The classroom where Kay Morgan teaches her first-and second-grade pupils at Terraset Elementary School in Reston is a 1977 version of the little red schoolhouse.

The 30 or so seat-desks are placed in orderly rows in the one-room building in front of Mrs. Morgan and the blackboard. The arrangement is in striking contrast to the informal scattered clusters of desks in the open classrooms found in many of the county's new schools.

When a pupil wants a drink of water, he doesn't go down the hall - there isn't any hall. He does what grandma or grandpa had to do 50 years ago - he goes outside. In the 1977 version, though, the trip is to a modern, heated building - the main school - next door.

Terraset Elementary School temporarily consists of 11 portable trailers and wooden cabins painted schoolhouse red - five of them at Dogwood Elementary and six at Hunters Woods Elementary, both in Reston. They are Fairfax County's solution to finding classroom space before permanent schools are ready to open or before the county as the money to begin construction.

Although the temporary structures are not as roomy or attractive as the multi-million dollar permanent schools beside which most of them are parked, Fairfax teachers and school officials say there have been few complaints from parents whose children have to attend class in them. In fact, some teachers say, the trailers are sometimes thought of as a cozy refuge from the bigness of the permanent schools.

The pupils of Terraset will move into a strikingly modern building, set in the side of a hill and heated by solar energy, on Feb. 22. But since September, Terraset (the name means "set in the ground") has existed a couple of feet above ground in the jack-up trailers and other temporary buildings at Dogwood and Hunters Woods.

While 325 Terraset students have been going to school in the "tempos," as they are called, another 400 have been going to regular classes at Floris Elementary, just outside of the new town of Reston.

Presiding over this farflung student body is principal Margie W. Thompson, who believes good education can take place in a one-room schoolhouse or in a pioneering solar-heated building. Sitting in her combination office-storeroom at Dogwood, she said:

"There was an educator, Hark Hopkins, who once said something like, 'if you're at one end of the log, and I'm at the other, I can learn.'"

Though the tempos, in layout, are an almost exaggerated version of the traditional classroom, which has been criticized for making learning a passive experience, Mrs. Thompson says Terraset students do just as well as students in the open classrooms.

In Mrs. Morgan's first-second grade, the students, asked what they dislike about their one-room schoolhouse, list two things on the board: it is hot and smaller than the big school, which they use for some special classes, gym and lunch.

Under "likes," one student lists "party" - she can make noise and won't bother another class.

In new, open "classrooms without walls," noise has led school officials to break up the openness by cracting more partitions.

Hundreds of Fairfax students spend most of their day in the 158 tempos parked at overcrowded schools. There have been no evaluations of how the buildings affect education.

Terraset fourth-graders ranked higher than the countywide average in standardized test scores, but the tests were given in early October, just weeks after their experience in the tempos began.

Mrs. Thompson says a trailer/schoolhouse has some advantages for teachers: "I found a nest-like quality, closer relationships, simply by virtue of the geography. I had freedom of movement I was not tucked into the master building . . . I enjoyed it. The single most important factor was autonomy."

Reflecting the still unsettled philosophy about open classrooms, the new Terraset, which Mrs. Thompson had a major part in designing, will atempt to capture the advantages of both open and closed classrooms - its half and half.

The purpose of the two-way layout, Mrs. Thompson said, "is to provide for those students who, in our opinion or the parents', need reduced stimulus - auditory or visual."

Many of Fairfax County's tempos have been added at a time when the school-age population is declining. But the decline has been more than offset by growth in the rapidly developing western part of the county. The need for classrooms there is running against the trend in the older sections, where some schools are underenrolled, and even being closed.

"Unfortunately, you can't pick up a school building and move it to a place where it's needed more," Col. Paul E. Cevey, chairman of the County Council of Parent-Teacher Associations, said.

Fairfax's practice, school officials said, has been to "build schools when they are needed." But that practice has run up against a new political reality. The constituency that can be counted on to vote for multimillion-dollar school-construction bonds is shrinking. In fact, only 43.5 per cent of the county's residents are now parents, down from 60.7 per cent in 1974.

Tempos are not likely to disappear soon, according to Cevey. "With the present mood of the taxpayers," he said, "I think they are going to be around for a long time to come."

The new Terraset school, though it has not yet opened, may be overcrowded as early as next September. If that happens, tempos may have to be stationed at the school, but they are not likely to be solarheated.