DALLAS — Michael Hinojosa was about to enter the ninth grade in Dallas when a federal judge ordered the city’s public schools to integrate.

It was 1971, and Mr. Hinojosa, the Mexican-American son of a preacher, was suddenly reassigned to a new school, whose football coach told him that it was too late to join the squad — its roster had been set months earlier.

“I had a traumatic experience” with desegregation, Mr. Hinojosa said.

So, too, did Dallas. Like many cities, it replaced one form of segregation with another, as white and middle-class families moved to the suburbs or put their children in private schools.

Now Mr. Hinojosa is the superintendent, and the Dallas school system, one of the country’s most segregated urban districts, has become a national leader in trying to figure out how to encourage students of all backgrounds to willingly go to school together.