Parents of children with developmental disabilities “are seeing the benefits of arts education,” said Lisa Cooney, 46, director of education for Paper Mill. “And they’re a lot more proactive than they used to be.”

Those who run the programs find them rewarding as well. The children “give so much to us,” said Mickey McNany, the director of Paper Mill’s Theater School, after the recent class. In it, her 10-year-old granddaughter, Mary McNany, who has Down syndrome, identified Mozart as the composer of “Eine kleine Nachtmusik,” performed an improvised roller-skating scene and used sign language, as well as her voice, to sing a song.

Ms. Fanelli, the teacher, said an awareness of the short attention spans of children with developmental disabilities was crucial to reaching them. She tries to divide her class into different activities lasting around 10 minutes each; at the recent class, because the theatrical signing and charade-type games were “really cooking,” she said, she allowed them to run longer.

“I have to be in the moment,” she said. “If something’s not working I have to drop it, and when something is working I’ll extend it.”

The idea for the Paper Mill class began taking shape last year, according to Ms. McNany, 61, of Springfield, when she threw a birthday party for Mary and her friends, including some from Stepping Stones, a school in Roseland for children with Down syndrome. “There must have been 10 or 15 kids there, and we told a story and then acted it out, and afterward all the mothers came up to me and said, ‘Wouldn’t it be great if we could do more of this?’ ” Ms. McNany said.