Full context:   Various theories of the general mechanisms and stages of cognitive development have been proposed. Jean Piaget's theory divides cognitive development into four stages, each marked by an increasing capacity for abstraction and systematic understanding. In the initial sensory-motor stage, from birth to about two years, children explore sensory impressions and motor capacities, learning that things continue to exist when not observed. During the pre-operational stage, up to about age seven, children begin to understand and use symbols intuitively. In the following stages of concrete and formal operation, children first apply logical reasoning to concrete physical objects and then, from around age twelve, also to abstract ideas.