Jean Piaget (1896-1980) was a renowned psychologist of the 20th century and a pioneer in developmental child psychology. Piaget did not accept the prevailing theory that knowledge was innate. Instead, he believed a child’s knowledge and understanding of the world developed over time, through the child’s interaction with the world. By observing that interaction, Piaget was able to perceive how children created schemas that shaped their perceptions, cognitions, and judgment of the world. He classified the child’s development into four sequential periods: (1) The sensorimotor period from birth through the first 18 to 24 months, (2) the pre-operations period between the approximate ages of two and seven years old, (3) the concrete operations period that begins around age seven and continues through about 11 years old, and (4) the formal operations period that begins around age 11 and continues through adolescence.[1][2]

Over his lifetime, Piaget contributed significantly to the study of cognitive development in children. However, he is best known for his stages of cognitive development.[3]

The sensorimotor period begins at birth and continues through the child’s first two years. It focuses on the development of schemata through perceptions and bodily movements. There are six stages within the sensorimotor period. Stage 1 includes inborn motor and sensory reflexes, like the sucking and palmar reflexes. Stage 2 observes the primary circular reaction in which an infant experiences an event and then attempts to repeat the action. Stage 3 is a secondary circular reaction when an infant repeats an action with a specific,  desired consequence or to achieve an unrelated consequence. Stage 4 comprises the use of familiar means to obtain ends. It entails deliberate planning of steps to meet a goal or objective. Stage 5 is a tertiary circular reaction in which an infant experiments with their environment using the properties of one object to manipulate another object, in other words, using an experimental object, like a stick, to push a ball that then makes a noise. Insight characterizes stage 6, wherein the child observes other people manipulate the environment to reach the desired goal, then the child applies that knowledge to obtain the desired goal. The culmination of stage 6 and the sensorimotor period is the child’s understanding of object permanence and the ability to abstract that objects have an existence independent of the child’s interaction with them. Classic examples of understanding object permanence include a child’s realization that when a parent leaves, the parent continues to exist, or the child’s attempt to recover a hidden toy, indicating the child’s understanding that the toy still exists outside of view.[4]

The preoperational period, which begins around age 2, is defined by semiotic function, or representational thought through signs and symbols, exhibited by five characteristic behaviors: imitation, symbolic play, drawing, mental image, and verbal evocation of events. The first behavior, imitation (or, more specifically, deferred imitation), is when child models observed behavior even after the disappearance of the thing the child is imitating. For example, the child may mimic a person’s limp, even after the person is no longer present. The next behavior, symbolic play, is a step beyond imitation. This “make believe” or “play pretend” behavior is characterized by the child’s ability to project an idea onto an object. “Let’s pretend that I am the mama and this is my baby,” and the child points to a stuffed animal. In this example, both the child and the stuffed animals are generated symbols. The third identified behavior, drawing, begins early in the preoperational period, and incorporates both play and imitation. Drawing often begins with scribbles and proceeds to graphic imagery with the representation of objects that are present in the child’s world. Through drawing, the child may represent family members with stick figures, with the key characteristic being that the child understands that the stick figures are only representations of the family, not the actual family members. The scope of these first three behaviors grows as the child develops mental imagery which is the product of the child's perception, something he creates. This is often reflected as the child persistently asks adults to name or identify objects, so that the child can associate the name of the object with the mental image of the object. Finally, a verbal evocation of events, which is the culmination of semiotic function, is the child’s use of language to imitate and reflect events that occurred in the child’s past. Mastery of semiotic function indicates that a child can think and assimilate knowledge rather than to merely act on present objects.[5]

Concrete operations flow from mastery of semiotic function and are observed in children from seven through 11 years of age. In this period, a child learns to apply logical rules to concrete or tangible objects and mentally transform, modify or manipulate what he sees and hears. An essential skill developed in concrete operations period is the child understand the concept of conservation, where values remain unchanged in the course of visual transformation. For example, the conservation of quantity is classically demonstrated when water from a short, stout glass is poured into a tall, slender glass. At this stage, the child unknowingly uses logic to deduce that the amount of liquid did not change, only the container that holds it. Over time, the child builds on the basic understanding of conservation to master concepts of greater complexity. Early in this stage, the child would understand that when play-doh is transformed from a circle to a square, the volume or amount of Play-Doh has not changed, only the shape. Around age 9, the child would understand that weight is also conserved even when the shape changes. Conservation is mastered when the child fully comprehends that properties of an object do not change when the object undergoes a perceived transformation. Included in the basic understanding of conservation is the concept and application of cardinal numbers, or counting, to determine that an amount or quantity can be consistent even when spread over a larger area. A child developing this concept would compare two rows of five dots, one with the dots one centimeter apart and the other with the dots one inch apart, and understand that the amount or quantity of dots in each row is consistent, even when spread over a greater area. As the child’s understanding of conservation develops, he will also begin to reverse-engineer the logic rules. This “reversibility” falls into two categories: inversion and reciprocity. Refer back to the different sized glasses with the same amount of water. When the child saw the water poured from the shorter glass to the taller glass and understood that the amount of water did not change, the child understood conservation. When the child is subsequently able to mentally invert the liquid from the taller glass to the shorter glass, or vice versa, and understand that the amount of water has not changed, he or she masters reversibility by inversion. A child masters reversibility by reciprocity when the child understands that the different glasses can hold the same amount of liquid because what one container loses in height, it makes up in width; and vice versa, what the slender container loses in width, it makes up in height. Concrete operations are not restricted to conservation and reversibility. Class inclusion, which is the child’s ability to categorize objects by shape or type, is a form of concrete operations, as are relations, which is the child’s ability to apply logical rules to a series of items with gradual changes, like categorizing objects from smallest to largest.[4]

Formal operations are the final period of cognitive development, generally observed in adolescents, beginning at age eleven and persisting until adulthood. In this period, the adolescent learns to apply logical rules to abstract concepts, analyzing the environment and moving beyond concrete facts (what is) to problem-solving (what is possible). Key thought processes developed in this period include hypothetical-deductive thought, propositional thought, and, ultimately, isolating variables and examining combinations. First, the adolescent developing hypothetical-deductive thought takes general information from the real world, synthesizes the information to apply it to a more singular, particular testable idea or hypothesis, then deduces a solution through reasoning. Second, the adolescent moves forward and into developing propositional thought, which does not require real-world, concrete information to develop or allow inference. Propositional thought allows the adolescent to manipulate multiple variables and abstract the results without testing the specific variable in question. For instance, if A is less than B, and B is less than C, then A is less than C. Adolescents developing propositional thought can take real-time results and postulate future, untested results from that data. Finally, the adolescent learns to isolate variables and exam combinations of variables to understand cause and effect, based on the information deduced through hypothetical-deductive thought and propositional thought. A common illustration of this concept is asking the adolescent to find what determines the frequency of swing of a pendulum. Unlike a concrete thinker, who learns from factual, real properties as they are observed (e.g., the frequency of swing is determined by the experimenter’s push), the formal-thinking adolescent is able to apply concrete data and extrapolate how isolated variables (i.e., push, length of string, and weight of the bob), will affect independent interactions.[6]

Through assimilation and accommodation of the object, Piaget’s schema of cognitive development is characterized by a stepwise move toward adaptation. Assimilation is the integration of external events on the organism while accommodation is the tendency of an organism to adapt to a particular environmental event. Piaget presents assimilation and accommodation as a paradigm that produces equilibration, a dynamic and balanced system that when undergone together results in the further cognitive development of children. From Piaget we have an understanding that a child’s cognition develops further as he passes from one stage to the next.