Dr. Visser’s analysis of Georgia Medicaid claims found about one in 225 toddlers being medicated for A.D.H.D., or 760 cases in that state alone. Dr. Visser said that nationwide Medicaid data were not yet available, but Georgia’s rates of the disorder are very typical of the United States as a whole.

“If we applied Georgia’s rate to the number of toddlers on Medicaid nationwide, we would expect at least 10,000 of those to be on A.D.H.D. medication,” Dr. Visser said in an interview. She added that MarketScan data suggested that an additional 4,000 toddlers covered by private insurance were being medicated for the disorder.

Dr. Visser said that effective nonpharmacological treatments, such as teaching parents and day care workers to provide more structured environments for such children, were often ignored. “Families of toddlers with behavioral problems are coming to the doctor’s office for help, and the help they’re getting too often is a prescription for a Class II controlled substance, which has not been established as safe for that young of a child,” Dr. Visser said. “It puts these children and their developing minds at risk, and their health is at risk.”

Very few scientific studies have examined the use of stimulant medications in young children. A prominent 2006 study found that methylphenidate could mollify A.D.H.D.-like symptoms in preschoolers, but only about a dozen 3-year-olds were included in the study, and no 2-year-olds. Most researchers on that study, sponsored by the National Institute of Mental Health, had significant financial ties to pharmaceutical companies that made A.D.H.D. medications.

Some doctors said in interviews on Friday that they understood the use of stimulant medication in 2- and 3-year-olds under rare circumstances.

Keith Conners, a psychologist and professor emeritus at Duke University who since the 1960s has been one of A.D.H.D.’s most prominent figures, said that he had occasionally recommended it when nothing else would calm a toddler who was a harm to himself or others.

Dr. Doris Greenberg, a behavioral pediatrician in Savannah, Ga., who attended Dr. Visser’s presentation, said that methylphenidate can be a last resort for situations that have become so stressful that the family could be destroyed. She cautioned, however, that there should not be 10,000 such cases in the United States a year.