The sensorimotor stage lasts from birth until about two years of age. During this stage, the child thinks about the world solely by interacting with it. The bundle of reflexes and needs with which the child is born drive it to interact with the world in particular ways and for particular purposes, but the child has little or no independent representations of the world. The child performs what Piaget called "circular reactions": actions that produce pleasing consequences on the infant's own body or on aspects of the environment are repeated. These circular reactions form the basis of the child's later concepts of the world: eventually, the reactions become completely internalized so that the child no longer acts to produce a consequence but simply imagines it instead. The child begins to experiment actively with the world, trying out various reactions to stimuli in systematic and exploratory ways. By the end of the sensorimotor period, the child has a set of basic concepts about time, space, causality, objects, and so forth--the basic building blocks of reality.

The preoperational stage lasts roughly from age two to age seven. During this stage, the child acquires a number of abilities that were absent during the sensorimotor stage. Language is, of course, one of them. Another important advance is the recognition of object permanence, the fact that objects continue to exist even when they are out of sight. This is one of the most striking failures of cognition during the sensorimotor period; children at that stage seem to believe that an object that has disappeared behind a screen, for instance, no longer exists. During the preoperational stage, however, children are increasingly able to maintain in mind representations of hidden objects. However, although children have mastered this basic task, they still fail on a variety of tasks that test their ability to apply operations on their representations of the world--thus they are "preoperational." For instance, children fail to understand that the mass of an object is generally conserved no matter what "operations" are performed on it: a certain amount of milk has the same volume whether it is poured into a wide glass or a narrow glass, and a certain amount of clay has the same mass no matter what shape it takes.

It is only in the concrete-operational stage, between the ages of seven and eleven, that children begin to understand that a variety of operations can be conducted on objects in the world that alter the objects' appearance but leave their basic essence unchanged. During this period, children also become less egocentric than they were in the preoperational stage; they begin to understand that other people do not always share their perspective. However, although children are now able to understand the various operations that can be conducted on real objects, and the kinds of relations that can obtain between them, their cognition is still not entirely adult-like. They have yet to master the use of logical operations on purely logical or verbal statements, an accomplishment that comes in the formal-operational stage.

The formal-operational stage begins around age eleven; by age fifteen, most of the dramatic changes in cognition associated with this stage have taken place. Development over the rest of the life course, according to Piaget, is gradual and incremental. During the formal-operational stage, the adolescent starts to think in a truly logical fashion. When they are faced with problems, adolescents formulate hypotheses about the possible causes and solutions and systematically test those solutions. They are able to conduct purely mathematical or logical operations on symbols, without any references to concrete objects in the world.

How is it that children are able to progress from each stage to the next? What are the basic drives or abilities that allow a sensorimotor child to transition to the preoperational stage, or a concrete-operational child to transition to the formal-operational stage? Piaget proposed that there were two invariant mechanisms that drove development: assimilation and accommodation.

"Assimilation" was Piaget's name for the way in which one construes one's perceptions to fit one's conception of the world. Each time we make a judgment about something that we have seen or heard, our judgment is influenced by our assumptions about the way the world works.

"Accommodation" is assimilation's complement. Just as we often adjust our perceptions to fit our conceptions, we often are forced to adjust our conceptions to fit our perceptions. When assimilation fails--when the world is too dramatically different from what our assumptions tell us it should be--we change our assumptions.

How do assimilation and accommodation work together to drive development? Piaget hypothesized that both processes were involved in every cognitive act performed by the infant. Successful adaptation reflects a balance between accommodation and assimilation such that new experiences are interpreted in the light of one's views of the world, but one's views of the world are subject to change when the evidence against them becomes significant. Over the course of development, the child goes through stages of equilibrium, during which the child's concept of the world is relatively stable and the focus is on assimilation, and stages of disequilibrium, during which the child's concept of the world is being challenges by new experiences and the emphasis is on accommodation.