The Concrete Operational Stage, from Piaget’s theory of cognitive development, occurs between ages 7 and 11.
During this period, children develop logical thinking skills related to concrete physical objects and situations, but they still find abstract or hypothetical thinking challenging.
How can I tell if a child has reached the concrete operational stage?
- Reversibility: They mentally reverse actions, like understanding that reshaping clay doesn’t change its amount.
- Decentring: They consider multiple aspects of a situation simultaneously, rather than just one. Like recognizing that their friend might not want the same birthday gift as they would, because everyone has different likes and interests.
- Conservation: They recognize quantity stays the same despite changes in appearance. For example, they understand pouring juice into a different-shaped glass doesn’t change the amount.
- Classification: They can group items logically by multiple features, such as sorting toys by both color and size simultaneously.
- Seriation: They easily arrange objects in logical order according to size, weight, or length (e.g., pencils from shortest to longest).
Conservation
Conservation is understanding that something stays the same in amount, even if its appearance changes.
This concept applies to things like volume, number, length, or the mass of a substance.
Piaget developed a standard way to test this: he asked the child a pre and a post-transformation question.
He presented children with two identical rows of counters or two glasses of water with equal amounts.
After changing the appearance (for example, spreading out counters or pouring water into a taller, narrower glass), he asked again if the amounts were still the same.
Younger children (around age 5) typically said the amounts had changed because they looked different.
In contrast, most children around age 7 correctly understood that the amounts remained equal despite the appearance changes (Piaget, 1954b).
Piaget and Szeminska (1952) showed younger children (under 7 or 8) often mistakenly believed that spreading counters apart increased their number, or flattening a ball of clay reduced its amount.
Piaget also observed that not all conservation skills develop simultaneously—children master some (like conservation of number or mass) before others (like conservation of volume).
He named this uneven progression horizontal decalage (Piaget, 1954b), highlighting that conservation skills emerge gradually rather than all at once.
Classification (grouping similar things)
Classification is the ability to group objects based on shared features, organize these groups into meaningful hierarchies, and use this information logically to solve problems.
During Piaget’s concrete operational stage, children significantly improve their classification skills.
Classification involves:
-
Grouping objects by shared features (color, size, shape).
-
Using multiple criteria simultaneously (decentration).
-
Understanding hierarchical relationships (class inclusion).
-
Recognizing categories can exist within other categories (nested hierarchy).
Mastering these classification skills significantly enhances logical thinking and problem-solving abilities during childhood.
Class Inclusion:
Class inclusion is the cognitive skill of recognizing that a smaller group (subcategory) belongs within a larger group (category), and understanding that the larger group contains more items.
In the pre-operational stage, children struggle with class inclusion.
For example, when shown four red flowers and two white ones and asked “are there more red flowers or more flowers?”, a typical five-year-old would say “more red ones.”
This occurs because children can’t easily recognize that the broader category (flowers) includes both red and other colors (subcategories).
During the concrete operational stage, children can group physical objects by common features, such as grouping animals into birds, mammals, reptiles, etc.
One component of classification skills is the ability to group objects according to some dimension that they share, such as color, shape or size.
Multiple Criteria
Concrete operational children move beyond classifying objects based on single criteria, becoming capable of using multiple criteria and forming more complex classifications.
Children can understand that objects can belong to multiple categories at the same time (e.g., a dog is both a pet and an animal).
For instance, they can classify objects based on both color and shape, or size and weight.
Hierarchical Classification:
Another key achievement is hierarchical classification, recognizing that categories can be nested inside larger groups (e.g., poodles are dogs, which are animals).
Piaget emphasized the recursive nature of classification—categories themselves can become parts of larger, increasingly complex systems.
This deeper understanding of hierarchy helps children realize that larger categories (e.g., animals) contain more objects than smaller, specific groups (e.g., cats or dogs).
Evaluation of Classification Tasks
James McGarrigle designed an experiment that tested Piaget’s explanation that a child is unable to compare class with sub-class because of centration.
Centration refers to a child’s tendency to only deal with one aspect of a situation at a time.
Piaget’s class inclusion test used wooden beads, some white some brown.
He found that children in the preoperational stage were unable to give the right answer to the question, “Are there more brown beads or more wooden beads?”
McGarrigle used a slightly different version of this test. He sued four model cows, three of them black, and one white. He laid all the cows on their sides, as if they were sleeping. Six-year-old children were then asked:
- Are there more black cows or more cows? (This is the question Piaget asked)
- Are there more black cows or sleeping cows?
Results: 25% percent of the children answered question 1 correctly, but 48% of the children answered question 2 correctly.
This suggests that children are capable of understanding class inclusion rather earlier than Piaget believed. This is probably because the task was made easier to understand.
McGarrigle concluded that it was the way Piaget worded his question that prevented the younger children from showing that they understood the relationship between class and sub-class.
Seriation (ordering Items Logically)
Seriation is the cognitive skill of arranging objects logically in order based on measurable features, like size, height, weight, age, or color.
For instance, children who have developed seriation can line up sticks from shortest to longest, sort coins by date from oldest to newest, or arrange colored pencils from darkest to lightest.
This ability demonstrates a significant advancement in a child’s cognitive development, as it requires an understanding of multiple dimensions and characteristics of objects, as well as the ability to compare and contrast these characteristics.
As children transition to the concrete operational stage, they develop the capacity for reversibility, which is essential for seriation.
This helps children recognize inverse relationships. For example, understanding that if stick A is taller than stick B, then stick B must be shorter than stick A.
Although related, seriation is distinct from classification.
Classification involves grouping objects based on common features, such as sorting toys by color or shape. Seriation, on the other hand, specifically involves placing items in a logical order.
Both skills rely on logical thinking, but seriation emphasizes ordering and sequencing, whereas classification emphasizes grouping and categorizing.
Reversibility (mentally reversing actions)
Reversibility is the cognitive skill of mentally reversing actions, allowing objects or numbers to return to their original state in a child’s mind.
It is a key skill developed during Piaget’s concrete operational stage, closely related to other logical abilities such as conservation, classification, and seriation.
Initially, children develop reversibility by interacting with real, physical objects and situations.
For instance, when water is poured from a short, wide container into a tall, narrow one, children who grasp reversibility can mentally imagine pouring the water back into the original container, realizing that the amount remains unchanged despite its altered appearance.
Understanding conservation specifically relies on reversibility.
Conservation involves recognizing that certain properties (like volume, number, or mass) stay constant despite changes in appearance.
Without reversibility, younger children tend to mistakenly assume the quantity has changed simply because the appearance is different.
Reversibility also supports classification.
When grouping objects by shared attributes, children use reversibility to mentally reorganize items between categories. This flexibility helps them understand that items can belong to multiple categories depending on the criteria they choose.
Reversibility also enables children to:
-
Perform Logical Operations: Children can mentally manipulate and reorganize objects and numbers, aiding skills like addition, subtraction, seriation (arranging items logically), and classification (grouping by shared characteristics).
-
Reason with Increasing Complexity: As cognitive skills mature, reversibility expands beyond concrete tasks. In the later formal operational stage, adolescents begin applying reversibility to abstract ideas and hypothetical scenarios, facilitating deeper logical reasoning and complex problem-solving.
Piaget noted that reversibility develops gradually.
For example, reversibility involving numbers and mass usually emerges earlier, while understanding volume often appears later a developmental progression he called horizontal decalage.
Thus, reversibility is foundational not only for practical problem-solving but also as a building block for advanced, abstract reasoning skills developed later in adolescence.
Decentering
Decentration is the cognitive ability to think about multiple aspects of a situation at the same time.
It marks significant progress from the earlier centration stage, where younger children focus only on one obvious aspect.
Without decentration, children typically focus only on one striking aspect of a situation (centration), making accurate logical reasoning challenging.
For example, a child who can decenter understands that a tall, narrow glass can hold the same amount of water as a short, wide glass by considering both height and width at once. Younger children might only see the height difference, mistakenly concluding the amounts differ.
-
Conservation: Decentration helps children simultaneously consider multiple dimensions (e.g., height and width of a glass) when recognizing that quantity remains constant despite appearance changes.
-
Classification: Decentration allows children to consider multiple attributes (e.g., color and shape) simultaneously, enabling them to group objects by multiple criteria rather than just one.
-
Seriation: Decentration supports ordering objects by allowing children to compare multiple objects simultaneously across dimensions like height or weight.
-
Social Thinking: Decentration helps children understand that other people can have different viewpoints or feelings (theory of mind).
However, at this stage, decentration is mostly limited to real, physical situations.
The ability to decenter in abstract or hypothetical scenarios develops later, during Piaget’s formal operational stage.
Interconnectedness Among Skills
Each of these skills (conservation, classification, seriation) is deeply interlinked through foundational abilities (decentration and reversibility).
Mastery of one skill supports and strengthens others, highlighting Piaget’s view of interconnected logical operations as the hallmark of concrete operational thought.
-
Decentration and Reversibility underpin Conservation. Decentration lets the child consider multiple features, while reversibility mentally confirms unchanged properties.
-
Reversibility aids Classification by allowing children to mentally rearrange items between categories, ensuring flexibility in logical grouping.
-
Seriation also heavily relies on Decentration and Reversibility. Children mentally compare multiple objects at once (decentration), then mentally reorder and rearrange sequences (reversibility), confirming accurate logical ordering.
Example of Conservation (Liquid)
-
Initial Observation: The child sees two identical glasses filled equally with water. The identical shape and water level clearly suggest equal amounts.
-
Change in Appearance (Transformation): Water from one glass is poured into a different-shaped glass (taller and narrower). The height of the water rises significantly, making it appear different.
-
Initial Superficial Assessment: Initially, the child may think the amount has changed because of the striking visual difference, such as the water level rising.
-
Activation of Decentration: The child mentally shifts from focusing on a single aspect (the height of the water) to simultaneously considering multiple features. They now notice not just height but also width, understanding that the new glass is taller but narrower.
-
Mental Reversibility: The child mentally “undoes” the pouring action, imagining the water flowing back into the original, shorter, wider glass. This mental reversal confirms that the quantity would return precisely to its original appearance and level.
-
Logical Conclusion (Conservation Achieved):Using decentration and reversibility together, the child logically concludes that the water amount remains unchanged despite the transformation. They have mentally verified the quantity is consistent, overcoming the superficial visual difference.
Example of Classification (Grouping Similar Items)
-
Initial Encounter with Items: The child sees a variety of toys scattered, differing in color, shape, and size.
-
Activation of Decentration (Multiple Features): The child mentally assesses multiple attributes simultaneously. Instead of focusing solely on one attribute, like color, they now simultaneously consider size, shape, and even function.
-
Mental Reversibility in Sorting: Mentally, the child imagines rearranging toys between different categories. For instance, they might initially group toys by color, then mentally “undo” this categorization, reorganizing the same toys by shape or function.
-
Logical Verification of Relationships: Through this mental shifting (reversibility), the child verifies hierarchical relationships (class inclusion). They clearly grasp that some toys belong in multiple categories, such as a small red car belonging simultaneously to categories like “red toys,” “small toys,” and “vehicles.”
-
Logical Categories Clearly Formed: The combination of decentration and reversibility solidifies the child’s ability to flexibly create clear, logical groups. This allows the child to classify precisely, demonstrating an advanced and interconnected cognitive ability.
Example of Seriation (Ordering Sticks by Length)
- Initial Observation: The child is given several sticks of varying lengths placed randomly on a table.
- Change in Appearance (Task Introduction): The child is asked to arrange the sticks in order, from shortest to longest.
- Initial Superficial Assessment: Initially, the child may attempt to organize the sticks based on a single obvious feature (such as grouping shorter sticks), but may not yet systematically compare all sticks together.
- Activation of Decentration: The child mentally considers multiple sticks at the same time, comparing each stick’s length relative to the others, rather than just focusing on one stick individually.
- Mental Reversibility: As the child places sticks in an initial order, they mentally rearrange and adjust their placement. They mentally “undo” incorrect sequences, imagining how the sticks can be reordered to reflect the correct length order.
- Logical Conclusion (Seriation Achieved): By simultaneously considering all sticks (decentration) and mentally rearranging their sequence (reversibility), the child successfully arranges the sticks in precise order from shortest to longest, demonstrating clear, logical seriation.
Critical Evaluation
| Strengths | Criticisms |
|---|---|
| Identifies key cognitive skills of childhood: Piaget pinpointed logical abilities (e.g. conservation, classification, seriation) that reliably emerge in middle childhood, marking a crucial developmental shift. | Underestimates children’s abilities: Some studies show these cognitive skills can appear earlier than Piaget thought under supportive conditions. Younger children have succeeded in Piaget’s tasks when questions are phrased appropriately or training is provided. |
| Guides educational practice: The stage concept helps teachers design age-appropriate learning activities. For example, instructors use concrete objects and examples for 7–11 year-olds, aligning with their capacity for tangible logical thinking. This ensures teaching matches the child’s developmental readiness. | Ignores individual variability: Piaget’s strict stage model assumes all children progress uniformly. In reality, cognitive development varies widely – children do not reach milestones at the exact same ages. Rigidly adhering to stages can overlook individual differences in development pace and style. |
| Child-centered learning emphasis: Piaget highlighted that children are active learners who construct knowledge. This strength led to classroom practices encouraging exploration, discovery, and peer learning, rather than rote instruction. It recognizes that children think in qualitatively different ways than adults, which has been influential in curriculum design. | Limited cultural scope: Piaget derived his stages largely from Western, educated children, and he downplayed cultural and social factors in cognitive growth. Cross-cultural research shows that the attainment of concrete operational skills can depend on schooling and cultural context, which Piaget’s theory did not address. |
| Innovative research approach: Piaget’s use of open-ended interviews and observation (the clinical method) provided rich insights into how children reason. This approach was novel and allowed children to explain their thinking in their own words, shedding light on cognitive processes in detail. | Methodological flaws: Piaget’s studies had small, homogeneous samples and often lacked rigorous controls. He sometimes asked children confusing or repetitive questions, which may have influenced their responses. Such flaws raise questions about the reliability of his concrete-operational-stage findings and whether they generalize to all children. |
Educational Applications
Piaget’s concrete operational stage identifies a major turning point in cognition, when children become capable of logical operations on concrete information.
Around this age, kids develop skills like conservation (understanding quantity remains the same despite changes in shape), classification, and reversibility, marking the beginning of true logical reasoning.
This framework provided a clear structure for educators and parents to recognize typical cognitive milestones in middle childhood.
Piaget’s work has profoundly influenced teaching practice.
He argued that children should be taught at the level for which they are developmentally prepared, and his stage theory encourages hands-on, concrete learning activities in primary education.
In the concrete operational stage, educators often use tangible objects (blocks, visual aids, real-world examples) and peer interaction to help children grasp logical concepts, aligning instruction with the child’s cognitive readiness.
This child-centered approach is a direct strength of Piaget’s theory in practical settings.
However, there is a flipside: critics argue that strictly adhering to Piaget’s stages can sometimes lead educators to underestimate children or to be too slow in introducing new concepts.
Research in educational psychology suggests children’s development can be accelerated or supported with the right guidance.
For instance, targeted teaching or interventions can help some children grasp “above-level” concepts earlier than Piaget’s framework might predict.
If a teacher rigidly decides “this child isn’t in the concrete stage yet, so I won’t introduce concept X,” they might hold back a student who could learn it with appropriate support.
In fact, Piaget’s original stance was somewhat against direct instruction of concepts before the child discovers them independently, but later evidence shows that guided instruction and social interaction can advance cognitive skills in ways Piaget didn’t fully account for.
Thus, the concrete operational stage has valuable practical applications – emphasizing developmentally appropriate, hands-on learning – but educators are cautioned to use it as a flexible guide rather than a strict rulebook.
A balanced approach acknowledges the typical cognitive capabilities of 7- to 11-year-olds while still observing individual students and providing scaffolding to those ready for more challenge.
Cultural Differences in Cognitive Development
Piaget’s stage model does not fully account for cross-cultural and individual differences.
For instance, in some communities without formal schooling, children developed conservation understanding later than Piaget’s Swiss participants, whereas certain spatial skills emerged earlier in those contexts
Dasen (1994) showed that different cultures achieved different operations at different ages depending on their cultural context.
Dasen (1994) cites studies he conducted in remote parts of the central Australian desert with 8-14 year old Aborigines. He gave them conservation of liquid tasks and spatial awareness tasks.
He found that the ability to conserve came later in the aboriginal children, between ages 10 and 13 ( as opposed to between 5 and 7, with Piaget’s Swiss sample).
However, he found that spatial awareness abilities developed earlier amongst the Aboriginal children than the Swiss children.
Such a study demonstrates cognitive development is not purely dependent on maturation but on cultural factors too – spatial awareness is crucial for nomadic groups of people.
Greenfield (1966) states that schooling influenced the acquisition of such concepts as conservation.
Likewise, neurodivergent learners (such as children with developmental delays) may follow a similar sequence of cognitive development but at a different pace, indicating that the stage’s timing is not one-size-fits-all.
Methodological Limitations
Piaget’s research methods have been widely criticized.
His conclusions about the concrete operational stage were based on small and non-representative samples (often his own children or children of well-educated families), raising concerns about bias and generalizability.
Additionally, the artificial nature of some tasks has been criticized.
A child might fail Piaget’s test not because they lack the concept, but because the situation is unfamiliar or the question framing is confusing.
For example, repeatedly asking a child about quantity after a transformation (as Piaget did) might imply to the child that their first answer was wrong, prompting them to change it, whereas in a more natural setting the child actually does understand the concept
Evaluation of Conservation Tasks
Several aspects of the conservation tasks have been criticized, for example, that they fail to take account of the social context of the child’s understanding.
Rose and Blank (1974) argued that when a child gives the wrong answer to a question, we repeat the question in order to hint that their first answer was wrong.
This is what Piaget did by asking children the same question twice in the conservation experiments, before and after the transformation.
When Rose and Blank replicated this but asked the question only once, after the liquid had been poured, they found many more six-year-olds gave the correct answer.
This shows children can conserve at a younger age than Piaget claimed.
Samuel and Bryant (1984)
Samuel and Bryant (1984) investigated whether Piaget’s tests of conservation were flawed because the children were responding to being asked the same question twice.
Research questions:
- How does asking only one question about conservation affect the ability of children over a wide age range?
- Are conservation of mass, number, and volume all affected?
Procedure:
- 252 boys and girls aged 5½ -8 years old were divided into four groups (by age).
- This study used an independent measures experimental design.
- Each group was subdivided into three conditions: standard (pre and post-transformation questions); one judgment (post-transformation question); fixed array (child didn’t see transformation).
- Squashed cylinders were used to test mass, spread out rows of counters for number and tall/narrow glasses for volume.
Findings:
- Children performed better with only the post-transformation question (for most ages and most
materials, oddities being due to chance) - Older children were better at all tasks than younger
ones. - The standard Piagetian was harder than both the post-transformation question only and the fixed array situation.
- The number task was the easiest.
Conclusion:
- Samuel & Bryant conclude that the problem lies with the effect of the experimenter asking a second question and unwittingly implying to the participant that a different answer is required.
- Asking both the pre and post-transformation questions causes children who can conserve to make conservation errors.
Evaluation:
- Samuel and Bryant tested 252 children which is a large sample. They tested children from the age of five to the age of eight which allowed them to draw conclusions about the age at which children started to be able to conserve.
- They all came from one area of the country (Devon) which might mean that they are not representative of children from other areas of the country. For example, if Devon used different teaching strategies to other parts of the country this might have an effect on the children’s cognitive
abilities. - This is not really a criticism of the study and overall the sample is large enough to allow generalisations to be made.
- The task itself is quite an artificial one. It is not an everyday occurrence to ask children this type of question, although the skills that are being tested are everyday skills.
- Perhaps a more ecologically valid method would have been to ask children to choose which of two beakers of juice or rows of smarties they would prefer to have. This would be more ‘real’ to the children as well as demonstrating clearly that they could conserve.
- There are some difficulties in evaluating the actual question used as the researchers do not tell us the exact wording of the question. Asking a child ‘are they the same?’ may be a slightly ambiguous question.
- There are many ways in which this question might have been asked and it is possible that children may
have interpreted the question differently.
Porpodas (1987)
Porpodas (1987) found that asking more than one question wasn’t really the problem.
This research suggested that the questions provided ‘verbal interference’ which prevented children from transferring information across from the pretransformation stage.
This implied that the problem was a cognitive one, but not exactly of the nature originally suggested.
Baucal & Stepanovic (2006)
In an attempt to address the question of whether children’s failures on conservation tasks result from cognitive immaturity or from conversational factors (such as language use or power dynamics between the child participant and adult experimenter), Baucal and Stepanovic (2006) analyzed the results from multiple tests examining the repeated-question hypothesis.
They also conducted an additional test designed to distinguish cognitive effects from social effects.
In this test, they repeated a question about a transformation that had not actually changed (e.g., pouring liquid back into the original glass), meaning only the repeated questioning – not the transformation itself – could influence responses.
Interestingly, the results did not match expectations. They predicted that children’s responses would remain consistent across the standard and modified tasks, but this was not the case.
Ultimately, the researchers could not conclusively determine whether repeating the question caused the observed effects.
Arcidiacono and Perret-Clermont (2009)
Research has gone on to explore the ‘conversation about conservation’ idea which underpins the interview method.
Arcidiacono and Perret-Clermont (2009) suggested that children’s statements about conservation are not, as Piaget claimed, simply a product of their cognitive level but of their social interaction with the interviewer.
This suggests that the child’s reasoning is ‘co-constructed’ during the testing process.
If adult ‘accept’ wrong (or right) answers without asking for a justification (argument about why it is so), which is what Piaget was really interested in.
McGarrigle and Donaldson (1974)
Another feature of the conservation task which may interfere with children’s understanding is that the adult purposely alters the appearance of something, so the child thinks this alteration is important.
McGarrigle and Donaldson (1974) devised a study of the conservation of numbers in which the alteration was accidental.
When two identical rows of sweets were laid out and the child was satisfied there were the same number in each, a “naughty teddy” appeared. Whilst playing around, teddy actually messed up one row of sweets.
Once he was safely back in a box the children were asked if there were the same number of sweets.
The children were between four- and six-years-old, and more than half gave the correct answer.
This suggests that, once again, Piaget’s design prevented the children from showing that they could conserve at a younger age than he claimed.
Educational Implications
Understanding Piaget’s concrete operational stage has important implications for effectively teaching and supporting children (ages 7–11):
-
Hands-On Learning: Children at this stage learn best through active, practical experiences. Providing opportunities for direct engagement – such as experiments, building projects, and interactive games – helps solidify concepts and encourages deeper understanding.
-
Visual Aids and Real-World Examples: Because abstract thinking remains challenging, children benefit significantly from visual supports (e.g., diagrams, charts, physical models) and real-world examples. Linking lessons clearly to tangible, everyday experiences makes learning more meaningful and accessible.
-
Scaffolding Toward Abstract Thinking: Through carefully structured questions and guided problem-solving, known as scaffolding, children can progressively learn to transfer concrete skills toward more abstract reasoning.
Activities Suitable for Children in the Concrete Operational Stage
1. Sorting and Classification Activities
-
Sort objects by multiple attributes simultaneously, such as shape, color, texture, and function (e.g., grouping blocks by color and size, or organizing buttons by color and shape).
-
Create classification charts or collections, like sorting leaves by type or insects by characteristics.
2. Measuring and Comparing Activities
-
Use measurement tools such as rulers, scales, measuring cups, and tape measures to explore concepts like length, weight, volume, and distance (e.g., measuring furniture or comparing heights of plants).
-
Engage in cooking activities that involve precise measurement of ingredients, emphasizing comparisons and relationships between quantities.
3. Logical and Strategic Games
-
Play structured games requiring logical thinking, strategy, and planning, such as chess, checkers, dominoes, or Sudoku.
-
Introduce puzzles, riddles, and brainteasers to enhance logical problem-solving skills.
4. Math Problem-Solving Activities
-
Solve practical math problems involving real-life scenarios, such as sharing snacks evenly, calculating change when shopping, or measuring ingredients for recipes.
-
Explore simple multiplication and division visually with objects (e.g., grouping candies or coins) to support concrete understanding.
5. Simple Experiments and Hands-On Exploration
-
Conduct experiments to explore scientific concepts, such as testing magnet strength, observing water absorption in different materials, or measuring plant growth under various conditions.
-
Encourage predictions, hypotheses, and logical reasoning by asking children to explain observations during experiments.
6. Visual Representation and Organization
-
Create visual aids like maps, charts, and diagrams to represent information clearly and logically, such as mapping out a route, illustrating family trees, or creating weather charts.
-
Develop timelines or sequence charts to help children understand chronological order or procedural steps.
7. Building and Constructing
-
Provide construction materials like Lego, blocks, magnetic tiles, or recyclable materials to encourage design planning, creativity, and spatial reasoning.
-
Challenge children with structured building tasks, such as constructing bridges, towers, or models that require balance and stability.
8. Language and Communication Activities
-
Introduce or practice a new language through interactive games, songs, vocabulary cards, or simple conversation scenarios.
-
Encourage children to express ideas clearly through storytelling, debates, or collaborative storytelling activities.
9. Reading and Ethical Discussions
-
Read and discuss stories containing moral or ethical dilemmas, asking children to explain their reasoning and consider multiple perspectives.
-
Facilitate group discussions where children can share viewpoints and debate character decisions or outcomes.
10. Role-playing and Simulations
-
Organize role-playing activities and dramatic scenarios to help children explore social roles, resolve conflicts, or practice empathy and cooperation.
-
Simulate real-life situations such as running a store, planning a community event, or handling a friendship dispute, prompting logical and social thinking.
References
Arcidiacono, F. & Perret-Clermont, A.N. (2009) Revisiting the piagetian test of conservation of quantities of liquid: argumentation within the adult-child interaction. Культурноисторическая психология, 3 : 25-33.
Agheana, V., & Folostina, R. (2015). The development of the logical operators in students with intellectual disability. Procedia-Social and Behavioral Sciences, 197, 2369-2376.
Dasen, P. (1994). Culture and cognitive development from a Piagetian perspective. In W .J. Lonner & R.S. Malpass (Eds.), Psychology and culture . Boston: Allyn and Bacon.
Greenfield, P. M. (1966). On culture and conservation. Studies in cognitive growth, 225-256.
McGarrigle, J., & Donaldson, M. (1974). Conservation accidents. Cognition, 3, 341-350.
Piaget, J. (1954). The development of object concept (M. Cook, Trans.). In J. Piaget & M. Cook (Trans.), The construction of reality in the child (pp. 3-96) . New York, NY, US: Basic Books.
Piaget, J. (1954b). The child’s conception of number. Journal of Consulting Psychology, 18(1), 76.
Piaget, J. (1968). Quantification, conservation, and nativism. Science, 162, 976-979.
Piaget, J. & Szeminska, A. (1952). The Child’s Conception of Number. Routledge & Kegan
Paul: London.
Porpodas, C. D. (1987). The one-question conservation experiment reconsidered. Journal of Child Psychology & Psychiatry, 28, 343-349.
Rose S. A. & Blank, M. (1974). The potency of context in children’s cognition: an illustrationthrough conservation. Child Development, 45, 499-502.
Samuel, J. & Bryant, P. (1984). Asking only one question in the conservation experiment.
Journal of Child Psychology & Psychiatry, 25 (2), 315-8.
| Aspect | Concrete Operational Stage | Formal Operational Stage |
|---|---|---|
| Type of Thinking | Logical thinking about real, tangible objects and events. | Abstract, logical thinking about hypothetical and abstract ideas. |
| Conservation | Mastered (e.g., understanding quantities remain the same despite appearance changes). | Fully mastered; conservation extended to abstract concepts and propositions. |
| Reversibility | Can mentally reverse actions or transformations on concrete objects. | Can mentally reverse and manipulate abstract ideas and propositions. |
| Classification | Understands hierarchical relationships in concrete categories. | Understands hierarchical relationships among abstract concepts and theories. |
| Hypothetical Reasoning | Limited; struggles with abstract or hypothetical scenarios. | Strong; able to reason through hypothetical scenarios and abstract problems systematically. |
| Problem-solving Strategy | Relies primarily on trial-and-error, concrete experimentation. | Uses systematic, logical, and deductive reasoning. |
| Egocentrism | Diminishes significantly; recognizes multiple perspectives concretely. | Further reduced; can consider abstract perspectives and hypothetical viewpoints effectively. |
| Educational Implication | Learning relies on concrete aids, hands-on activities, and visual examples. | Capable of learning through abstract instruction, theoretical discussions, and hypothetical problem-solving. |
FAQs
Why do children in Piaget’s Concrete Operational Stage still struggle with abstract thinking despite having developed strong logical reasoning about concrete objects?
They demonstrate skills such as conservation, reversibility, classification, seriation, and decentration clearly and effectively.
Abstract thinking involves mentally manipulating ideas, concepts, or hypothetical scenarios without direct physical experiences or tangible objects.
This form of thought requires higher-level mental operations and a capacity to consider purely hypothetical or imagined situations, something not fully developed until Piaget’s formal operational stage.
Concrete operational children have well-developed logical reasoning, but it remains tightly tied to real-world contexts and immediate, tangible references.
Abstract thinking demands that children detach reasoning from immediate experience and manipulate ideas purely mentally—something children at this stage find challenging.
Consider a child who understands conservation of water (concrete operation). They mentally reverse actions to confirm quantity.
Yet, ask the same child a purely abstract question (Imagine if there were no gravity – what would happen?), and they struggle to reason because they can’t anchor their reasoning in a tangible experience or direct observation.
The limitation lies in the child’s cognitive maturity: concrete operational reasoning depends significantly on direct experience and tangible support.
Abstract reasoning requires advanced cognitive structures – such as systematically managing multiple hypothetical variables simultaneously – that emerge fully in Piaget’s formal operational stage.
How does Piaget’s theory apply to children with learning differences or neurodivergent profiles?
They might reach milestones of the Concrete Operational Stage at significantly different ages, sometimes earlier or later, or demonstrate skills unevenly across domains.
For example, an autistic child might quickly grasp classification or seriation but might take longer to master conservation or social aspects of decentration.
Children with ADHD might understand cognitive tasks quickly but struggle to demonstrate these consistently due to attention or organizational challenges.
Neurodivergent children often have uneven cognitive profiles, showing distinct strengths and difficulties.
They may excel in certain concrete, logical tasks such as sorting objects by precise categories, arranging objects logically (seriation), or memorizing factual information.
However, abstract reasoning tasks, such as handling hypothetical scenarios or understanding nuanced social cues (decentration and perspective-taking), may be more challenging.
Providing explicit instructions, visual aids, and structured, step-by-step teaching methods can help leverage their strengths while addressing areas needing additional support.
What do children struggle to do in the concrete operational stage?
During this stage, children begin to develop logical thinking skills and can perform operations on concrete objects and events. However, they still struggle with certain cognitive tasks:
Abstract Thinking: Children in the concrete operational stage often struggle with abstract and hypothetical concepts.
They tend to think in very concrete, literal terms and have difficulty understanding metaphors or hypothetical situations.
Systematic Problem-Solving: While children in this stage are better at problem-solving than in previous stages, they often struggle with systematic problem-solving.
They may be unable to plan out all the steps in a problem and execute them in the most efficient order.
Conservation of Volume: While children in this stage understand the conservation of number and mass, they often struggle with the concept of conservation of volume.
For example, they may not understand that water poured from a short, wide container into a tall, thin container is still the same amount of water.
Dealing with Contradictions: Children in the concrete operational stage may struggle when their concrete observations contradict their understanding of how the world works.
They may have difficulty reconciling these contradictions.
Thinking from Another’s Perspective: While children in this stage better understand others’ perspectives than in the preoperational stage, they may still struggle with more complex forms of perspective-taking.
Remember, these are general trends and individual children may progress through these stages at different rates.
How does the Concrete Operational Stage specifically impact a child’s mathematical reasoning and problem-solving skills?
However, their mathematical reasoning remains limited by the inability to handle abstract mathematical concepts until the formal operational stage.
At ages 7–11, children master logical operations on concrete objects.
Key skills include conservation (understanding quantity permanence), classification (grouping logically), reversibility (mentally reversing operations), decentration (considering multiple dimensions simultaneously), and seriation (ordering logically).
Conservation directly relates to understanding mathematical invariants (e.g., quantity, volume, mass remain constant despite transformations).
Classification helps organize numbers, shapes, and operations into logical categories.
Reversibility enhances skills such as addition/subtraction or multiplication/division, as it enables children to mentally reverse mathematical operations clearly.
Seriation contributes to numeric understanding like ordering, sequencing numbers, and measurement.
Decentration supports considering multiple properties simultaneously, crucial for solving multi-step math problems.
A child solving the problem “If you have 10 candies and give away 4, how many do you have left?” uses reversibility.
They mentally reverse the subtraction (“giving away 4 candies”) and confirm the original quantity.
A child arranging numbered blocks from smallest to largest demonstrates seriation and logical ordering.
Solving a word problem involving multiple variables (e.g., size and quantity simultaneously) showcases decentration.
Concrete operational children can solve math problems effectively when related to tangible, visible, or easily imagined contexts.
However, they struggle with mathematical tasks involving abstract concepts (such as algebra), purely symbolic reasoning, or hypothetical scenarios not directly tied to concrete reality.
In Piaget’s Concrete Operational Stage, how do children’s improved cognitive skills influence their social interactions and understanding of social relationships?
Improved cognitive skills enable children to understand social dynamics more deeply. Specifically:
Decentration allows children to grasp that others have different perspectives, feelings, and motivations simultaneously.
In a conflict, a child can recognize both their perspective and their friend’s simultaneously, leading to better empathy and resolution strategies.
Classification helps children mentally organize social roles (friends, teachers, family) into logical groups, understanding the hierarchy and relationships within groups.
A child categorizes peers into groups like “best friends,” “classmates,” and “neighbors,” clearly understanding varying degrees of closeness and social expectations.
Reversibility enables children to mentally reconstruct social situations and see the consequences of actions clearly, such as reversing roles in conflicts.
After a disagreement, a child mentally retraces steps in the conflict to understand where misunderstandings occurred and how reconciliation might happen.
Conservation helps children grasp fairness and equity in interactions, recognizing that quantity and value remain consistent despite appearance changes.
A child understands fairness in sharing snacks, recognizing equal distribution even if appearance differs (e.g., a larger but thinner cookie vs. a smaller but thicker one).
Seriation can help children understand hierarchies and sequences within social contexts, like friendship closeness or authority structures.
A child understands ranking friendships by closeness or importance, which guides appropriate social behavior (e.g., who to invite first to an event).
Despite improvements, social reasoning at this stage still remains largely concrete, based on observable interactions and tangible scenarios.
Abstract social reasoning (e.g., understanding complex social justice concepts, hypothetical scenarios without concrete examples) remains challenging until formal operational development.
Concrete operational cognitive skills substantially enhance children’s social interactions, enabling clearer empathy, structured categorization of social relationships, fair reasoning, and more effective conflict resolution.
Yet, deeper abstract social understandings require further cognitive maturation in later developmental stages.
