AURORA, ILL. -- The first clue that this is a special high school stands no farther than the trophy case in the cavernous front lobby.

After the school's first year, it already is filled with the winnings of a chess tournament, a history contest and several in mathematics -- 14 prizes in all. But here in the heart of the Midwest, where fervor for high school sports runs deep, there is not a single athletic trophy.

This is the Illinois Mathematics and Science Academy, a controversial public boarding school that culls a few hundred of the brightest teen-agers from throughout the state and gives them an unusual, publicly subsidized chance to excel at a cost of $19,000 per student.

For three years, they will live and study at this school 40 miles west of Chicago, where flat farm fields are yielding to the gleaming buildings of high-technology companies. Nurtured by creative teachers, sophisticated equipment, and -- eventually --

access to working scientists, these students will graduate with the equivalent of a year of college education and, more importantly, an especially expansive way of thinking.

The prospect of such a school in Maryland has captured the imagination of Gov. William Donald Schaefer, who seized on the idea after visiting the prototype, a highly successful seven-year-old state-run mathematics and science high school in Research Triangle, N.C., during his 1986 campaign.

Such a school in Maryland, Schaefer emphasized in his State of the State address to the General Assembly on Thursday, would help avert a growing shortage of scientists and mathematicians. It would, he believes, provide a crucible for imaginative courses and teaching methods that could be shared with local school systems, and it would help lure prized high-tech companies to Maryland by demonstrating the state's commitment to new technologies.

The governor's idea will have to surmount deep reservations in the General Assembly, whose 188 members are being asked to approve the school in time for it to open next year, probably in Greenbelt.

Already, some lawmakers, parents and educators are questioning whether it would drain talent from local high schools, whether it would draw enough minority and poor students, and whether it is worth spending an expected $13,000 per student annually -- the equivalent of tuition at an Ivy League university.

If the Illinois academy is a guide, Maryland's school could be a vibrant, creative environment that stretches fertile young minds to their limits.

There are lessons here in calculus, Japanese, astrophysics and literature, and a social science course in which students comb local flea markets for scraps of Americana.

Teachers, one-third of whom hold PhDs, offer evening tutorials, and science laboratories are open on weekends. Everywhere there is talk of independent thinking and of transcending barriers between academic disciplines.

"You get sucked into falling in love with a subject you didn't even know you liked before," said Portia Bloom, a junior.

But in spite of this fervor, and in contrast with the experience in North Carolina, the academy has had crippling growing pains. Doubts about its value, mirroring arguments certain to emerge in Annapolis during the next three months, have persisted since the school opened in September 1986, and they nearly forced it to close this month, midway through its second year.School Runs Into Obstacles

The obstacles have been many: Although the school is required by law to approximate Illinois' racial and geographic composition, it has not been able to attract poor black youngsters from Chicago, reinforcing fears of Baltimore legislators who predict that their constituents would be underrepresented in a special Maryland high school.

Although Chicago's 60 percent black school system makes up about one-fourth of the state's school enrollment, city residents account for just 14, or 3.7 percent, of the academy's 380 students. Of the 14, three are black.

After promising legislators that they would raise a significant chunk of money from private businesses -- a pledge that Schaefer also made in Maryland -- the Illinois school has had little luck so far in wooing donors.

It had no computers most of its first year because it could not find a company to donate any, and many businesses have been unwilling to contribute to a public high school. And while it has now raised $1 million, administrators concede that their initial prediction, $15 million over three years, was "totally unrealistic," according to the school's former fund-raising director, who quit in November, exhausted by her job's long hours.

Most critically, the school was nearly squeezed out of existence this year because of a partisan fight in the Illinois General Assembly. The legislature gave the school only as much money as it had last year, although it was doubling in size. The school's trustees vowed last summer to close it this month unless they got more money.

In November, the school won for the moment, obtaining enough money to finish the academic year after an intense lobbying campaign in which students staged classes in the Statehouse rotunda in Springfield, 200 miles away.

In the aftermath of the struggle, the school "is still fragile," said Leon Lederman, director of the Fermi National Accelerator Laboratory, a few miles from the school, and one of its founders. Administrators are preparing for another budget battle this spring, and the school's legislative opponents remain determined.Funds Distribution Debated

Among the most potent is Woods Bowman, a Democratic state representative from Evanston, an affluent Chicago suburb, who is chairman of the House's Appropriations Committee. The academy, he said, "will completely subvert" his attempt over the past decade to increase Illinois' subsidy of special programs for the state's 87,000 gifted students. (Currently, Illinois spends $120 per gifted student. Maryland has no such state subsidy.)

"If we knew how to engineer geniuses," Bowman said, "you could make a real good case for concentrating resources on this one school and pumping out 500 Nobel Prize winners down the line. But the fact is, we don't know enough about what sparks creativity and intelligence. Not knowing that, we need to give more kids a chance, distribute it more evenly around the state."

Stephanie Marshall, the academy's director, said that the arguments mustered by the school's opponents -- for instance, that the price tag this year of $19,000 per student is five times Illinois' average per-pupil expenditure -- mask a more fundamental ambivalence.

"Establishing schools for very bright people is inherently incongruent with our notion of an egalitarian, democratic society," said Marshall, who formerly was superintendent of a small, neighboring school system. "With finite resources, is it fair?"

Such discomfort is intrinsic in any state that undertakes this kind of a school, said Julian Stanley, a psychology professor at Johns Hopkins University, who is an authority on the education of mathematically gifted students.

"This is a wonderful idea, if you can get past the political problems," said Stanley.

In Illinois, politics has bedeviled the school from the start.

Because of fears that Republican Gov. James R. Thompson, who supported the school, might lose his reelection campaign last year, the academy was opened at breakneck speed, without a planning year that Schaefer is suggesting for Maryland.

Dormitories, which stand across the school's parking lot, were not finished until April. Boys slept in science labs and girls in the band room.

A $3.2 million budget -- just three-fifths of what the school's founders had sought -- left the academy unable in its first year to hire a principal, counselors, art and music teachers or a librarian. It also lacked the money last year to start an effort, similar to one proposed in Maryland, to work with the state's school systems by exporting programs and offering workshops for students and teachers.

A year and a half later, the school is still evolving, trying to structure a flexible class schedule and design a "library without walls" that will eventually connect students via computer to university libraries and education data bases -- a process expected to take five years to complete.

But there are the beginnings of a routine. Classes meet four days a week. Wednesdays are an "exploration day" for students to take field trips, attend seminars or work independently. The school closes once a month for long weekends, when students are required to go home.

Students can eat all their meals in the school cafeteria. During the school day's first period, Principal John Court, hired this year, personally makes wake-up calls to the dormitory rooms of a few stragglers.

Students must volunteer to work three hours a week in the school, mopping halls, for instance, or working in the cafeteria. Performing 40 hours of community service is among the graduation requirements.

The 34 teachers -- the student-teacher ratio is 11 to 1 -- are exempt from the state's certification rules, allowing the academy to hire several college professors and a few scientists from private companies. There is no tenure system, a feature also proposed by Schaefer, which has turned Illinois teachers unions into opponents of the academy.

Science and math courses do not monopolize the curriculum. While the classes are advanced -- one-third of the juniors are taking calculus -- the course work is less remarkable than the climate created by the interaction of unusually bright, motivated students.

"For most of the kids, this is the first opportunity to have it be okay to be bright," said Michael Sloan, a science teacher. "No one is going to point at them and say, 'Oh, teacher's pet,' for answering the question. Everyone is doing it."

Mehmet Guler, a junior from the southern tip of Illinois, nearly 400 miles away, agreed: "I discuss ideas with friends, with faculty constantly, over breakfast, lunch, dinner. That's what really makes this place neat."

The intensity comes, in large part, from the fact that students live at school, they and their teachers say. "You have curriculum as good as ours and teachers as good as ours," said Neill Clark, a humanities teacher. "But when you bring it here and make it residential, you open up the opportunities for kids to learn from one another."

The benefits are social as well as academic. "I have more friends and closer friends," said Elizabeth Doyle, a junior, who said she "didn't really fit in very well" at her former high school in Springfield.

The students are smart. For admission, they are required to take the Scholastic Aptitude Test as ninth graders. Their average score is 1,150 -- more than 100 points higher than the average score of college freshmen at the University of Maryland at College Park.

In selecting students, the admissions officers look at grades, extracurricular activities and teacher recommendations as well.

Students include the offspring of downstate hog farmers and of scientists from nearby high-technology firms. The youngest student is 11. City Recruiter Being Hired

But administrators are struggling to attract more Chicago applicants, who they concede are seriously underrepresented. The academy is now hiring a recruiter to work full time in the city.

Marshall, the director, speculated that inner-city school principals may be reluctant to relinquish their brightest students. Those students also are recruited heavily by East Coast prep schools, she noted. In some instances, academy officials suspect, the application forms simply do not filter through layers of bureaucracy of the state's largest school system.

"If they don't get more Chicago kids," said legislator Bowman, "they will have a very large, very hostile {Chicago} delegation in Springfield trying to erase them from the face of the earth."

Stanley, of Johns Hopkins, said any public boarding school for gifted students may face a similar quandary. In Maryland, "the moment you see the highest level of quality is from Montgomery County and Baltimore County, and not the Eastern Shore, it is going to be unpleasant for the legislators donating the money," he said. "That's the intrinsic dilemma."

The Illinois school is already vulnerable in Springfield, where it has been caught in a fight between legislators and Gov. Thompson over a state tax increase. The legislators rejected the increase and decided to freeze the academy's budget, stunning its administrators.

The school's trustees were forced to choose between turning away students already accepted for the second class and taking the risk of running out of money halfway through the year. They chose the latter course.

Marshall told faculty members that they would be hired on six-month contracts. Most came anyway. "I felt this was the very best high school in the United States," said math teacher Carol Kajor, who joined the academy faculty last fall. "I thought even if we were only here until January, even for a little while, I wanted to be a part of it."

Marshall hired a full-time lobbyist and a public relations firm. She persuaded parents to write hundreds of letters to legislators. And she carted students to Springfield one day last fall, armed with computers and superconductivity experiments and the Japanese teacher, who conducted a class in the Statehouse.

In the end, additional money for the school became part of a compromise in which it received an extra $3.2 million, and the 431,000-student Chicago school system, recovering from a teachers strike, got $5 million.

But the governor has, once again, recommended not increasing the school's budget for next fall, when it is scheduled to phase in its third class. The political pandemonium "has been an incredible load," said David Workman, a science teacher. "There is a feeling your destiny is not in your hands. You don't function as well as we're able to."

Jill Howk, a junior, said she despaired at the possibility of having to return to her former small-town high school. "It kind of really turned my world upside down," she said. But administrators predict the school's fortunes will stabilize once it begins to produce graduates.

"All we have to do is save one Jonas Salk," the Fermi lab's Lederman said, "and we would pay for the school for 100 years."

............... 600 Grades........................ 10-12 ............... 10-12 Cost per Student.............. $19,474 ............. $13,000 Operating Budget.............. $7.4 million ........ 8.2 million

Capital Expenses.............. $25.7 million *...... $10-12 million ** STATEWIDE PROFILE------------- ILLINOIS------------- MARYLAND Enrollment in Grades 9-12..... 575,845 ............. 203,933 Number of School Districts........ 993 ............. .... 24 Average per Pupil Expenditure 1985-86....................... $3,809 .............. $3,991 1986-87....................... unavailable ......... $4,323

Gifted Students Identified.... 87,000 .............. 55,000

Eventually 800.

Cost by third year, when school has phased in all three grades. * In first two years. ** Over five years. SOURCE: Illinois and Maryland departments of education, Illinois Math and Science Academy and Maryland Governor's Office.