At his public school in New York, Arad Horovitz was a popular honors student with a knack for math. After his family moved to Israel in 2009 and the 13-year-old transferred into an Israeli middle school in Ra’anana, however, his grades plummeted and he had trouble making friends.

“He totally shut down,” said his Israeli-born mother, Yael. “It was all because of the language. He just...