Final answer:
Children master the concept of object permanence when they realize that objects continue to exist even when not visible, a developmental milestone observed typically between 5 and 8 months old, as defined by Jean Piaget.
Step-by-step explanation:
When a child recognizes that objects continue to exist, even when they are no longer in sight, they have mastered the concept that Jean Piaget referred to as object permanence. This cognitive development occurs during Piaget's sensorimotor stage, typically between 5 and 8 months old, indicating that the child has started to understand that physical things continue to exist even if they cannot be seen or heard. This concept differs from others such as conservation, which is the understanding that certain properties of objects remain the same despite changes in the form or arrangement, egocentrism, which is the inability to see a situation from another person's point of view, and abstract reasoning, which is a later developmental stage where children can think about things that are not concretely present.
Piaget's studies, like the one with the hidden toy, showed that infants with developed object permanence would search for the toy, knowing it still existed. This is fundamental to the development of cognitive abilities and leads to activities like hide and seek, and the understanding that people who leave the room will return. The development of object permanence is a critical milestone in a child's cognitive growth.