Final answer:
A child's first display of active imagination is characteristic of Piaget's preoperational stage, which ranges from approximately 2 to 7 years old, where the child uses symbols for pretend play and begins using language.
Step-by-step explanation:
A child first showing an active imagination is characteristic of the preoperational stage of development. This stage, according to Jean Piaget's theory, occurs from approximately 2 to 7 years old. In the preoperational stage, children begin to use symbols to represent words, images, and ideas, which enables them to engage in pretend play. Additionally, they begin to understand language, though they cannot yet perform mental operations or understand adult logic. An illustrating example of this cognitive period could be a child playing with a stick as if it were a sword, showcasing emergent symbolic thought and imaginative skills.
During the early childhood phase, typically categorized as 1 to 5 years old, cognitive development takes place in several areas. Preschool-age children (3-5 years old), in particular, show the ability to think symbolically and enjoy pretend play, reflecting a rapid expansion in their imaginative abilities.