The school cafeteria is a microwave oven on the teacher's desk. The nurse's office is a first-aid kit on the piano. The gymnasium is a floor mat. The auditorium is a plywood stage set up in the corner each December for the Christmas play.

In a picture-perfect white clapboard schoolhouse beside a grove of dark green cottonwoods, just below the soaring brown peaks of the Bridger Range, the student body of the Springhill School -- nine cheerful children ranging from second to eighth grade -- is experiencing one of the hot new ideas in American education: the one-room school.

One-room schoolhouses, those humble, sturdy icons of a simpler America, rural outposts where the McGuffey Readers held sway for most of a century, died out years ago -- didn't they?

They didn't. They are alive and well in 1985 -- and enjoying a modest but unmistakable revival.

After declining precipitously for 50 years, the number of one-room public schools in the United States has begun to grow again, according to figures from the federal Department of Education and the Rural Education Center at Brigham Young University.

The education establishment has taken a new look at this historic relic and pronounced it good -- even better, for some purposes, than the consolidated city schools that were all the rage a generation ago.

"The one-room school was the best school we ever had," wrote the prominent child psychologist Bruno Bettelheim in an influential 1981 article that helped spark the new interest.

Educators once again are finding virtue in the elements of one-room education: emphasis on basics, individual instruction and a deliberate mixing of grades and ages so older students help teach their younger brethren -- and learn from repetition.

Montana is a hotbed of the revival. The number of one-room schools here has been growing, slowly but steadily, for a decade. When the school year started this month, the state opened three new one-room schoolhouses to accommodate the growing demand.

Legislatures across the Plains and the mountain West have been rewriting school laws to reverse the consolidation trend advocated by earlier generations of educational reformers. The movement reached West Virginia this month when officials waived the rules so the state's last one-room school, at Auburn in Richie County, could remain open.

Private schools everywhere -- from tiny Christian schools across the Midwest to the fashionable $12,000-per-year academies of uptown Manhattan -- are adopting the one-room concept of a "community" where pupils from different grades are taught together.

Even the nation's newest breed of public school -- the so-called "Harvey Milk" school in New York, set up specifically for homosexual pupils -- is structured on the traditional mixed-grade pattern of the old one-room school.

Numerically, the one-room, one-teacher schoolhouse represents a minute portion of America's public education structure. Brigham Young University in Utah counted 835 one-room public schools in 1984 -- fewer than 1 percent of the nation's elementary and junior-high schools but more than the all-time low, 798, reported by the Department of Education in 1982.

These public one-room schools are strictly rural phenomena -- small red brick or white clapboard buildings with wonderfully evocative names that proud parents have painted over the front door: Two Dot, Hiawatha, Fertile Prairie, Faranuff (all in Montana), Red Willow, Sunny Hillside, Mud Springs, (Nebraska), Pocohontas, Ringthunder, Alfalfa Valley and Twilight (South Dakota).

But school counters have no sound census of the fastest-growing sector of one-room education: small private schools. Rural education scholars say there are hundreds, perhaps thousands, of one-room parochial schools, from the traditional schools run by the Amish of Pennsylvania and the Hutterites of South Dakota to the new fundamentalist academies that spring up by the score each year in the South and Midwest.

Even with the private schools included, however, an operating one-room school is a novelty, indeed a tourist attraction, in most of the country today.

When Franklin D. Roosevelt became president, the United States had 150,000 one-room, one-teacher public schools, with about half the total school population. The number had dropped to 1,500 by the time John F. Kennedy took office and kept dropping until two years ago.

This was the work of educational reformers who demanded consolidation into large central schools that could provide better facil- ities with much lower per-pupil costs.

Almost every state passed laws setting a minimum number of students -- usually 30 or more -- required to maintain a local school. Along with the urbanization of the nation, these laws almost killed one-room education.

But some states with large rural populations resisted the trend. Once considered educationally backward, they are now leaders of the one-room revival. Half the one-room public schools in the country are on the high plains of Nebraska, Wyoming, South Dakota and Montana.

Even in the wide-open rural West, though, the one-room school has been endangered.

The school in Cooke City, Mont., serves a remote, mountainous tri-city area, population 80, and when its last eighth-grader graduated in 1984, the little school faced a life-or-death crisis. Under Montana law, schools can remain open with only one pupil but must be shut down, usually for good, if there are none.

The residents of Cooke City, a tourist town on the northern edge of Yellowstone National Park, were despondent. "We'd been running that same school since at least 1923," said Joan Humison, short-order cook at the Cooke Pass cafe and a school board member.

"And it was important to our community to keep our own school. No town can attract new people if their kids have to ride a bus 65 miles to the next school."

To Cooke City's immense delight and surprise, a new first-grader showed up at the schoolhouse steps in September 1984. This year the student body doubled -- to two.

Cooke City's teacher, Michael Lavrich, a chipper, energetic 38-year-old who has always wanted to teach in a one-room school, likes to involve both his first- and second-grader in projects that combine many academic subjects. On a recent day he put together a joint music, art, science and geography class by having his two students draw colored maps of Montana's rivers while Smetana's "Die Moldau" blared from the record player.

Things are somewhat more complicated here in the Springhill school, where Linda Rice, the school's all-in-one principal, teacher, janitor, nurse, coach, and counselor, has to deal daily with nine students spread across six grades.

"The only thing I'm thankful for is that we don't have a kindergartener this year," she laughed. "I mean, I'd be a fruitcake."

As it is, Rice's teaching day makes her seem like a juggler with nine balls in the air. While teaching two junior-high students Montana history, she spins to her left to help a fourth-grader ("Remember, Jacob, put a period after those abbreviations"), turns right to take a quick peek over a second-grader's shoulder ("Jimmy, you're writing 'd' instead of 'b' again"), then slides neatly back to Montana history without missing a beat.

But the advantages of the one-room situation are evident here. At one point, Rice dispatches a fifth-grader to help that struggling second-grader get his letters right. "Frankly," she noted afterward, "the older boy can use the practice, too."

The big lesson for Springhill's seventh-grader this day is a geography assignment asking which way the rivers of Montana flow: In the arid West, it is never too early to learn about water. It is hardly news that rivers east of the Continental Divide flow to the Atlantic, and those west to the Pacific. But the teacher has a surprise in store: "Did you know that some Montana rivers flow north?"

"Oh sure," the student replied calmly. "They drain into Hudson Bay."

"Now, how did you know that?" Rice demanded.

"I overheard it when you were teaching the seventh-grade last year," the boy replied.

Observing all this is Ralph Kroon, an educator with the Rural Education Center at Western Montana College and an expert on the one-room revival.

"Did you see that boy in the geography class?" Kroon asked. "That's the kind of thing that used to happen all the time when everybody went to one-room schools. They learned their own lessons, and they listened in on everybody else's, too.

"We had one of the great teaching mechanisms ever," Kroon concluded, "and we almost let it slip away and die."