participants were as old as 17 before they could use the systematic approach characterized by the formal operational stage.

Is this relevant in the modern day?

Considering the multiple criticisms and the fact that these theories are decades old, do they have any relevance to us nowadays? Many developmental psychologists would certainly say so. Piaget’s influence on the education system can still be seen today in schools worldwide.

The concept that children learn through experiences and experimentation, but that these should be pitched at a level appropriate to their stage of development, can be seen in most school curriculums. He summed it up with the following:

“Each time one prematurely teaches a child something he could have discovered himself, that child is kept from inventing it and consequently from understanding it completely.”

Thinking specifically about the formal operational stage, Commons, Miller, and Kuhn (1982) argue that formal operational thinking can be seen in real world activities, not just in simple psychological experiments.

They found that even though high school grades were the same, students who demonstrated more formal operational styles of thinking were more likely to take maths and science subjects at college and to get higher grades than those who showed more concrete operational thinking. Thus, it can be argued that the formal operational stage is still relevant in the modern-day and can have some real-life applications.

Some psychologists have even added an additional stage after the formal operational stage, stating that some adults continue to develop their cognitive reasoning even further.

For instance, Sinnott (1998) states that “postformal” thought allows us to adapt to our situations and make decisions based on what is realistic, rather than idealistic goals. This helps us to maintain our social relationships and be a productive member of society.

All of this demonstrates that although it may not be perfect, there is still some merit to Piaget’s theory of cognitive development and the formal operational stage.


Barbel Inhelder and Jean Piaget (1958). “The Growth of Logical Thinking from Childhood to Adolescence: An Essay on the Construction of Formal Operational Structures”. 

H. Fischbein (1975) “The Intuitive Sources of Probabilistic Thinking in Children”. 

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

Michael L.Commons, Patrice M.Miller & DeannaKuhn (1982) “The relation between formal operational reasoning and academic course selection and performance among college freshmen and sophomores” Journal of Applied Developmental Psychology,1-10.

Baron-Cohen, Simon (1991), “Precursors to a theory of mind: Understanding attention in others”, in Whiten, Andrew (ed.), Natural theories of mind: evolution, development, and simulation of everyday mindreading, Oxford, UK Cambridge, Massachusetts: B. Blackwell, pp. 233–251,

Shulamith G. EcksteinMichal Shemesh May (1992) “The rate of acquisition of formal operational schemata in adolescence: A secondary analysis”.

Jan D. Sinnott (1998)”The Development of Logic in Adulthood: Postformal Thought and Its Applications”. Plenum Press.

Haggbloom, Warnick, Warnick, and Jones (2002) The 100 Most Eminent Psychologists of the 20th Century. Review of General Psychology

Wubbena, Zane (2013). “Mathematical fluency as a function of conservation ability in young children”. Learning and Individual Differences. 26: 153–155.

Chandrashekhar M Badakar, Prachi J ThakkarShivayogi M Hugar, Pratibha Kukreja,  Harsha G Assudani, and Niraj Gokhale (2017) “Evaluation of the Relevance of Piaget’s Cognitive Principles among Parented and Orphan Children in Belagavi City, Karnataka, India: A Comparative Study”.