Stage of formal operations represents the culmination of a child's cognitive development. In this stage, adolescents develop the ability to think abstractly and reason hypothetically. They are no longer limited to concrete, tangible concepts and can conceptualize ideas and possibilities that extend beyond their immediate experience. This stage is characterized by the emergence of deductive reasoning, where adolescents can develop hypotheses and systematically test them. They start to think about theoretical possibilities and can understand abstract concepts like justice, love, and free will. Their problem-solving abilities become more systematic and logical, including the ability to consider multiple variables and potential outcomes. Adolescents in the formal operational stage also exhibit metacognition – the ability to think about their own thought processes. This self-reflection enables them to analyze their reasoning and the conclusions they reach, enhancing their ability to learn and adapt.

In this stage, infants and toddlers learn primarily through sensory experiences and manipulating objects. Their understanding of the world is based on physical interactions and experiences. A key characteristic of this stage is the development of object permanence, the understanding that objects continue to exist even when they cannot be seen, heard, or touched. Initially, infants act as if objects removed from their view cease to exist, but by the end of this stage, they start to search for hidden objects, demonstrating their grasp of object permanence. Motor skills also develop significantly during this stage. As infants interact with their environment, they learn to coordinate their sensory experiences (such as seeing and hearing) with physical, motor actions. This stage lays the foundation for further cognitive development, as it helps children understand the world around them through physical interaction and sensory exploration.

In stage of concrete operations, children begin to think logically about concrete events. They gain a better understanding of the concept of conservation — the idea that quantity remains the same despite changes in shape or arrangement. This reflects their growing ability to decenter, or consider multiple aspects of a situation simultaneously. Children in the concrete operational stage also start to understand reversibility, recognizing that objects can be changed and then returned to their original form. They can classify items into different sets and subsets and understand their relationship, an ability known as class inclusion. At this stage, children are better at problem-solving, especially for tangible, real-life problems, but they still struggle with abstract and hypothetical thinking. Their reasoning is very much tied to concrete, physical reality, hence the term 'concrete operations'.