For the first time in four years of home rule, the D.C. Board of Education is close to getting enough money to pay the rising cost of running the school system.

But school officials say the City Council's tentative decision to grant an education budget of $264 million for the 1980 fiscal year will merely keep abreast of current needs, and will not permit improvements in the city educational program.

The debate is over what constitutes fiscal "needs." School officals say these are system's basic and manadated costs, such as paying personnel. Council members insist they are books and other teaching materials.

The annual encounter over school financing was played out before the council, which voted approval this week of an amended version of the city's $1.4 billion operating budget submitted by outgoing Mayor Walter E. Washington.

Final enactment of the council's budget bill is expected Nov. 14. If the bill survives possible vetoes by the mayor of disputed items, the measure must follow a labyrizthime course through the White House and Congress before it is enacted into law. The 1980 fiscal year begins Oct. 1, 1980.

The $364 million above the mayor's proposal and $11 million more than this year's budget. The Board of Education sought $162 million more than the mayor recommended. For reasons that are confusing, most of the remaining $10 million gap may turn out to be more illusovy than real.

According to Betty Ann Kane, finance committee chairman of the school board and the Democratic nominee for an at-large council seat, the council's $6 million increase brings the school system within about 1 million of having enough money to pay all of its necessary cost in the 1980 fiscal year.

The problem is which cost?

Beaching the answer will spotlight basic contradictions of the Washington school system which has both spearking new buildings and decrepit, poorly maintained old ones, and a generally well-paid staff teaching students with a scarcity of texbooks, many of them old and tattered.

The school system's "crying need," said Marion Barry, Democratic nominee for mayor and a former school board president, "is books and supplies and equipment - that's what the teachers parents talk about."

In an attempt to nudge the school board to spend of these purposes, the council adopted language in its official report calling for spending for books and other classroom materials over costs for personnel. However, the council has no legal authority to dictate how the money must be spent.

The course was propsed by outgoing council Chairman Sterling Tucker, who recommended the council's $6 million increase in the school budget."

Because of fund shortages in recent years, the school board suspended textbook purchases, causing a shortage that teachers and parents have depicted as a crisis. In the current 1979 fiscal year, book buying has been resumed.

The school board views the spending priorities differently. It looks first at "mandatory" costs, those required by law or contract, or which result from forces outside the school system's control such as rising utility expenses.

Salaries and benefits consume more than 80 cents of every school dollar. Supplies, equipment and textbooks account for less than 4 cents.

According to Kane, the $364 million school budget approved by the council will contain almost enough to pay all the so-called "mandatories" that the school system has been forced to absurb during the past few years by cuting services.

Those mandatories include $39 million for longevity pay increases for teachers, $2.9 million for court-ordered improvements to educational programs for handicapped pupils, $1 million to pay teachers to earn advanced degrees, nearly $1 million to hire staffs at four newly renovated schools and $745,000 to pay higher untility bills.

The new budget does not allow for new and improved services, however.

Moreover, Kane wrote in a memo given Monday to the school board finance committee, "The school system cannot begin to catch up in any sense with programs such as summer school and cultural arts and foreign languages already jettisoned in previous budgets."

At Kane's urging, the committee voted unanimously to ask the council to create a study commission to explore school finances and recommend procedures to provide support in the future.

In its proposed 1980 budget, the school board included a shopping list of $9.6 million in improved school programs and services. The three biggest items would be $2.8 million for more classroom supplies and $2 million each for the expansion of pre-kindergarten programs and for hiring 100 new high school teachers.

Despite a city-wide decline in enrollment, Kane said the drop has occured in the elementary schools but not in the upper grades.The school system in recent years has reduced staffing in the lower grades.

While disappointed that the council did not grant even more money, Kane said in an interview that she was pleased with what was gained. "I feel very good that we are finally getting our message through," she said.

Part of the school financing problem seems to come from the structure of the city government, which gives the school board its own budget-writing and spending powers, but relies upon the mayor and council to provide the actual money.

The council education committee recommended a few weeks ago that the council approve every penny the school board wanted, covdring mandatory costs plus all the proposed new services.

William R. Spaulding (D-Ward 5), the committee chairman, said he was taking the school board's word that all the money was needed. But he said he was not prepared to defend the request in detail.

Other council members, recognizing limits to the city income, notably from taxes, favored a cutback. In the end, Tucker recommended the $264 million spending level and the full council, including Spaulding, went along.

The proposed level of school spending is $11 million greater than the current year's school budget of $253 million. Earlier this year, the mayor informed the school board that it should not ask for more than $258 million for next year. The board asked, however, for $274 million.

On paper, that looks like a shortfall of $10 million. But it isn't necessarily the case.

The $10 million would form part of a fund to finance pay increases expected next Oct. 1 for teachers and other school employes. These are estimated to cost $124 million.

(The figures do not appear to add up precisely because of various intricate budgetary adjustments.)

There is no danger that the school system will lack the needed $124 million, however, because it is tucked away elsewhere in the mayor's budget. It is part of a $47 million fund that the mayor set aside to finance pay increases for all city employes, including those who work for the schools.

In other words, the money for the pay increases shows up twice in the budget documents - once in the school board's version and once in the mayor's.

Kane said the school board included it because it wanted to adopt an "honest" budget. But there is another reason, too.

A coalition of 23 parent and educational organizations, calling itself the Ad Hoc Coalition for Full Funding of the D.C. Public Schools, stated that reason in a recent letter to Tucker.

The school system, the coalition declared, "needs timely use to all its salary funds so that it will not have to 'reduce it force' at the beginning of the fiscal year while it waits to see when, and how much, of its pay-raise money will be released by the mayor."