On a recent spring day, a slight second-grader ran up to his teacher in the hallway to say that a classmate had been hitting him. Before the teacher had a chance to respond, he whipped around and started screaming curses, threatening his classmate with language that would be shocking from an adult. From a child so small, the words were only sad. He has a home, a school staff member said, as well as a sick family member and experience in foster care.

“I would say 80 percent of our kids could benefit from some kind of counseling,” said Jessie Solomon-Greenbaum, who worked as a therapist at P.S. 188 until earlier this year, with a nonprofit group called the Jewish Board of Family and Children’s Services.

On the standardized state tests taken every year, its scores are flatly disappointing. Only 9 percent of its students met state standards in English last year, compared with 30 percent of students citywide. Just 14 percent of children scored at grade level in math, less than half of the citywide rate of 35 percent.

But over the past three years, nearly 50 of its students have been accepted at some of the city’s most competitive high schools, including Brooklyn Technical, Stuyvesant and Millennium, Ms. Ramos said. Of the three high schools that students from the Island School attended the most last year, two have above-average graduation rates, while the other caters to children who are still learning English.

On annual school surveys, families and teachers give the school and its principal very high ratings. Teachers say they trust the principal and one another. Students say they feel safe and respected, and that they know what their teachers want them to learn. At the Island School, there are outbursts and fights, but the hallways usually feel calm. Children walk from class to class in neat rows, or a rough approximation of them.

To Ms. Ramos, when she looks back at the end of the school year and asks herself how the school did, her definition of success reaches far outside the classroom. Is a child who needs counseling now receiving it? Did a father write a résumé? Did a mother get a job?