Piaget (1936/1953) identified the end of the second year of life as a major turning point in cognitive development, marked by the advent of the symbolic function - the ability to use symbols to represent or stand for perceived objects and events. The symbolic function takes several distinct forms as the child moves into the third year of life: deferred imitation, symbolic or pretend play, mental images, and language.

In deferred imitation, children observe the behavior of a model and imitate that behavior after a delay and, in some cases, when the model is no longer present. The child maintains modeled behavior in symbolic form over time, imitating the behavior only when it becomes adaptive to do so. The ability to defer the imitation of modelled behavior requires that the child store and later retrieve information about the model's behavior from memory. Infants display deferred imitation only with brief delay after a behavior has been modelled (Heimann and others, 2013). For example, a ten-month-old may imitate her father's use of the spoon several minutes after observing her father use that utensil. The infant would not be expected to defer that imitation hours or days later without additonal repetitions of the modelled behavior.

As the structure and function of the brain mature through early childhood, children's ability to engage in deferred imitation is substantially improved. Advances in perception allow the infant to engage in a more detail study of the model's behavior. Improvements in memory allow the child to retain the modelled behavior for longer periods (weeks and months), and developmental improvements in physical and motor capabilty enable more precise imitation of complex modelled behaviors. By age 4, children's imitation of a model's behavior becomes highly nuanced. For example, one study showed that children show superior deferred imitation when the model's behavior helps the model achieve specific goals . The model's behaviors that are not related to the model's specific goals are less likely to be imitated.

In symbolic or pretend play , children pretend that an object is something other than what it really is. For instance, an 18-month-old lifts an empty cup to his face, tips it as if to drink, licks his lips, and looks at his mother with that telltale grin that indicates he knows he did not really drink. A somewhat older child transforms a doll into a "real" person or pretends that a wooden block is a boat, sailing the treacherous waters of the bathtub. Symbolic play transforms virtally any situation into an unlimited world of make-believe for preschool children, with pervasive effects on their social and emotional development.

Lashonda, Devon, and Tamara climbed through the basement window into the open courtyard behind the Jackson family's 100 year-old, three-story brownstone apartment, now a wasteland of mounds of garbage, abandoned cars, and discarded drug-related paraphernalia. Like any other preschoolers, Lashonda and her friends were preparing to play house, but in Bed-Stuy there were no plastic eating utensils, rubber food items, or simulated kitchens appliances - only the courtyard and its debris.

The children rummaged through a nearby mound of trash, feverishly searching for props to support their pretend play. They quickly transformed hubcaps, tin cans, and assorted sticks and scraps of metal into dinner ware; chips of concrete, chunks of wood, and rusty wire simulated food for dinner; the hulled-out interior of an abandoned 1973 Ford Mustang became a kitchen and dining area.

Although there were only three children, there were several imaginary guests - some friendly and others not-so-friendly. One reason the game was so much fun was that this make-believe world was far more controllable than the real world in which these children live.

Although the ease with which Lashonda and her friends transformed a pile of junk into a game suggests a simple underlying process, research has identified a number of distinct cognitive skills required to initiate and sustain pretend play (Rubin, Fein, & Vandenberg, 1983). Each of the pretend skills follows a unique course of development:

The symbolic function is also expressed in the ability to form mental images , internal representations of external objects or events. Mental images free children from the here and now, enabling them to think about objects when the objects are not physically present, and to think about events before, during, and after their occurrence. For the first time, the child can integrate experiences from the past into the present to plan for the future.

The three forms of symbolic function mentioned thus far - deferred imitation, pretend play, and mental images - express private, idiosyncratic meanings derived from personal experience. For example, one child may pretend to eat by exaggerated motions of the arms and mouth, while a less demonstrative child may simply move an empty spoon back and forth from her plate to her mouth. The private and idiosyncratic nature of the symbolic function in young children limits their ability to communicate their thoughts to others, challenging caregivers' interpretive skills and patience.