The Montgomery County Board of Education voted early today to request $44,162,000 in state building funds for next year despite the fact that the state has said it will probably provide only about $3.5 million.

Last night's request to the Montgomery County Council, which will make the final decision on how much to seek from the state, set the stage for a vigorous debate over school construction funding in coming weeks with the county government, which will be asked to make up the difference between what the state provides and the school system wants.

The $44 million would fund renovations for deteriorating school buildings in the southern part of the county and new construction in the north.

"We need a big increase because we have big needs," said board member Blair Ewing. "One thing we won't get is something we don't ask for."

However, Jacqueline Rogers, director of the county Office of Management and Budget,said before the board meeting that "the program request, should it need to be funded locally, is not affordable. We have a real challenge."

Rogers said County Executive Charles W. Gilchrist has recently asked the school system to modify its request, but "to date, Gilchrist's pleas have not been acknowledged."

The school system is faced with repairing 30-year-old schools in the southern part of the county and the need to build new schools in the north to accommodate a population surge. Rising enrollment has reversed a decade-long trend that has led the board to close nearly 70 schools since 1970.

The school system noted recently that 533 of its classrooms became overcrowded when 831 students more than expected enrolled this year. To cope with the problem, two weeks ago the board requested $838,995 in emergency funds from the county to pay for 58.5 additional teaching positions.

The majority of the construction funds being requested would go for a new high school and elementary school in the Gaithersburg-Germantown area, modernizing Twinbrook Elementary in Rockville, a second gymnasium at Springbrook High in Silver Spring and new administrative offices in the northern area of the county.

The county executive and school officials will meet this Friday and next week to negotiate the construction funding request. The state's funding allocation will depend on the amount of bonds it will issue, which will be decided in the legislature in January.

Last year the county appropriated over $28 million for school construction and renovation and the state gave $3.4 million.

From 1972 to 1979 the state invested heavily in school construction financed by state bonds. This year the state's allocation for school construction throughout Maryland will be less than the request by Montgomery County alone, said Rogers.