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As children age, they begin to understand the world in new ways. In this lesson, we’ll look at Piaget’s concrete operational stage of development and cognitive gains made during that time, including classification, seriation, and transitivity.

Concrete Operations

Marty is nine years old. He’s not like other kids, though. He likes order.

He lines his socks up inside the drawer so that they are coordinated by color. He puts his pencils on his desk in a line from largest to smallest. He finds it fascinating that things vary and likes to tease out the differences between things and sort them in different ways.Marty is in the period of childhood known as middle childhood, which lasts from age seven to twelve. Psychologist Jean Piaget named this time of life the concrete operational stage of development. He called it this because this is the time of life when children begin to perform mental operations, which is when you manipulate the world in your mind to solve problems.

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To understand mental operations, imagine that you have a big puzzle on the table in front of you. One of the pieces has a side that has a rounded edge sticking out from the side. You know that you need to find a piece that has an indentation that will fit the piece that you have.When you look at the other pieces on the table, you notice that some have indentations and others don’t. Not only that, but some have colors and shapes that seem to go along with the piece in front of you. With each piece, you imagine putting the piece next to the one you have and try to figure out whether it might be a match, based on color and whether it has an indentation or not. Then, if you find a piece that’s a possibility, you pick it up and try to connect it to your piece.

But if you ask a toddler to solve a puzzle, they can’t do the same deductions that you or I could. Whether the piece has an indentation or not, whether the colors are right or not, they will pick up every single piece and try to fit it. They can’t mentally imagine whether each piece will fit. They cannot yet perform mental operations.


As part of the concrete operational period of development, children begin to think differently. Not only can they begin to perform mental operations, they also begin to make logical deductions about the world around them.

One example of this is the task of classification, which involves understanding that one set of items can include another set of items. Remember Marty? He loves to sort things. One of the ways to sort things is through classification.Marty’s friend Beth has a new poodle. Marty knows that a poodle is a dog and a dog is a mammal and a mammal is an animal.

When he was younger, he didn’t understand how these classifications worked, but now that he’s older, he understands that each set of things nests inside of the others. He knows that poodles are dogs and dogs are mammals, and therefore, he knows that poodles are mammals.


Remember how Marty likes to arrange the pencils on his desk or the socks in his sock drawer? This might seem a little odd to many people, but to Piaget, it was just part of development. Marty is demonstrating seriation, which is the ability to order items with respect to a common feature.When it comes to socks, Marty puts them in order based on their color. With pencils, he focuses on length.

Either way, he’s choosing a single feature and ordering the objects based on it. Seriation is part of the concrete operational stage of development and is closely related to classification. In both instances, the person is using an organizational schema, or system, to make sense of the world around him.


Classification and seriation aren’t the only type of organization that kids begin to use in the concrete operational stage.

Transitivity involves ordering things by comparing them to a benchmark piece.For example, the other day Marty was picking up his playroom. He had several books that needed to be put on the shelf, and he decided to put them in order from largest to smallest.

There were three books that were really similar in size, and he didn’t have a ruler to measure them. So, he compared book A to book B and then book A to book C. He realized that book A was larger than book B but smaller than book C, so he drew the conclusion that book C was larger than book B.

Essentially, Marty was comparing the books to each other, but instead of putting all the books next to all the other books, he used the shortcut of comparing books B and C to book A. From there, he could figure out the relationship between all of them. This is transitivity at work.

Lesson Summary

Psychologist Jean Piaget named middle childhood the concrete operational stage of development.

It involves the ability to perform mental operations, as well as to think logically, including utilizing classification, seriation, and transitivity.

Learning Outcomes

After you have finished with this lesson, you’ll be able to:

  • Describe the concrete operational stage of development
  • Explain the concepts of utilizing classification, seriation, and transitivity during this stage

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