Raea Gragg, 9, working to correct her double vision. The string forces her to focus her eyes, training them to merge images correctly. (Thor Swift for The New York Times)

"She touched faces and would bring everything to mouth," said her mother, Kara Gragg, of Lafayette, California. "She would go up to people, sniff them and touch their cheeks."

Specialists conducted a battery of tests. The possible diagnoses mounted: autism spectrum disorder, neurofibromatosis, attention-deficit hyperactivity disorder, anxiety disorder.

A behavioral pediatrician prescribed three drugs for attention deficit and depression. The only constant was that Raea, now 9, did anything she could to avoid reading and writing.

Though she had already had two eye exams, finding her vision was 20/20, a school reading specialist finally suggested another. And this time the ophthalmologist did what no one else had: He put his finger on Raea's nose and moved it in and out. Her eyes jumped all over the place.