The Montgomery County school board approved a record $420 million plan last night to build and renovate schools over the next six years, including the opening of 19 new schools to keep pace with a rapid influx of children into the school system.

The capital budget calls for a burst of school construction that would be unprecedented in Montgomery, with most of the new schools intended for the northern and western parts of the county, where residential development is flourishing.

"We have tried to be fiscally and educationally responsible," board President Marilyn Praisner said after the unanimous vote.

The spending plan, which must be approved by the County Council, includes $77.5 million for the 1989 fiscal year, which starts in July.

The request for next year includes money to build an elementary school in the Olney area that is scheduled to open in 1990. It also includes funds to begin planning five new schools: an elementary school in the Quince Orchard area, two in Gaithersburg and an elementary and a middle school along the Rte. 29 corridor.

In addition, the board is asking for money to begin planning to replace Walt Whitman High School in Bethesda and to renovate or build additions to 29 other schools.

The capital budget is the largest the school system ever has submitted and about $45 million higher than the $376 million, six-year plan it turned in to the County Council a year ago. The council pared that request to $326 million.

The school system's building and renovation program does not translate immediately into an increased burden on county taxpayers, since the projects are financed primarily through the sale of long-term bonds by the county government.

Praisner noted that the spending plan is almost identical to the capital budget recommended to the board this month by Superintendent Harry Pitt, who assumed his job in July.

Pitt said the main reason that this year's request is significantly higher than last year's was his decision this month to ask permission to build 19 new schools -- six more than previously anticipated -- by 1993. The school system's enrollment is expected to grow from about 96,500 to more than 120,000 within six years, approaching its all-time high of 127,000 in 1972.

At a hearing last week on the capital budget, Pitt cautioned that the sums could be underestimated, particularly in the later years of the six-year plan. "We're using today's construction costs," he told board members. "They're not going down. The cost is at this point a conservative estimate."

Despite the magnitude of the building program, the school board last week heard three nights of testimony from parents who said the school system was not moving quickly enough to repair older buildings and to alleviate overcrowded classrooms.

Robbie Milberg, a chairman of the PTA Modernization Committee at Travilah Elementary School, said the 27-year-old school west of Rockville "is a functionally obsolete facility." Its plumbing, sprinkler system, heating and lighting all are deficient, according to a rating of school facilities, although the building is not scheduled to be renovated until 1991, she said.

Moreover, she said, the school is expected to enroll 50 percent more children by 1991 than it was meant to accommodate. "Our already deficient physical plant will . . . be burdened further," Milberg said.

Among the dissenters were parents of students at Rockville High School and nearby elementary schools, where enrollments are significantly below the schools' capacities. Parents from these schools said the school system could reduce the need for new buildings by changing attendance boundaries.

But in some instances, the complaints of crowding came from communities that have just gotten new schools. "We currently are slightly over capacity with all of the classrooms being used," said Terry Shoemaker, a PTA president at Jones Lane Elementary School in Gaithersburg, which opened in the fall. She asked the school board to give the school eight portable classrooms next year.

At the end of last week's hearings, Philip H. Rohr, the school system's director of facilities planning, estimated that the requests from the community, if incorporated into the capital budget, would add "on the order of 20 percent" to the $419 million building and repairs program.

As they pored over specific plans, board members differed over how quickly they should seek to accomplish the district's construction needs. Although the County Council made unprecedented cuts in the board's requested operating budget last spring, board member Blair Ewing said the board should be ambitious in making its capital budget request.

"There are funding needs that need to be met," Ewing said, "and we ought to meet them in the sense of asking for what we think is right."