Virginia Gov. John. N. Dalton's proposed budget has placed the conservative governor on a collision course with the state's teachers and education officials over what many claim is Virginia's tight-fisted approach to paying for public education.

The educators, many of them in the Washington suburbs, say they are bitter and frustrated by the Republican governor's belief that education costs can be held down simply because the number of students is falling.

Few are angrier than William J. Burkholder, acting superintendent of Fairfax County schools, the largest local system in Virginia."My reaction is one of very keen disappointment, bordering almost on disgust," Burkholder said after seeing Dalton's proposed budget this week.

The governor's critics charge Dalton's plan will force local governments to raise more money to pay for state-mandated programs or else lead to cuts in services and smaller pay raises for teachers. In Fairfax County, school administrators say the governor's plan will force them to trim $10.5 million from their proposed budget for the coming year.

The Dalton proposal is enough, says Fairfax's Burkholder, to make some localities sue the state to force it either to provide more funds "or reduce (its minimum) standards of quality."

One reason the educators are troubled by Dalton's budget is that it is far below the funds needed for what the State Board of Education, which sets many of the state's education standards, says Virginia schools should be doing.

The confrontation between the governor, who wants to be known as the executive who held the line on state spending, and the educators comes after months of protests by Northern Virginia teachers who claim their benefits are being eroded by inflation and tiny pay raises.

Barbs aimed at Dalton's budget have been especially pointed in Northern Virginia were educators say their budgets are being squeezed by a relative decline in both state aid and federal impact aid.

The Northern Virginians are not alone in their discontent. State School Superintendent S. John Davis, a recent Dalton appointee, said through a spokesman yesterday that he hopes the legislature "will make some increase" in the governor's budget.

According to a spokesman, Davis, a former Fairfax school superintendent said he wanted more state spending on schools even though he was "aware of the fiscal constraints under which the governor must conduct state activities." The spokesman added, "He empathizes with him."

Dalton has proposed a modest boost in state spending for education, up 12.3 percent to $1.9 billion during the next two years. But once inflation's impact is considered, Dalton has boasted that his budget will mean fewer dollars going into the state programs, a claim that has angered the educators.

They note that the state school board cited Virginia's relatively low national standing in terms of financial support to schools in calling for a sharp increase in state school aid.

Under Dalton's proposal, state spending on schools during 1980-82 would be $205 million more than during the current two years, but far less than the $513 increase -- a 31 percent jump -- requested by the state board. The board's proposal is enthusiastically supported by the Virginia Education Association and many local school boards.

Even though Dalton's proposed increase is below the current rate of inflation, the governor has said that an expected 5 percent drop in school enrollment by 1982 should allow school programs to continue the way they are or even make a modest improvement.

To Dalton, declining school enrollments are the key."I am hopeful that school board and school superintendents can reduce the number of teachers and administrators as school enrollments decline and use the savings to increase th quality of the remaining personnel . . ." he has said.

Arlington School Superintendent Larry Cuban calls such reasoning "fallacious" and says Dalton has failed to consider the huge fixed costs that school districts face and the need to keep basic programs intact.

"Costs are increasing for everything," Cuban said. "Budgets for every school system in the county have been increased. Gov. Dalton knows that. I just don't think that this is a good policy decision."

Good decision or not, it is proving to be controversial. Many of the 140 legislators in Richmond who will have to approve Dalton's plan say some further increase in state education spending is certain.

Lobbying for an increase in Dalton's plan began almost as soon as he released it. "We have to remind our legislators of our interest -- $10.5 million-plus now," said Fairfax School Board Chairman Rodney Page. "We have to do what we can in this country to get support for this budget. We need to do a little campaigning among our constituents."

According to the National Education Association, the share of school spending in Virginia shouldered by the state government was about 40 percent last year. This was up from 37 percent a decade earlier but still much less than the 47 percent of school costs that are paid by state governments nationwide.

In Northern Virginia, however, the state share has dropped -- from 30 percent to 26 percent in Fairfax during the 1970s and from 24 percent to 17 percent in Arlington.

The reason for the decline, state officials said, was a change in the formula for distributing education monies. In an effort to equalize spending, the state gives far more per pupil to poor areas, such as rural counties in Southside Virginia, and much less to relatively wealthy areas such as Northern Virginia.

Northern Virginia school systems also have been hurt by cuts in federal impact aid, which is tied to the number of children of federal workers attending local schools.

In Fairfax, for example, federal aid has dropped from 10.5 percent of school spending in 1971 to 6 percent now. Local officials expect it to drop to just over 4 percent next year.

But Fairfax administrators had hoped to keep the share from local taxpayers unchanged with the increased aid requested by the state school board.

William H. Cochran, Virginia state deputy school superintendent, said the state board based its request on the average amount it actually cost local school districts to meet state minimum requirements in 1978. He said this figure was increased by 8.5 or 9 percent a year to account for inflation.

"These are realistic costs," Cochran said. "If we don't use them, we are shifting a burden to the localities that should be carried by the state."

J. Wade Gilley, Dalton's secretary of education, rejected Cochran's reasoning, saying the state board's formula is "not mathematically sound.

"You can't use a statewide average as the minimum for the state. You could never catch up," Gilley said, "because there always have to be a lot of districts under the average."