Concrete Operations Stage

The concrete operations stage begins at age six or seven, when the schoolage

child becomes capable of keeping in mind and logically manipulating

several concrete objects at the same time. The child is no longer the prisoner

of the momentary appearance of things. In no case is the change more

evident than in the sort of problem in which a number of objects (such as

twelve black checkers) are spread out into four groups of three. While the

four-year-old, preoperational child would be likely to say that now there are

more checkers because they take up a larger area, to the eight-year-old it is

obvious that this transformation could easily be reversed by regrouping the

checkers. Piaget describes the capacity to visualize the reversibility of such

transformations as “conservation.” This understanding is fundamental to

the comprehension of simple arithmetical manipulations. It is also fundamental

to a second operational skill: categorization. To the concreteoperational

child, it seems obvious that while Rover the dog can for other

purposes be classified as a household pet, an animal, or a living organism, it

will still be a “dog” and still be “Rover.” A related skill is seriation: keeping in

mind that an entire series of objects can be arranged along a single dimension,

such as size (from smallest to largest). The child now is also capable

of role-taking, of understanding the different perspective of a parent or

teacher. No longer egocentric (assuming that everyone shares one’s own

perspective and cognitively unable to understand the different perspective

of another), the child becomes able to see himself or herself as others see

him or her and to temper the harshness of absolute rules with a comprehension

of the viewpoints of others.