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“Bilingualism carries a cost, and the cost is rapid access to words,” Ms. Bialystok said. In other words, children have to work harder to access the right word in the right language, which can slow them down — by milliseconds, but slower nonetheless.

At the same time, bilingual children do better at complex tasks like isolating information presented in confusing ways. In one test researchers frequently use, words like “red” and “green” flash across a screen, but the words actually appear in purple and yellow. Bilingual children are faster at identifying what color the word is written in, a fact researchers attribute to a more developed prefrontal cortex (the part of the brain responsible for executive decision-making, like which language to use with certain people). Ms. D’Souza said that both of her sons lagged their peers by almost a year in verbal development. Her pediatrician recommended speech therapy, and one son’s preschool teacher expressed concern that he did not know the alphabet. But when both started speaking, at around 3 years old, they were able to move fluidly among three languages. She said that her older son tested in the 99th percentile for the city’s gifted and talented program. “The flexibility of their thinking helps them in nonlinguistic abilities like science and math,” she said, speaking of her children. “But at the same time the normal things — the alphabet — they have trouble with that.”

George P. Davison, head of school at Grace Church School, a competitive downtown school, said that bilingualism tended to suppress verbal and reading comprehension test scores by 20 to 30 percent for children younger than 12. “If anything, it can have a negative effect on admissions,” he said.