Final answer:
The child's assertion that the picture is 'my baby' instead of 'your sister' as stated by their parent is an example of egocentrism, a characteristic of the preoperational stage of cognitive development according to Jean Piaget.
Step-by-step explanation:
The conversation between the parent and the 4-year-old child about the picture of the sibling is an illustration of egocentrism, which is a type of thinking commonly found in preschool-age children. The key feature of egocentrism is the child's inability to understand and assume the perspective of others. In this case, the child insists that the picture is 'my baby' because from their own point of view, that is how they see the sibling, without recognizing the parent's perspective.
Jean Piaget's research on cognitive development in children identifies the preoperational stage, which typically occurs from approximately 2 to 7 years old, as the time when children exhibit egocentric thinking. They may engage in pretend play and have a personal logic that makes sense to them due to their limited experience of the world, but they cannot yet perform mental operations such as understanding someone else's view or the concept of conservation. Egocentric children assume that others see and understand the world in the same way they do, which is illustrated through the Three-Mountain Task and easily seen when children choose gifts based on their own preferences.