Cognitive Development: Piaget’s Concrete Operations

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The mental (cognitive) changes children undergo during the middle childhood era are often more pronounced and noticeable than their physical changes. Children's ability to consciously, thoughtfully and pro-actively choose to pursue goals (instead of simply reacting to the environment) appears during this developmental period. In addition, children's thinking style gradually becomes more logical, organized, and flexible as they enter Piaget's "Concrete Operational" thinking stage.

Piaget's Concrete Operations


A mental operation, in the Piagetian way of thinking, is the ability to accurately imagine the consequences of something happening without it actually needing to happen. During a mental operation, children imagine "what if" scenarios which involve the imaginal transformation of mental representations of things they have experienced in the world; people, places and things. The ability to perform mental arithmetic is a good example of an operation. Children at this age become capable of mastering addition and subtraction and similar operations and consequently are able to tell you that if they eat one cookie out of a jar containing five, that there will be four cookies left in the jar. Importantly, they can do this without actually eating a cookie and then counting the remaining cookies in the jar because they are able to model the cookie jar in their minds and operate on the contents of that mental jar so as to arrive at the answer without having to actually do the experiment.

These sorts of operations are "concrete" because they are based on actual people, places and things that children have observed in the environment. Children's mental representations remain concretely linked to things they have seen and touched throughout the middle childhood period. Because their representations are limited to the tangible, touchable and concrete, their appreciation of the consequences of events is similarly limited, local and concrete in scope. At this age, children can easily tell you that if the fence breaks open, that the dog will be able to get out. However, they cannot easily think about more abstract things like what it will really mean for the family if a parent loses her job. In the Piagetian theory, it is not until children enter adolescence that they become capable of more abstract "formal" operations involving representations of things that are intangible and abstract (without any tight link back to a tangible person, place or thing), such as "liberty", "freedom" or "divinity".

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Piaget described multiple operations that children begin to master in middle childhood, including conservation, decentration, reversibility, hierarchical classification, seriation, and spatial reasoning. These are technical terms, all of which will be described below in greater detail. Obviously, children do not learn the names of these various operations or proudly point out to their parents that they've mastered these skills. Children just start doing these things without having realized what they've accomplished. However, these new skills are often noticeable by outside observers familiar with children's progress. In their own subtle way, children's mastery of these operations is a tremendous accomplishment, easily as impressive a feat as any physical accomplishment children might learn.

The stage-by-stage nature of Piaget's theory, with each stage linked to an age group for whom the stage is typical, strongly suggests to many people that at a particular age, children are supposed to be functioning at a particular stage. It's important to keep in mind that Piaget's theory is intended to talk about how an average child might be functioning at a particular age; it is not a pronouncement about how any particular individual child should be functioning. Children develop uniquely and at their own pace depending upon their temperament (the inherited component of their personalities), genetic makeup, supports available to them in their environments, and their learning experiences. Different children will show mastery of specific operations sooner than will others, or display them in some situations but not in others. Newer research also shows that context affects children's abilities as well. Most children will display more advanced operations when in familiar or mandatory environments (e.g., at school, working on school tasks). They may tend to become confused and perform more poorly when confronted with novel situations.

Let's now explore the various concrete operations children start to master during this middle childhood stage of their development:


Conservation involves the ability to understand when the amount of something remains constant across two or more situations despite the appearance of that thing changing across those situations. The idea of conservation can be applied to any form of measurement, including number, mass, length, area, volume, etc. Piaget's famous example of conservation was performed using liquids poured into different shaped containers. Though the volume of liquid remains constant across the two containers, each container has a very different visual appearance, with one being tall and thin, while another was short and wide. Using this setup, Piaget was able to show that middle childhood-aged children were able to appreciate that the total amount of liquid was unchanged despite being poured into differently shaped containers. Younger children were characteristically fooled by the appearance of the containers and tended to conclude that wider, shorter containers held less water than taller, thinner containers.

In everyday life, children demonstrate conservation of number (of counting) when they realize that 10 cookies will remain constant in number no matter whether they are spread out or stacked into a tower. Children who grasp conservation of mass realize that their body weight will remain consistent, whether they stand up straight or sit cross-legged on a scale. Similarly, children who understand conservation of length understand that a rope is the same length regardless of whether it's laid out straight or coiled up. Children who understand conservation of area know that the total space on a tabletop remains constant regardless of whether it is cluttered with objects or cleared. Recent research suggests that children in Western cultures tend to achieve conservation of number by age 7, conservation of mass and length by age 7 or 8, and conservation of area by age 8 or 9.

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