Imitation is the outward manifestation of Imagery.
Piaget suggests in those instances, where the child doesn’t think to search, that we should only partially hide an object; and then gradually decrease the amount left showing until the child learns to image it in its absence.
At this point we would say the child is also demonstrating object permanence.
Imitation: Piaget also notes that the outward manifestation of imagery is imitation. To imitate is to image.
Hence, ”copy cat" games are good for imagery. Patty-Cake from Mother Goose is a good example.
Pretending: Children love to be mother or daddy, or a policeman or a ballet dancer. This is a somewhat more complex form of imitation.
But it is where imagery and symbolization interface. Pretending in general is good for imagery and the symbolic processes.