The second stage is the preoperational stage. This stage spans from about the age of two until about the age of seven. "In this stage, children begin to represent the world with words, images, and drawings. Symbolic thought goes beyond simple connections of sensory information and physical action. Stable concepts are formed, mental reasoning emerges, egocentrism is present, and magical beliefs are constructed."(Santrock, 2004, chap. 6).
The third stage is the concrete operational stage. This stage begins at around age seven and ends at around age 11. It is during this third stage that children begin to think and reason about concrete events logically. "Children can perform concrete operations (operations that involve concrete objects) and logical reasoning replaces intuitive reasoning as long as the reasoning can be applied to specific or concrete examples."
The fourth and final stage in Piaget 's theory of cognitive development is the formal operational stage. This stage begins about age 11 or 15 and continues throughout adulthood. "During this stage, more logical, deductive, abstract and hypothetical thinking begins.
References: Santrock, J. W. (2004). A Topical Approach to Life Span Development (2nd ed.). Dallas, TX: Stephen D. Rutter.