"You don't need drag your kid in for testing, but you should be luring your child with tiny steps into learning and exploring," said Alice Sterling Honig, professor emerita of child development at Syracuse University and author of "Encyclopedia of Infancy in America," among other works.
Occasionally, parents of very bright children expect behavior of a much older child, but Honig said much more trouble might come in school.
"The thing that I worry about is that, number one, that you would not acknowledge their gifts. The other thing I worry about is that you're pushing too hard when he's not as genius as you think he is," said Honig.
"But the other thing I worry about is that they're isolated in school," said Honig, who said it's not uncommon for other children to resent a brilliant child's answers or for a brilliant child to feel disconnected from his or her peer group.
"If the child has been tested and is very, very bright, you still need to make sure this child has a friend," she said.