The grim task began immediately after the school board met last week to consider and implement the $37 million cut made in its budget by the County Council.

Workers in the school system's personnel office in Upper Marlboro labored through the weekend, deciding who would have to go, position by position, name by name. Secretaries began typing letters to affected employes, telling them their tenure with the Prince George's County Public Schools has come to an end.

School officials say all employes should know their fates by Thursday. The tally: 927 people will lose their jobs, including 265 regular classroom teachers. These will be genuine lay-offs, school officials say, not simply positions left unfilled. As for attrition, Superintendent Edward J. Feeney had already trimmed 328 jobs when he proposed his budget, school officials said.

When the school system's 112,000 students arrive for school next September, their classes will be larger, by an average of two students. None of their textbooks, none of their library books, will be new. If they live farther than one and a half miles from school they will have to walk.

If they are special education students they will find diminished services. If they are athletes, they might find their favorite sport cut. They will pay the bus fare for school trips. Their after-school clubs may not find funding.

This is the way the battle over the school budget has ended. It began last December, when Feeney said he needed $336.5 million to run the schools next year. County Executive Lawrence J. Hogan said the money wasn't needed, and wasn't available anyway. Hogan raised property tax revenue to the maxiumum allowed under the TRIM charter ammendment, but said he could still muster only $300.9 million for schools.

Last week, the County Council found another $5.4 million for the schools, but Feeney still was left with less money than the $308.4 million he had this year. To school officials, it seemed more like slashing than trimming.

Despite the cuts, the amount spent per pupil continues to rise and Hogan, who disagrees with the school board over what is fat and what is lean, is quick to point this out. This year, the county spent $2,654 for each of its 116,200 students. Next year, per pupil spending will go up to $2,732, because enrollment will drop by 5,148.

Still, per pupil spending in Prince George's remains by far the lowest in the Washington area. The District of Columbia, which is the next lowest, will spend 23 percent more per pupil than Prince George's next year. Alexandria will spend more than 60 percent more per pupil than Prince George's will.

While the biggest individual cuts were made in school maintenance, two of the most seriously affected instructional areas will be special education and library and media services. Feeney sought to absorb the cuts "without damaging basic classroom fundamentals," according to school spokesman Brian J. Porter. "A group of auxiliary services were identified for the cuts, hence libraries and special education."

Special education serves about 15,000 students a year and, according to administrative assistant Jane Riggin, that number is slowly rising despite enrollment declines. Special ed will lose more than $1.5 million in programs and employes, and Riggin says the losses are spread as widely as possible.

Special education summer school will be shortened this year, and summer camp for handicapped students will be moved from the Eastern Shore to Brandywine, and will operate on a reduced program.

Three learning problems resource specialists, who help teachers deal with handicapped students, will lose their jobs. The entire contingent of six "mainstream specialists," who work to keep special education students in regular classrooms, will be laid off. Fifteen special education aides, who worked with special education students, will not return to the classrooms in September.

Six special education resource teachers, six speech therapists, and two hearing and speech specialists, also will lose their jobs.

The school system hopes to save $900,000 by buying no new textbooks next year. Another $2.574 million in library books, and salaries for library staff will be cut. The school board eliminated 55 elementary school librarians and 55 library aides in secondary schools. Feeney said the gap will have to be filled by adult and student volunteers.

Library and media supervisor Edward W. Barth said schools will be able to continue their magazine subscriptions, but the system will not be able to buy about 100,000 books, at a cost of $891,000, as it had planned to do.

Barth said the longer the moratorium continues, the more serious its effects will be, as books become older and more out of date. "We'll still be a media center," Barth said, "but I'm hoping for a more beneficial economic climate next year."

At University Park Elementary School in Hyattsville last week, principal R. Dean Powell watched his media specialist, who will work half days beginning in September, show a film to children in the school's well-furnished media center. "We will lose half of her next year," Powell said. "It will really hurt."

The media center is an integral part of the school's teaching, Powell said. "Of course, it's about to be crunched . . . We're so proud of our school and of our kids. We want more. It hurts to think about less."

At Rogers Heights Elementary in Bladensburg, principal Charlotte A. Mason was also contemplating cutbacks. "I'm particularly distressed at the prospect of losing my media teacher and my reading specialist," she said. "She's just a marvelous resource to our school."

Rogers Heights has a special need, she said, because its reading and language scores are slightly below national and county averages. "Many of our youngsters have not had pre-school experience," she said. "We have to start from scratch."

In the high schools, principals are faced with cutbacks in the inter-school sports programs. The Board of Education cut $400,000, or 40 percent, from the schools' athletic program. Most of the money is used to pay coaches and game officials in 14 sports, and next year students may find fewer sports to choose among.

Early this week athletics supervisor Thomas Paskalides was drawing up proposals for Feeney on how to implement the cut. Inter-school sports in junior high and middle schools were eliminated three years ago to save money. There is no inter-school athletic competition in elementary schools.

This year, the basketball team from High Point High School in Beltsville won the state championships. "Athletics bring out the best in kids," principal Francis G. Tracy said the day after the cuts were voted. "I'm very worried about what will happen."

Other specific cuts approved by the school board include an end to free instrumental and vocal music lessons in elementary schools, reduced subsidies for field trips, and fewer elementary reading instructors. A textbook writing project, which cost $95,000 a year, will come to an end.

Maintenance and security will be reduced, eliminating 55 jobs, but saving almost $4 million. Traveling instructors in the talented and gifted program in junior high schools will lose their jobs, which will be taken over by regular teachers.

When the school board made its cuts last week, it set aside a reserve fund of $1 million, to pay for unemployment compensation. Board members told union representatives they would consider reinstating jobs if the unions would forego higher wages and benefits. The board of directors of the Prince George's County Educators' Association has voted against such concessions, and Porter said no other offers have been received by the school administration.

Educators' association president John Sisson said last week that teachers must consider whether they want to fight through political channels for higher school funding, and target council and county executive candidates for support or defeat. "We're not done with Larry Hogan or the County Council," Sisson warned.

In the meantime, Porter said, the school system will simply do what it can in this unprecedented situation. "We all know that we've been gored," he said. "But we just can't stand around and watch ourselves bleed to death."