The child is not able to see from another's point of view, either psychologically or physically. This is called irreversibilitycentrationegocentrism and is characteristic of the preoperationalconcrete operationalformal operational stage.

The child is able to plan a series of coordinated movements in order to get what he wants. This is called object permanencegoal-directed behavioursymbolic thought and first appears in the sensorimotorformal operationalpreoperationalconcrete operational stage.

Children first become capable of logically dealing with the concepts of time, number and space in the formal operationalpreoperational stageconcrete operational stage. 

Children or teenagers who are able to solve the pendulum problem by isolating variables show the kind of systematichaphazard and concretelogical thinking that is characteristic of the formal operationalpreoperationalconcrete operational stage stage.

Children who display the ability to complete these three tasks are able to conserve (a) volumemassnumber, (b) volumenumbermass and (c) numbervolumemass. This suggests that they can mentally rewind a process, which is called decentrationreversibilityirreversibility, and also take into account more than one aspect of a problem in order to solve it. This is called centrationdecentrationegocentrism. These skills, according to Piaget, are characteristic of the formal operational stageconcrete operationalsensorimotor stage.

Children or teenagers who can mentally simulate a range of complex future possibilities in a speculative situation are displaying the capacity of hypotheticalconcretereversible thought, which is characteristic of the preoperationalformal operational concrete operational stagestage.