Pablo Picasso was a child prodigy. But so was William James Sidis, a math whiz who graduated from Harvard at age 15—and grew to despise math so much that he worked mindless clerical jobs until his death.

One reason tragic cases like Sidis's haven't gotten much attention is that researchers have ignored the study of exceptionally talented kids, contends Boston College psychologist Ellen Winner, author of Gifted Children: Myths and Realities. As a result, misconceptions about prodigies thrive, even among educators.

For example, most schools screen for budding geniuses by measuring overall intelligence. But more often than not, precocious children are lopsided in their abilities, says Winner. Some show remarkable talent in one area, yet are learning disabled in others.

It's also important to remember that being gifted isn't always a gift, especially for young girls. While academically superior boys are more popular among their peers, gifted girls are less popular—and hence often underachieve to gain acceptance. Similarly, instead of taking pride in their accomplishments, girls with great grades are prone to low self-esteem and depression.

Another misconception about gifted kids: Their overbearing parents pressure them to succeed. "These children push themselves," says Winner, so they tend to burn out when saddled with pushy parents: Sidis bitterly resented his dad, who drove him to learn six languages by age 10.

The best approach for parents is to give children the resources to pursue their particular interests and talents—and then gently encourage them.