By soundly rejecting a measure to raise the TRIM property tax ceiling during the recent election, Prince George's County voters did more than force the county government to continue to fund its schools at this year's low levels. They also forced school officials to start talking about redefining public education for some 107,000 students next year.

"There are decisions to be made about what exactly we mean by a public education in Prince George's County," says Brian Porter, a spokesman for the county school system. "You can't cut more positions, new text and library books, without sacrificing basic programs for kids."

School board president Doris Eugene cannot yet say specifically where cuts will be made for the school year 1983-84, but vulnerable areas, she says, besides positions, include programs in student guidance and discipline, academic enhancement, special education and other classes designed to meet the needs of what is now a 54 percent black school system.

"I've had people say, 'Mrs. Eugene, I only care about what happens to my school and my child,' " said Eugene. "If you don't feel that your child has these kinds of needs you may ask, 'How much do I have to pay to take care of society's problems?' "

What particularly concerns school officials is that such cuts come at a time when they have established some courses essential to the image of a superior school system -- an image they've been trying to build for years -- and at a time when their students are beginning to show academic progress.

Prince George's County scores on standardized tests, for example, equaled and in some instances exceeded national averages last year for the first time since the early 1970s. An elite science and technical program begun last year at Eleanor Roosevelt High School was so popular that a second program opened this year at Oxon Hill High School, offering gifted students a course of study rare in the metropolitan area.

The schools date their fiscal problems to 1978, when voters passed TRIM (Tax Reform in Maryland) amendment to the county charter that limits property tax collections to the amount collected that year, which was $143.9 million.

Republican County Executive Lawrence J. Hogan, an avid booster of TRIM, kept property tax collections below the TRIM limit and attempted to cut school funding requests, but the all-Democrat County Council restored most of his cuts. Last spring, however, even with the maximum collection permitted under TRIM, the council was forced to cut Superintendent Edward J. Feeney's budget request for this year from $337 million to $306 million, about $2 million less than last year's budget. Next year's budget will fare no better, and probably will do worse, according to school leaders, who start the budgeting process next month.

This year's $31 million cut resulted in the layoffs of 507 teachers. At the high school level, there are now 46 professionals per 1,000 students, compared with 56 professionals per 1,000 students in neighboring Montgomery County. The cut also forced 3,500 nonprofessional employes to give up contracted wage increases pending new county funding.

The most obvious result of these actions has been increased class sizes, but other effects have been felt throughout the system: Students from kindergarten to senior high are walking an extra half-mile to save on the purchase of new buses, no new textbooks or library books were purchased this year, and paper and other supplies are scarce, according to teachers. Also, fewer courses are offered in music, art and athletics, and more teachers are being asked to teach subjects outside their fields.

TRIM Plus 4, the measure on last Tuesday's ballot, was designed to permit the county to collect slightly more revenue--4 percent more than the previous year's collections each year plus revenue generated by new construction. It would have raised an additional $6.4 million next fiscal year and the schools, which spend about 60 percent of the county's budget, would have gotten some of that.

But now, the schools must continue to make do with less money, at least for the next two years. No one, it seems, is immune:

Linda Colomo, a 13-year English teacher at Suitland High School, must continue to teach 30 to 40 or more students for most of her classes. Suitland High School kept its 20 English teachers this year but picked up 200 extra students when a junior high school was closed and the ninth graders were all sent to Suitland.

Colomo starts her school day at 8 a.m. facing 40 students. Such large classes are very frustrating, she said during one recent lunch hour as she gave makeup exams during her lunch hour.

"I don't feel you can educate 42 people in 50 minutes," Colomo said. "I don't think I'm doing the best I can. I feel bad. I know I'm not getting their papers back as soon as I should. How can they see their progress if their papers are buried under a pile?"

Sharon Kingrea, a senior in Colomo's first-period class, said that in September, when there were 47 students enrolled, a student who didn't get there early might not get a seat.

"I knew I'd have to pay more attention in a big class," said Kingrea. "With 40 or 50 people, even whispering is a lot of noise."

Teachers are scurrying to get training in other fields. "All the computer courses at Prince George's Community College are filled up," said Ken Brown, a guidance counselor at Oxon Hill Junior High School. "I'm taking one and I can name six others on the faculty who are taking them."

The students at Oxon Hill Junior High are selling candles to raise money for school necessities. Principal Milton Steinbaum, who hopes the sale will net $2,000 to $3,000, will determine how the money is spent. The librarian needs paperback books and a filmstrip projector, he said; the gym teachers want an exercise bike; academic teachers want paper and supplementary workbooks.

Budget cuts have not gone unnoticed by Oxon Hill students other than Kingrea, as evidenced by comments from several eighth graders in the library one day recently:

"The tag talented and gifted program was cut," complained 13-year-old Scott Wilson.

Amma Hawks chimed in, "We were learning logic, computer skills and weather maps--not the kind of things you usually learn in school."

Danita Smith said she can no longer take an orchestra class. Since orchestra classes were cut from daily to once a week, she said, she can't work them into her schedule along with her required courses.

"I don't think they have enough books in the library," Kevin Aanetad, another eighth grader, said. "I read a lot so I know what's new and what's not."

The students also complained about outdated history books and that teachers fumble around sometimes when they are teaching out of their field.

"We have to be more on the ball," said Hawks, "but it makes it harder on us."