Not many cities would take pride in such a statistic, but a school system often derided as the nation’s worst appears to have turned a corner. Citywide, the percentage of Chicago high schoolers who meet national norms rose this year from 21 percent to 25 percent in reading; in math the percentage leaped from 22 to 30. Elementary-school test scores jumped last year, and officials expect still more gains when this year’s scores are tabulated.

It would be heartwarming to trace the gains solely to inspirational efforts in the classroom. But the Chicago reversal, still in its early stages, is as much about sticks as carrots. District officials threatened to close schools, remove educators and hold back students if performance didn’t improve. The state legislature, tired of Chicago’s failures, had given these extraordinary powers to Mayor Richard M. Daley. In turn, Daley appointed his former budget director, Paul Vallas, to head the sinkin g system, and told him to fix the schools - or else. ““We set high standards,’’ Vallas says. ““Then we let everyone know the consequences of not meeting them.’’ Last fall Vallas put 109 of the city’s 557 schools on academic probation.

Those schools have been deluged with extra help from the central district. ““It wasn’t “Let’s look for who’s to blame’,’’ says Thomas Reece, head of the Chicago Teachers Union. ““It was “Let’s look for how to improve,’ which was pretty well receive d.’’ Each probationary school has been given the services of outside experts, often from university education departments. The outsiders began by posting on classroom walls simple lists of what each student is supposed to learn in each subject. ““We can make major gains just by getting the basics under control,’’ says Melissa Roderick, a University of Chicago professor who is tracking the system’s turnaround.

Schools have been ordered to stop the practice of ““social promotion’’ of students who can’t do the work. And teachers are trying new approaches. One experiment is to drill students in the vocabulary they’ll need to comprehend a subject before the teacher launches into the material itself. Another involves diagram- ing, in chart form, every lesson imaginable. That reduces abstractions to visuals: time lines in history class, plot development in English, how to spike a volleyball in phys ed.

Many teachers say there’s another factor at work, too. For the first time, many kids think someone cares whether they succeed or fail, and they are responding. Now there’s a reason to burst into tears of joy.