standing that objects exist even when the child cannot see them and the mastery of goal-directed activities. This earliest stage begins with the child's first attempts to imitate, remember, and think in an extremely fundamental way.
The preoperational stage usually takes place over the next five years. This stage is characterized by the gradual ability to use language and symbolic thought (such as pretending that a table is really a spaceship). As children in this stage begin to learn to read (using symbols for sounds and objects) and perform simple math problems, they are not yet able to understand conservation, "the principle that some characteristics of an object remain the same despite changes in appearance." Children at this stage also have difficulty understanding that their thoughts, feelings, and experiences could be any different from anyone else's.
At the concrete operational stage of the next four years, children begin to master logical thinking and conservation and learn that events and structures can be changed and then restored to their original state. Piaget argues, "Some students remain at the concrete-operational stage throughout their school years, even throughout life."
The final stage, most often begun around age 11, is the formal operational stage. At this point, the individual begins to master abstract problems, understand scientific thinking, and become concerned
...