In the steamy summer morning, small children wearing shorts and leaning under the weight of book-filled backpacks trudge head first into half-empty schools, where time seems to race faster than the desk fans whirring in classrooms with no air conditioning.

For 25,000 failing pupils, mandatory summer school in Chicago has been about time and the test, six weeks to rev up to academic speed or face the shame of repeating a grade. Teachers whip through the summer curriculum, following citywide scripts for each grade level, presenting identical lessons at virtually the same moment. When pupils lose focus, teachers warn them: This kind of question will be on the standardized test that you must pass to advance to the next grade.

Chicago has led the nation in moving to end "social promotion," the longtime practice of allowing failing pupils to move on to the next grade rather than holding them back. Social promotion has been debated since the 1940s, but seems finally to have fallen out of public favor. In the past few years, two dozen major cities have ended social promotions and a third of the states--from California to Virginia--have moved away from the practice. President Clinton, Vice President Gore and Republican presidential front-runner George W. Bush have all spoken out against social promotions.

The cornerstone of Chicago's effort to end social promotion is a 1996 mandate that pupils who fail the third, sixth or eighth grades go to summer school. At the end of six weeks of remedial classes, the pupils must pass what one boy calls "the big test" or be held back. The program has been cited as a model by the Education Department, and has been copied in several cities including the District, where several thousand failing pupils had to attend classes this summer.

But Chicago's experience shows that ending social promotion is no easy task. The school district is spending $50 million per year on summer school and other remedial programs intended to help pupils move to the next grade. Yet last year, fully half the pupils in mandatory summer school did not pass the big test and were held back, a situation that creates its own set of problems. And 1,300 15-year-olds with failing scores were promoted anyway, to academic halfway houses between the eighth and ninth grades, because they were considered too old to remain in schools alongside younger students.

Traditionally, supporters of social promotion have defended the practice as a way to protect the self-esteem of failing pupils. Although there are no reliable statistics on the prevalence of the practice, a national survey of teachers in 1996 found that a majority said that in the previous year they had promoted pupils who were not ready for the next grade. But with the nationwide movement to toughen academic standards and increase accountability in schools, social promotion has seen its political popularity wane, and today few educators openly advocate a general policy of promoting pupils for social reasons.

This is not the first time there has been a high-profile effort to curtail social promotion. In the early 1980s, New York City made just such an attempt, but abandoned it after several years in the face of ambiguous results. This time, however, the movement against social promotion is far broader.

Critics have long argued that, despite the benign intent, social promotion hurts struggling pupils by taking away incentives to master the skills they will need to succeed in life. "Kids knew they were going to be promoted, so they didn't put in the time or effort to learn the material," said Therese Dozier, an adviser to Education Secretary Richard W. Riley, recalling her days as a teacher.

But studies conducted over the past two decades have shown that the simplest alternative to social promotion--holding failing pupils back--is not a solution either. Such pupils are more likely to drop out of school--almost certain to, in fact, if they are held back more than once. Without special academic attention, few pupils learn more by repeating a grade than they would if they had moved on to the next grade. And pupils stigmatized for flunking are likely to be disruptive in class, making it harder for their schoolmates to learn.

"I'm very much against retention," said Lynn Babcock, president of the National Association of Elementary School Principals. "I think people are looking for quick fixes."

And so educators in school systems such as Chicago's have been looking for a way out of the no-win choice between promoting failing pupils to the next grade and simply holding them back. In addition to the mandatory summer session for failing pupils, the Chicago schools have instituted voluntary summer classes for first- and second-graders who have fallen behind, after-school tutoring and supper for pupils who have been held back, midyear testing to give repeaters an earlier chance to move to the next grade and even free vision tests, which revealed that an astonishing 30 percent of failing pupils needed glasses.

"Our goal is earlier, more often and constructive intervention," said Cozette M. Buckney, who oversees academics for Chicago's 430,000 students. And although progress has not been dramatic, school officials believe the city has made headway: This year, 12 percent fewer pupils failed and had to attend summer school than two years ago.

For those who are forced to come back for summer classes, Chicago has a time-bound curriculum in basic math and verbal skills, closely tied to the Iowa Test of Basic Skills, which many districts around the country use. Lessons as brief as several minutes--one third-grade teacher sets a kitchen timer to stay on schedule--may actually suit video-age children with habitually short attention spans, but some teachers complain they do not have enough time to check whether every pupils gets it.

Not all do, or even try to. It turns out the time pressure has disciplined teachers more uniformly than pupils. For some of those attending summer school, the threat of being held back is enough to motivate them to work hard. Reina Martinez, a third-grader at Barry Elementary on the city's north side who failed math, eagerly tackled the problems she was assigned to do in class. Other pupils--for example those who wound up in summer school because they had a bad test day--also fare relatively well.

But many of the pupils have a tougher time, said Alice Vila, the principal of Reina's school. There are the recent immigrants who do fine in math but struggle with classroom English, Vila said. There are the pupils who are immature, and those who pose discipline problems.

Finally, there are the cases where "the kids just don't have it," Vila said, referring to pupils who have serious deficiencies in basic skills. Several of Reina's third-grade classmates, for instance, did not seem to have a clue about how to multiply and divide, producing such wildly inaccurate answers as 20 times 10 equals 140 and 20 divided by 10 equals 20. For such pupils, who need intensive tutoring, summer school is not enough.

"In the past, almost all have made it out of [summer school] for me," Vila said. "This year, I'm not so sure."

This week, Chicago's six-week summer session will end and pupils' results on the big test will answer the question of who moves on to the next grade and who is held back.

But for Chicago and other school systems around the country that have ended social promotions, the bigger question is how those who are held back can be helped to succeed academically when they return in the fall.