Pearl's behavior is unnatural for a child living in a strict, Puritan community such as that of Salem. Pearl's behavior is exacerbated by their ostracism from the community and her confusion over their plight. Hester is not imagining Pearl's behavior but feels guilt about the role she has played in creating such hardship for them both.
Pearl is symbolic as a name in that she is the gem in Hester's very dark world. Moreover, the price that Hester has had to pay for this child, this "Pearl," is very dear as she must bear her Scarlet Letter and her bastard child for the rest of her days.
Hester's knowledge of "hidden sin" allows her to see the hypocrisy that runs riot in the world.
The disciplining of children during this time was severe because when children acted out, it reflected badly on the parents. Therefore, a child edured a very strict, Christian upbringing that insisted upon conformity. It was not in Pearl's
nature to conform; she was conceived "out of wedlock;" hence, the laws of the Puritan society seem to be foreign to her. Had Hester tried to use discipline with Pearl, it would certainly have motivated her to act out even more aggressively than she did.
