17 Concrete Operational Stage Examples & Case Studies

concrete operational stage examples

The concrete operational stage is the third stage in Piaget’s stages of cognitive development. From the ages of 7-12, children develop increasingly advanced reasoning. Their thinking becomes better organized, more logical and systematic.

In this stage, they are able to apply the rules of logic to physical objects, and representing those objects mentally becomes much easier.

However, children still struggle with abstract reasoning. The concrete operational stage serves as a transition between the preoperational and formal operational stages.

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 yerasAdolescent develops inductive and deductive reasoning. They can use abstract thought and general principles to develop increasingly complex hypotheses.

Concrete Operational Stage Examples

There are several key characteristics of thinking which emerge during the concrete operational stage.

Although children go through Piaget’s stages sequentially, there is a great deal of variation across children regarding the age at which they develop a specific cognitive attribute.

In addition, research has identified variations in tasks and instructions used to assess cognitive development that lead to different outcomes at different ages.

1. Seriation

This term refers to the child’s ability to arrange objects in sequence, such as from smallest to largest or hardest to softest.

As long as the child can see the physical objects, then they can perform this type of task without great difficulty, but will need to concentrate fully.

For instance, children will often place two or three of the objects side-by-side to compare before deciding which one should be next.

2. Reversibility

Children are able to mentally reverse a sequence of events that they have observed.

As the child’s ability to control their thinking becomes more advanced, they are able to take their mind through simple sequences in reverse.

This means that they can mentally represent the original condition they witnessed previously.

Reversibility is the mental operation that enables children to understand the concept of conservation.

3. Classification

The ability of children to classify objects based on a shared characteristic continues to advance during the concrete operational stage.

This means that children can categorize objects based on one characteristic, but then also create sub-categories within each.

So, shapes can be put into the same groups, and then further divided into additional groupings based on other attributes.

4. Transitivity

Being able to recognize relationships that exist between two or more concepts is called transitivity, or transitive inference.

For instance, if A > B, and that B > C, then it is logical to conclude that A > C.

This is the kind of logical thinking skill that Piaget considered essential to a child’s intellectual abilities. It is a key developmental milestone in the concrete operational stage.

5. Conservation

During the concrete operational stage children will develop the understanding of conservation; that the mass of an object doesn’t change as a function of its shape.

The age at which children understand conservation varies, depending on the type of task, the instructions given, and even cultural factors.

6. Decentration

Decentration refers to a child’s ability to examine two features of an object or situation. In part, this is a function of attentional control.

No longer will the most salient feature of an object dominate their thinking. A child can control what aspect of the object or situation they are thinking about.

Furthermore, decentration can lead to a child understanding that others may have a different point of view. Because their thinking is no longer completely dominated by their own thoughts, they are more likely to perceive the opinion of others.

7. Overcoming Egocentrism

During the concrete operational stage, children become far less egocentric as they develop a theory of mind. They are beginning to see situations from the perspective of others and consider their point of view.

This results in them being able to more easily identify why another person may be upset.

Understanding the causal factors involved in another person’s emotional state is the foundation for emotional intelligence and leads to fewer interpersonal conflicts.

Concrete Operational Stage Case Studies

1. Testing for Seriation of Length

Piaget and other researchers have developed several ways to test for seriation. The procedure is quite simple, first the researcher will place various objects on a table before the child. Then, the child will be instructed to arrange the objects in a sequence, such as from shortest to longest.

The above video shows a simple demonstration of seriation. As you can see, the teacher has already prepared numerous strips of colored paper. She places them in a pile, making sure that the strips are not already suggesting a sequence.

The instructions are simple and straightforward:

The child gets right to it and quickly identifies the shortest strip of paper. From there, the process is methodical as the child clearly understands the principle.

The longer strips at the end of the process require a little more examination, so the child puts them in a separate group to make comparisons within that group.

Finally, the next strip is identified and the child proceeds to complete the task.

2. Demonstrating Reversibility

One major development in the child’s thinking processes is the ability to mentally reverse a sequence of events. The child does not need to physically manipulate the objects in the sequence. They can represent the objects and reverse the steps in the sequence mentally.

The above video shows children in the concrete operational stage going through two tests of conservations.

One test involves two balls of clay. The teacher shows the two equal sized balls of clay, establishes that the child agrees they are equal, and then flattens one ball in plain sight.

The teacher then asks the child if the two shapes have the same amount.

The other test involves liguid. Two glasses with equal amounts of a colored liquid are shown. The teacher confirms that the child understands the two glasses have the same amount of liquid.

Then the teacher pours the liquid of one into a taller, narrower shaped container. When asked if the two containers have the same amount of liquid, the child agrees.

After each test, the teacher then asks the child to explain the reason for their answer. Their ability to reverse operations is demonstrated in their explanation. 

3. The Three Mountains Test 

Piaget created the three mountains test to determine if a child is egocentric or not. The test involves showing children a relatively large model that displays three different-sized mountains.

Each mountain has distinct identifiers, such as a red cross or hut on top. Each one is also painted a different color to add to its distinctiveness.

The child is given an opportunity to examine the mountains by walking around the display.

Then, a doll is placed at different locations and the child is asked to select from a set of pictures the view that the doll can see.

Children that are egocentric will choose the wrong picture. However, when a child’s level of cognitive development has advanced sufficiently, they will be able to create a mental picture of the display from the doll’s point of view, and then identify the correct picture.

The above video shows children of different ages being tested using the three mountains test. The younger children (ages 4, 5, and 6) choose the wrong picture each time. However, Emmie (age 7) and Johnny (age 8) choose the correct picture easily.

4. Egocentrism and Family Relations

As young children grow older and their brain matures during the concrete operational stage, they exhibit less egocentrism. They are able to consider a situation from the perspective of others. This ability develops gradually over a period of years and can vary depending on the exact situation.

Egocentrism can be demonstrated in a variety of ways. The above video shows a mother asking her daughter about family members. When asked if she has any siblings, the daughter quickly says yes and names her baby sister.

When the mother asks if the baby sister has any siblings, the child says she does not. She then provides an explanation for her answer which is factual, but not completely logical.

We can see that the child is still egocentric and uses a flawed logic. She has not passed through the concrete operational stage far enough to overcome these cognitive limitations.

5. Demonstration of Classification

Classification refers to the ability to categorize objects based on a similar characteristic. As children reach the concrete operational stage, their ability to categorize becomes readily visible. They can easily categorize objects based on shape, size, or color.

The above video shows a young boy named Brayden that is capable of naming the shapes of paper in front of him and is able to put them into categories based on shape.

Even though some of the shapes are in different colors and sizes, and some have different patterns such as stripes or dots, he can easily focus on the one feature given in the task instructions. He then carries out the classification exercise based only on that feature.

6. Class Inclusion

This term refers to the understanding that a subordinate class (e.g., dogs) will always be smaller than the superordinate class in which it belongs (e.g., animals). Piaget considered the understanding of class inclusion as an advanced mental operation that occurs in the latter period of the concrete operational stage.

Although children in the concrete operational stage are able to classify objects based on a shared characteristic, and may be able to create subdivisions within those categories, understanding class inclusion may still be out of their reach.

Class inclusion depends on two logical operations: one involving the addition of classes (dogs + cats = animals) and the other involving a subtraction of classes (dogs = animals – cats).

For example: a child is presented with a picture of 7 flowers: five tulips and 2 roses. When asked the question “Are there more tulips than flowers,” most young children will say that there are more tulips. This is the wrong answer.

Children that fail this test have not reached a level of cognitive development that allows for an understanding of class inclusion.

7. The Transition of Egocentric Thinking 

Piaget based a substantial portion of his theory of cognitive development on his direct observations of children. He took detailed notes and then inferred the associated cognitive processes.

Although his theory is called a “stage” theory, it is more accurate to point out that children actually oscillate between stages for some time before making the full transition.

The quote below demonstrates how an aspect of cognitive development can even change as a function of the situation. The quote has been modified slightly for brevity. It is based on the notes of one of Piaget’s colleagues and the observations of her son at school.

“Our notes show…that at the beginning of his fourth year the child’s speech shows a greater coefficient of ego-centrism (i.e., it is less socialized in character) when speaking with adults than children of his own age (71.2% against 56.2%).
From the beginning to the end of the year the coefficient of ego-centrism becomes lower with the adult (from 71 to 43%, i.e., a lowering of 28%), whereas when speaking with children not so marked.
The measure of ego-centric language in verbal communication with adults and children changes from 63.7% to 44.7%”
(Piaget, 1959, pp. 143-144).

8. Decentration in Preschoolers

Since Piaget’s research in the 1900s, some researchers have identified methodological nuances that may lead to underestimating children’s abilities (Donaldson, 1985; Elkonin, 1989; Watanabe, 2017).

As Andreeva points out in her remarks about preschoolers engaged in role play:

“…taking on the role of another person in a game already presupposes some decentration, for it requires the child to act in accordance with the accepted role and to coordinate his/her own point of view with the points of view of other players” (Andreeva, 2018, p. 27).

To some extent, it is necessary that a child engaged in a role-play with another must not only consider the actions and motives of their classmate, but also the various dolls that might also be participating.

In summing up the conclusions of decades of research, Andreeva states:

“The decentration ability appears much earlier than the child reaches the stage of development that J. Piaget defined as the stage of concrete operations” (p. 28).

9. Integrating Graphic Representations   

Using visuals can help children understand difficult concepts, particularly those that are in their zone of proximal development. Teachers understand the educational value of graphs and charts and frequently integrate them into classroom instruction.

For example, displaying a chart that depicts animal classification can help children understand how animals are grouped together. Children can see the different features of animals that place them into various categories.

The chart will also show that within a category, there are subgroups. For example, dogs fall into the category of mammals. Teachers can then provide instruction on how subgroups exist within larger superordinate groups. This can facilitate a child’s understanding of class inclusion.

To take this instructional approach one step further, a teacher could also set a group of toy animals on a table and have students group them based on the rules of animal classification.

Animals that are furry with four legs in one category. Animals with feathers that can fly in another. The students can then be tasked with creating the subgroups within.

10. Using a Venn Diagram

There are many instructional methods that help facilitate students’ cognitive development. Using age-appropriate lessons involves correctly identifying a student’s level of cognitive development and then providing activities that stimulate that state.

Venn diagrams can be very useful in helping children overcome the limitations of centration. Typically, a Venn diagram involves identifying two concepts or objects, listing the characteristics that are unique to each and those that they share. 

Children that have very limited cognitive skills will be unable to perform this exercise. Therefore, the teacher will need to provide very directed guidance.

This can involve highlighting only one aspect of the target object at a time. Carefully pointing out the distinctive feature and allowing the child to generate the words that describe it will ensure they are engaging the appropriate thinking processes.

Going through the entire activity will set the building blocks needed for independent understanding. It may take some time, but with practice and instruction, Venn diagrams are excellent tools for facilitating students’ cognitive development.


The concrete operational stage is primarily characterized by the advancement of a child’s ability to perform logical operations mentally. Although limited to mostly physical objects, children in this stage demonstrate several key milestones in their ability to think systematically.

For instance, they can mentally reverse the sequence of steps they have observed. This gives them an understanding of conservation and can be demonstrated in a variety of testing procedures.

In addition, children become less egocentric and are able to understand the perspective of others involving perceptions of physical objects.

More advanced cognitive skills include being able to classify objects according to two characteristics and eventually understanding class inclusion.  


Andreeva, A. (2018). The formation of the decentration ability at preschool age. International Conference on Psychology and Education, 26-37. 10.15405/epsbs.2018.11.02.4.

Donaldson, M. (1985). Children’s minds. Moscow, Russia: Pedagogika.

Elkonin, D. B. (1989). Selected psychological works (pp. 306-361). Moscow, Russia: Pedagogika.

Piaget, J. & Szeminska, A. (1952). The Child’s Conception of Number. Routledge & Kegan Paul: London.

Piaget, J. (1954). The child’s conception of number. Journal of Consulting Psychology, 18(1), 76.

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. Watanabe, N. (2017). Acquiring Piaget’s conservation concept of numbers, lengths, and liquids as ordinary play. Journal of Educational and Developmental Psychology, 7(1). 210-217. https://doi.org/10.5539/jedp.v7n1p210

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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.

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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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