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On an average day this spring, more than 45,000 Chicago public school students-one of every nine in the system-were absent, school records show.

That`s more than all of the students enrolled in all of the elementary and high schools in the north suburban townships of Evanston, Northfield, Niles and New Trier in Cook County.

Chicago`s attendance problems were worst in the high schools, where one of every five students failed to show up on an average spring day.

And those are only the official figures. They don`t include students who were listed as dropouts or whose whereabouts were unknown by the school system or who were counted as being in school when they actually weren`t.

The inability of city`s public schools to attract and keep students costs the system millions of dollars a year in state revenue.

More important, it undercuts the education of youngsters, especially those who need schooling the most-children from low-income families who are the ones most prone to absences, truancy and dropping out.

School system records show that the problems are getting worse. Yet the Board of Education`s efforts to keep students in school are disjointed, and its record-keeping masks the true extent of the absences, a Tribune examination of the school system has found.

A major reason, according to critics, is an attitude that pervades the school system that encourages dropping out and chronic absences as a means of keeping hard-to-teach children and troublemakers out of the classroom.

”A lot of principals and teachers in the system see truancy as a benefit to them because they don`t have to deal with as large classes and they don`t have to deal with kids who are problems,” said Donald Moore, executive director of Designs for Change, a nonprofit education research group.

”The real attitude is that there`s not much they can do for the kids, so they`ll just deal with those kids who come of their own volition.”

But that also means less money for the schools because the state aid formula, which funneled $571.7 million to Chicago this year, is based on the number of students who attend school, and, in Chicago, those numbers have been going down.

This school year, the average number of students enrolled in the school system through April was 415,433, a drop of more than 8,000 from the average for the previous year. School officials blame the 19-day teachers strike in September for the enrollment decrease.

And, on top of the enrollment loss, there has been a drop in the attendance rate as the school system has had a daily average of 4,041 more absences this year than in 1986-87.

Based on the present state school aid formula, the combination of a lower enrollment and an increase in absences would cost Chicago public schools as much as $5.7 million next year, according to Michael A. Belletire, associate superintendent for finance and support services, Illinois State Board of Education.

The actual cost could be higher or lower depending on what changes the state legislature and the governor make this year in the state aid formula, Belletire said. But no matter what changes are made, Chicago`s lower enrollment and attendance will cost the schools money.

Because the formula permits a school district to use a three-year average for attendance, the full impact of the student drop won`t be felt until the 1990-91 school year, Belletire said.

Top school officials said families have the primary responsibility for making sure their children attend school.

”School can`t do it alone. You have to have cooperation from the family,” said William Gwynn, director of the school system`s bureau of attendance. ”The youngster may be out because he does not have adequate clothing, or there may not be sufficient food in the home. The family may be keeping the youngster in the home to baby-sit.”

But school system critics, such as Ald. Edwin Eisendrath (43d), a former Chicago school teacher, contended, ”Sometimes, we have schools that kids don`t want to go to.”

Gwynn acknowledged, ”Essentially, it`s an interesting school program that makes the difference. I do maintain that, once we get them there, something has to happen to maintain this interest and motivate them to keep coming.”

Last year, the official attendance rate at Crane High School on the West Side was 68.7 percent-the worst in the city. Each day, about 425 of the 1,400 students at Crane weren`t in school.

”They may not feel well,” explained assistant principal Delbert Bowden. ”Some get temporary jobs. Others might not have the clothes to suit them. Maybe they need a haircut. Someone threatens them, and they are waiting for things to cool down. Or they want to look at TV.

”I think the system cares, but it may not for the right reasons. It cares because schools get less money, or because there aren`t as many positions to offer worthy friends. That`s the typical reason for caring.”

Bowden said he found a fool-proof way of improving a school`s attendance rate-simply drop truant students from the enrollment list.

That`s what he did several years ago when he was the school`s attendance coordinator.

”We got a plaque,” he said. ”Most Improved Attendance.”

The school system`s attendance problems have long been hidden by its record-keeping.

For years, school system officials contended that the dropout rate was only about 8 percent. What they didn`t say was that that figure covered only a single school year.

The more complete figure-the figure that indicated the number of students who failed to graduate from high school-was actually around 45 percent, as independent studies by Designs for Change and the Chicago Panel on Public School Policy and Finance, released in 1985, found. The national norm is a 27 percent dropout rate, according to the U.S. Department of Education.

And those bleak numbers tell only part of the dropout story.

At 21 inner-city high schools, the dropout rate for the class of 1982 was 55.8 percent, according to a study by the Chicago Panel. And, at Du Sable and Austin High Schools, only about one of every three students graduates; the rest drop out.

During the 1986-87 school year, Chicago`s official attendance rate was 90.9 percent. Throughout the rest of Illinois, the attendance rate was 94.6 percent-just under the national goal of 95 percent.

So far this year, Chicago`s attendance rate is 89.7 percent, but it will probably end up somewhat lower because that figure doesn`t include the absence-heavy months of May and June.

Part of the reason for this year`s lower rate is a requirement by state school officials that the city school system strictly follow its attendance-counting policies. Previously, Chicago had ignored its own rule to count a student as absent for half a day if the student skips a class.

But the new, presumably more accurate figures for this year still don`t give a full picture of the system`s attendance problems.

By a twist of bureaucratic logic, Chicago public school officials use dropouts to improve the system`s attendance rate.

A student who is over the age of 16 and who is marked absent for 20 consecutive school days is ”automatically dropped” from the school system`s enrollment, said William Jones, director of dropout prevention programs for the system.

What this means is that the student is no longer considered absent, and that means that he or she is no longer dragging down the school system`s attendance rate.

Nonetheless, the attendance rate for the city`s high schools so far this year is 83.5 percent. Last year, it was 85.2 percent for the entire year.

During both years, the attendance rate went down through the year. In April, 1987, it was 83.4 percent. This April, it was 79.8 percent.

But those figures don`t take into account the thousands of teenagers who had enrolled in the system during the year but were listed as dropouts. Last year, there were 13,428 teenagers categorized as high school dropouts. Figures for this year aren`t available, school officials said.

Including dropouts, Chicago`s high school attendance rate for April, 1987, was really 74 percent. In other words, one of every four high school students who had been enrolled in the system during the school year was missing from school on an average April day in 1987.

But even those numbers may not be complete.

There were another 2,624 high school students, not listed as dropouts, who had been enrolled in a Chicago public high school at one time during the year but were no longer enrolled at the end of the year.

School officials speculated that most of those-if not all-transferred to other school systems, but they don`t know because they don`t keep track of those numbers because they aren`t required by the state to do so.

When elementary schools are included, the total number of students who weren`t dropouts but who somehow left the system last year was 24,193. School officials say most of those probably transferred.