ST. CHARLES, VA. -- Before his industrial arts students arrive on chilly mornings in this down-at-the-heels mining town, teacher Raymond Smith's first job is to carry in buckets of coal for the stove that warms his classroom, a stone building that once was a bus garage.

Smith runs the only vocational program for handicapped students in Lee County, where a quarter of the population lives below the poverty line.

He hopes to keep his half-dozen teen-age boys in school long enough for them to learn a skill, not an easy task in an Appalachian district where one of every three eighth graders will not finish high school.

"If they stay with me long enough," Smith said, "they do right well."

Smith's work at St. Charles Elementary School is paid for by a grant from the state, whose money is the lifeblood of this Southwest Virginia school system.

Local taxes cover less than one-fourth of the $18 million annual school budget for Lee County's 4,900 students; most of the rest comes from the state, which allocates aid on a formula based on a community's ability to pay.

That means that a lot of downstate school money comes from Northern Virginia, which is wealthy enough that local taxes pay for two-thirds of the local school budgets.

School officials at the two ends of the state are anxiously following the legislative debate in Richmond over how to balance education funding between Virginia's poor, rural communities and its well-off, northern districts.

Here in Lee County, they took heart from Gov. Gerald L. Baliles' promise to send more aid to the least able, but they are worried that lawmakers from the Washington suburbs will exercise their growing power to grab a larger share of the state purse, leaving less for their struggling schools.

Fairfax County school officials say the county alone pays 19 percent of the state's income tax and nearly 15 percent of its sales tax, but it receives less than 9 percent of the state education budget.

Northern Virginians say they must contend with larger costs for salaries, supplies and construction, as well as a higher incidence of handicapped and foreign-speaking students, who are expensive to educate.

They say that some downstate communities could afford higher local taxes but prefer to spend federal and state money.

"We are more than willing to help those counties that are less affluent than we are," said Joy G. Korologos, vice chairman of the Fairfax County School Board.

"On the other hand, we would like our fair share of what we send down there {to Richmond}."

Northern Virginia's case wins little sympathy in Lee County, whose entire assessed value of $390 million is about half of next year's proposed Fairfax County school operating budget.

The state's Joint Legislative Audit and Review Commission calculates that Lee County is the least able in the state to pay for its schools, and it has one-third of the per-pupil revenue capacity of a Fairfax County or a Falls Church.

The median income for married couples in Lee County in 1985 was $17,611, compared with $48,901 in Fairfax County.

So far, the have-nots are faring well in the legislature, where the House and Senate this month approved separate budgets along the lines Baliles proposed.

But the Senate resisted a downstate attempt to eliminate a proposed $48 million differential that would help Northern Virginia pay its higher salaries.

Some Northern Virginians oppose sending more aid to poor districts because they think "we're sending it to a bunch who may never improve themselves," said Lee County Administrator Steven B. Miner, who grew up in Lee County and returned after he graduated from law school.

"They're not watching . . . . They're not impressed with the notion that our children should get an equal education."

Lee County's schools are far from Northern Virginia's in more than the basics.

Instruction in art, music, drama and speech is infrequent, and computers are a luxury. Students at several schools eat in the gymnasium because their buildings do not have cafeterias. One school created a classroom by converting a coal bin. At Ewing Elementary School, Principal Jerry Hounshell brought in his own bulldozer to carve a parking lot.

Without adequate state funding, "There still would be schools, but you would turn the clock back 100 years on education," said John Howland, the county School Board chairman. Even with state aid, he said, "I don't think you can say the kids here get an equal opportunity with other children in the state."

It stretches the imagination to consider Lee County a part of the same state as the booming cities and counties of Northern Virginia.

A 450-square-mile wedge that adjoins Kentucky and Tennessee, Lee County is closer to the capitals of eight other states than to Richmond, a six-hour drive away.

The county's population of 25,000 is half what it was in the late 1940s because of hard times in the coal mines and on the tobacco farms that are the mainstays of the local economy. The unemployment rate is 8.1 percent, compared with Northern Virginia's 1.9 percent.

On the other hand, it is safe to park a car all day with the keys in the ignition in the center of Jonesville, the county seat. Drug problems in the schools are minimal, and students do not lock their lockers.

"You get to know the students very intimately," said Omer Elkins, principal of the Keokee Combined School, with 237 students in kindergarten through grade 12. "They develop a rapport and confidence with teachers that you don't have in a larger school."

Jimmy Woodard, a 12th grader who is the son of a retired coal miner, has derived hope from Keokee that he can go away to Virginia Intermont College in nearby Bristol, possibly on a basketball scholarship. "I would like to take business classes," he said.

Lee County also is proof that global culture has left few regions untouched. National Public Radio floats over the mountain passes from Johnson City, Tenn., the gospel hour on the local radio station is sponsored by Star Video, and the lunch menu at the Dryden Combined School (grades K through 12) Thursday will include tacos with meat sauce.

State and federal money has made the difference in lifting the level of opportunity in the county schools. In some buildings, including St. Charles Elementary, 70 percent of the students eat federally subsidized free lunches; school officials say more are eligible because of poverty but are too proud to ask. Federal funds pay for remedial reading and math instruction for low-scoring youngsters.

State funds subsidize everything from salaries to supplies. Money from Richmond has enabled the district to pay its 368 teachers a decent wage, a proposed average of $23,646 next year. (In Fairfax County, it will be $37,000.)

State funds allow schools to keep their textbooks up to date, provide a vocational high school that draws students from all over the county, permit some students to take classes by television that the county cannot offer, and pay for adult education courses.

In St. Charles, teacher Sharon Kimberlin said some of her students are so eager to learn that they walk five miles each way from their homes in mountain hollows.

The schools have trained students for jobs in business, construction or factory work, although many leave for Tennessee or Kentucky because of poor local employment prospects.

One-third of last year's high school graduates went on to four-year colleges, compared with more than two-thirds of Fairfax County's graduates. The dropout rate is down, and officials point out that fourth-grade reading scores are now above the 50th percentile nationwide.

But at Ewing Elementary School, only a few miles from Cumberland Gap, which offered pioneers the opportunity to head west, there are only three computers for the 180 students in grades kindergarten through seven.

Thomas Jefferson Elementary School in Falls Church, with 240 students in second through fifth grade, has 54 computers.

At Keokee Combined School, a 1939 Works Progress Administration brick building that is a half-hour ride up twisting mountain roads from St. Charles, the program for gifted students consists mainly of allowing them extra time on the computer.

There is no language laboratory, which is standard in better-equipped schools. Spanish is the only foreign language offered, and Roderick Griffith teaches the second- and third-year courses in the same period. He also teaches civics.

Change is coming in the fall of 1989, when the county plans to open a new, better-equipped high school that will absorb 1,000 students from Keokee and four other places, reducing the county's six high schools to two.

County officials are fearful that other programs may have to be cut later to afford the $11 million cost of the new school, but they say it is necessary to bring county education up to date.

"Until we have the facilities and all, we can't do as well with our programs," said Jimmie Whitt, the county's assistant superintendent.