For a gymnasium, students at the Field School in Northwest Washington use the second floor of a two-story brick carriage house in the backyard. A city park 1 1/2 blocks away is its only playing field.

Its building, a vintage 1890s mansion at 2126 Wyoming Ave., looks like one of those old Victorian houses that has seen its better days, now slowly being overtaken by a process of genteel decadence. Made-over parlors and drawing rooms with ornate woodwork and cracked plaster serve as class-rooms and a former dining room with a heavy wooden table is an impromptu study hall.

"When you don't have, you just have to make do," says Elizabeth ELy, Field's director who organized the school five years ago after a career of teaching in public and private schools in Virginia and the District of Columbia.

Nevertheless, with 107 students in grades 7 through 12, Field has reached the point in just five year where it turns away half of all students who apply because there is no room.

It is but one of an estimated 400 private or nonpublic schools in the Washington area and it is one of a score or more to have been organized within the last five years. Like most, it is not widely known.

And like most, its long suit is individual attention and motivation, not strictly academics, although that, too, is stressed.

"People are looking for a quality in life. The quality of attention. We take time to talk to individual students. We try to help them assume responsibilities for their studies and for their own lives. Sometimes we scream at them. We badger. We cajole. We try to give them interesting work," says director Ely.

"When you're in a small school like this, you can change. If you see something that doesn't fit your students, you can change it. It's easier than changing a big machine."

With 15 faculty members for its 107 students, Field is a prime example of how a small private school emphasizing individual attention can lure students away from public schools at costs - in Field's case - of $2,500 a year.

Academically, it staff will admit, Wilson High School and Deal Junior High - the schools where most Field students would be if they were not at Field - offer programs that are the scholastic equals or better than what Field has. Indeed, Wilson this year has seven National Merit Scholar semifinalists to none at Field.

Nevertheless, in its five years of operation, Field has now reached the point where it is logging reasonable success in college admissions, sending recent graduates to such institutions as Amherst, Bryn Mawr, Radcliffe and Williams.

Like many of the newly organized private schools, Field lived a hand-to-mouth existence for much of its life.

Many have operated in church basements or in lofts over carryouts, but for a variety of reasons their numbers are swelling.

In the suburbs, parental fears over what they perceive to be lax discipline and deteriorating moral values have contributed to the rise of Christian schools, set up and run in most cases by fundamentalist churches.

"We're trying to retain some semblance of the old American values," says the Rev. John C. Macon, who founded Maryland's Clinton Christian School in 1966 and has seen it grow in 10 years to more than 1,000 students.

Mr. Macon's school was the second Christian school in Maryland when he founded it. Today there are more than 40. In the Maryland and Virginia suburbs of Washigton, there are about a dozen.

In Falls Church, parental concerns over discipline and unhappiness with open classrooms have brought record enrollments to schools like Congressional, a kindergarten through 12th grade institution on a 40-acre campus near Seven Corners.

Cogressional, with 555 students, has experienced a sharp rise in enrollment in the last two years and for the first time has had to establish waiting lists, says headmistress Germine Farrell.

"We have a very structured program. Our students wear uniforms and they are not allowed to cut classes. We stress the basics. That's what the parents like. There is a lot of unhapiness over displine and open classrooms in the public schools," said Mrs. Farrell.

At Congressional, as there are at many of the Christian schools there is a dress code - boys to wear coats and ties, girls to wear skirts or slacks - and students can receive demerits for violations. An accumulation of demerits can mean position or suspension.

By contrast at many public schools, discipline often involves dealing with assaults on teachers, drug use and, sometimes, carrying of concealed and dangerous weapons.

Nevertheless, in National Merit Scholarship competition in Northern Virginia public high school students had 141 semi-finalists compared to 14 for the private schools.

Arlingtons Bishop O'Connell High School, a Roman Catholic school, had eight - more than any other Northern Virginia private school. Of the fundamentalist Christian Schools in the area, only one, Fairfax Christian, had a semi-finalist, while Cogressional had none.

While Cogressional does draw most of its students from Virginia, it sends buses all over the area. Every day they pick up a number of students from Washington, where many middle class parents are seeking an escape for their children from an urban school system that is overwhelmingly poor and black.

For many such parents, the decision to leave public schools, which enroll the overwhelming majority of children - 556,971 - in the area, is difficult. It means a break with a personal conviction that there is a civic responsibility to support public education.

John and Mary Ann Vardaman, for example, have had three children in public schools in Northwest Washington and would have preferred to hav kept them there. But two are now at Maret, a private school on Cathedral Avenue.

"We took our daughter out of Key School two years ago after her teacher left and there were no plans to replace her. They were just going to have a string of substitutes for the rest of the year. Barbara Sizemore was the superintendent then and there was a hirign freeze on. A decision had been made that no vacancies would be filled. The principal told us nothing could be done about it," Mrs. Vardaman said.

A son entered Maret after finishing sixth grade at Hardy.

"We just weren't prepared to face the junior high school. There were fairly well-substantiated problems of discipline and we just felt that when you get such overwhelming discipline problems, you aren't going to get and education."

A third child is currently in kindergarten at Horace Mann, a public school and part of a six-school cluster where a group of parents has been working hard to improve the quality of public education. Mrs. Vardaman said they are pleased with the education that child is receiving.

In the city especially, the beginning of junior high school in seventh grade and to a lesser extent the 9th grade are common exit points from the public schools.

To accomodate those pressures, Georgetown Day School added a high school, the first of whose classes graduated five years ago with 17 students. There were 60 in last year's graduating class and the school is full, says Director Gladys M. Stern.

"We like to think we'ver built a better mousetrap," she said, adding that since the school was founded in 1945, the black enrollment has remained constant at about 30 per cent.

When Ely began putting Field together in the summer 1972 - "I just felt there was a need for it" - she found she had 40 students before she even had a building.

"I put an ad in the paper saying 'new college preparatory school' and by August I had 40 students and I was looking for a place to put them."

Eventually, she found a suite of eight rooms in the second floor of a building on Connecticut Avenue over a carryout and a cleaners. Field School was on its way. The move to the Victorian mansion on Wyoming Ave. came two years later.

"This school is very hard academically, but the stress has been on cooperative education where the students don't compete for academic excellence, but assist each other," said Allie Hardwicke, an art teacher and assistant director.

To keep things informal and to build a sense of community, students and teachers call each other by their first names. Additionally, faculty members are required to host at least two dinners a year and one overnight trip for students.

"We're small enough to do individual scheduling and the kids progress through the school at their own rate. One girl is the only student in a calculus class that meets during the lunch hour and we have four tutors at school during the day for individual tutoring," Hardwicke said.

About 75 per cent of Field's students are Washington residents who were unhappy with the public schools for one reason or another.

Senior Chris Choppin came to Field five years ago from Deal Junior High School.

"I was doing poorly at Deal, fooling around a lot and having fun. My parents wanted me to come to Field, but I wasn't too crazy about the idea," Choppin said.

"Now I'm glad I did. It's small and I got the individual attention I needed to get back on the track."

Now Choppin is getting B grades and last summer won a National Science Foundation scholarship to attend a science seminar at Ball State University in Indiana. He'd like to go to Johns Hopkins next year.

A classmate, Hillary Canty, came to Field from Gordon Junior High near Georgetown.

"I was doing really well at public school, but I hated it," she said. "I never went to class, but I got straight A's. Academically, it's very hard for me now, but I'm learning a lot."