“We want to tell children, ‘You’ve got a difference, but not a disease,’ ” he said. “Michael Phelps is one of any thousands of examples of mega-successful people, C.E.O.s and brain surgeons and famous writers, inventors and entrepreneurs, who have A.D.H.D.”

Other experts, however, say that while such success stories can be inspiring, parents need to know that their children face real risks. Research shows that children with attention deficit have different brain patterns from other children, and that they are more likely to drop out of school, be involved in car accidents and use illicit drugs.

“This reframing A.D.H.D. as a gift, personally I don’t think it’s helpful,” said Natalie Knochenhauer, founder of A.D.H.D. Aware, an advocacy group in Doylestown, Pa. “You can’t have a disability that needs to be accommodated in the classroom, and also have this special gift. There are a lot of people out there  not only do their kids not have gifts, but their kids are really struggling.”

Ms. Knochenhauer, who has four children with the disorder, says they too were inspired by the astonishing performance of Mr. Phelps in Beijing. But she added, “I would argue that Michael Phelps is a great swimmer with A.D.H.D., but he’s not a great swimmer because he has A.D.H.D.”

Dr. Koplewicz, of N.Y.U., agreed. “There are lots of children in the world who have chronic illnesses or disorders like diabetes, allergies or dyslexia who accomplish great things in spite of the fact that they have these disorders,” he said. “I worry when we say A.D.H.D. is a gift, that this minimizes how real it is.”

Michael Phelps’s mother, Deborah Phelps, says she has spoken openly about her son’s diagnosis because she wants other parents to seek out resources and support. Her son stopped taking A.D.H.D. medication at age 10. But today, Ms. Phelps is a national spokeswoman for McNeil Pediatrics, which makes the attention-deficit drug Concerta. (Dr. Hallowell and Ms. Knochenhauer have also consulted for McNeil; Dr. Koplewicz has no industry ties.)