...Mr. Bloomberg’s policy of closing large, failing schools and replacing them with smaller schools is unpopular with teachers, many of whom have to find jobs elsewhere in the system. And some adults have emotional ties to a school, however terrible it has become. The city has sometimes made matters worse by handling closures badly. But replacing dropout factories with specialized schools that provide individual attention is a sound idea. Of the 142 schools the city has either closed or begun phasing out, many had outlived their usefulness.

A 2012 study by the nonprofit research group MDRC found that New York City students who attended small, specialized high schools that typically served about 400 students each were more likely to graduate than students at large, traditional high schools, some of which served 3,000 students or more. More striking, city data show that the average graduation rate for the large high schools that were in the process of phasing out during 2006 was only 38 percent. Last year, the average graduation rate for the schools that replaced them — often in the same building — was 70 percent.

Nevertheless, Mr. Thompson has said that as mayor he would “stop school closures and introduce a comprehensive system to support struggling schools.” Similarly, Mr. de Blasio promises to fight “unfair closures by standing up for struggling schools.” Ms. Quinn criticizes the current administration for “treating school closings like a goal in itself” and said closure should be used as a last resort when “all else has failed.” But the candidates should not shrink from closing schools that are no longer serving their students....

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