When 17-year-old saxophonist Diane Gilmore reports to Dunbar High School next weeek, she may have to strike instrumental music and band from her list of classes. Her band instructor has been "riffed."

College-bound Carolyn Hockaday may have to ask her mother to pay for math and English tutors. Advanced courses usually offered by Dunbar be scrapped.

At Hamilton Junior High, students of French will find substitute classes on their schedules. The only French teacher at Hamilton, 12-year veteran Gwen Paramore, was dismissed two weeks ago.

On Sept. 4, the District of Columbia's 97,000 public school students -- 6,000 fewer than last year -- will return to classrooms amid confusion, uncertainty and fury caused by the school system's largest layoff of teachers in seven years.

Under a $35 million budget cut, 706 school employes have received RIF, or Reduction in Force, notices. Among those fired are 600 teachers -- 350 at the elementary school level -- with from one to 10 years experience. Forty-five RIF notices went to probatinary assistant principals.

The drastic cuts in teaching positions threaten recent gains in student test scores, which last year inched toward national norms after years of decline or stagnation. In recent years, school administrators have put greater emphasis on educational basics, including math and reading.

The cutbacks, school officials and parents say, have punched large holes in the drive for educational excellence.

"I think the outlook will be devasting," said R. Calvin Lockridge, school board president. "I can almost predict that the test scores will fall. If they don't, it just means that people are more careful about their jobs."

But Lockridge warned of more teacher layoffs between now and December.

"We're perpetuating the weaknesses of youngsters," declared Athel Liggins, principal of Mckinley High School, talking of his efforts to aid noncollege-bound students.

"I wanted to upgrade my business department. I wanted to add some electronics courses. But you advocate these things and then you have to go back, instead of forward. How effective can you be with 40 in a classroom?"

Superintendent Vincent E. Reed said he is still committed to the District's competency-based curriculum, which he credits with the improvements, despite the problems presented by larger class sizes.

Hard hit by the current round of RIFs are some coaches, band directors and various music and art instructors; many were vulnerable because of low seniority and temporary hiring practices.

In some cases, "riffed" teachers will be replaced, although not necessarily by persons with the same skills or interests. In other cases, school will simply lose staff positions.

With only a few days left before teachers report to school, principals, in various stages of desperation, were unsure of who will join their staffs or what skills they will bring with them.

Harried principals were digging through piles of dossiers to fill slots in crucial areas such as remedial reading and math.

"I really have no idea what the cuts will bring," said Shirely Hammond, principal of Brookland Junior High School on Michigan Avenue NE. "The organization isn't complete yet. I haven't lost any positions but I've had 'riffed' teachers."

"I have no idea of what to expect out of this program," said Dennis Jackson, principal of Eastern High School on 17th and East Capitol Streets NE.

"I know I am to lose seven teaching positions which won't be replaced, and I may lose 18 or 19 teachers to "riffing,' who will be replaced on a one-to-one basis," Jackson said. "But if I get an instrumental music instructor, I don't know if he'll have a background in band music or in a marching band.I just don't know until we've completed our staff."

"We know who we've lost; we just don't know who we've got," said McKinley principal Liggins. "We've lost one of our extremely talented art teachers, the head of the peer tutoring program, the head of the school newspaper. You hope that their replacements will have their enthusiasm but you can't be sure." you can't be sure."

Not all of the administrators were quite as upset.

Herman Roebuck, principal of both the Carver and Merritt schools, said, "I think we're magicians. I have yet to receive a few teachers but you make contingency plans. When you work in the school system, you know how to make sure the ship sails in spite of rough seas. That's what we get paid for."

Superindent Reed said the schools had little choice about the cutbacks.

"People just don't understand how much $35 million is," he said. "We just closed school in June and then we get hit with this. This takes time. And furthermore, the personnel office has other responsibilities beside the 'riffing.'"

Returning students will find:

Driver's education has been eliminated in high schools, an early victim of the school board's budget scalpel.

Fewer schools will offer adult education high school equivalency courses in the evenings. Special programs, such as computer mathematics, advanced placement courses and shop classes will be restricted or eliminated in most high schools.

Class sizes will increase, although school officials differ on exactly how much. Superintendent Reed says the student-to-teacher ratio will increase only from 26-to-1 to-28-to-1.However, some principals say privately that classes will bulge to 35 to 40 students.

Reed replied: "They don't know what they're talking about. Any situation where there are 35 in a class, I'd like to know about."

A few school programs were saved at the last minute.

Until early last week, administrators at the Duke Ellington School for the Arts at 35th Street NW feared that all four department heads would be lost. All four, practicing artists who work full time at Ellington, are designated as temporary employes because they are not accredited academic teachers. Since then, Ellington principal Maurice Eldridge says the four positions have been saved through an administrative "compromise.

If there was any good news in the budget crisis, it was that the school system consolidated several offices helping handicapped students. The change came in response to a lawsuit by parents and public interest groups charging that the city failed to respond fully to the needs of handicapped students.

The Office of Special Education will conduct all of its testing and placement programs at the new Children's Study Center at the Logan School on G Street NE.

Formerly, parents of handicapped children had to find one of six regional offices in order to have a child evaluated and placed in a special program. The schools will now use the old special education office at the Webster Building at 10th and H streets NW, to provide workshops where parents and teachers can learn new techniques for assisting handicapped children at home and in the classroom.

Teachers in the special ed program did not suffer heavily from cuts; most of the budget trims were made on the administrative level. Even so, teachers who deal with handicapped students said they were worried about the impact of the budget cuts.

Judy Levy, a teacher in the Tyler School program for the visually handicapped, which has not suffered from extensive staff cuts, said she was worried that the "mainstreaming" of handicapped students into regular classrooms may be more difficult by larger class sizes.

Although painful to administrators and students, the staff cuts have focused attention on the District's longstanding problem of surplus staffing and underutilized buildings in the face of dwindling enrollment, according to Vice Superintendent Elizabeth Yancey.

Some teachers who recieved RIF notices over the summer, she said, were "excess teachers," instructors who had been retained even after their schools lost enrollment.

Complicating the picture are the enormously complex rules by which staff cuts were made. Teachers received seniority rankings within "competitive subject areas." They were then given seniority credit for outstanding ratings and for prior government service even if it were not in teaching.

The multimillion gap afflicting the schools comes about this way:

To operate at the same level as last year, the schools would need $279 million, said Yancey. However, the City Council and Congress allowed $252 million. Out of that, a set amount must be alloted to payments on the city's debts.

Thus, the current operating budget for schools stands at $246.2 million, with 88 percent going to teacher salaries. After various adjustments, the gap to be made up by budget cuts is about $35 million. School administrators felt that trimming teacher ranks was the only viable solution.

The school cutbacks result from Mayor Marion Barry's sweeping, and occasionally faltering, efforts to close a $172 million deficit in the city's budget in the face of the cash shortages, declining tax revenues and a shrunken federal payment -- the amount the United States government pays the city in lieu of taxes on federal properties.

During the last several months, Barry has been under pressure to stop the city from spending money on expensive services and postponing payments. But his efforts to halt the cycle have been hampered by a public outcry over cuts in human services, and by congressional reluctance to permit the city to float massive long-term loans.

The mayor, meanwhile, has decreed that $6 million be cut from next year's budget, possibly forcing the elimination of another 500 teaching positions.

And he recently asked school administrators to slice another $8 million from this year's budget. Superintendent Reed said he has placed a plan before the school board to save 400 jobs by furloughing all school personnel for 10 days without pay.

School employes would go without pay during spring break and at the end of June. The move would not effect pupils. If the school board does not accept the plan, then conceivably another round of RIF notices may darken other teachers' mailboxes before the end of September.