For the first time in her life, Brooke Ann Dugan, a senior at Alexandria's T. C. Williams High School, is in public school this year and she's thriving on it. In June, she left the cloistered environment of a string of private schools to seek the "kind of freedom you can find in a large high school" plus a diverse and varied curriculum that enables her to be one of only five students in a Russian language class.

At suburban Virginia's Langley High School last year, Carr M. Donald was skipping classes and cutting school days altogether. "I was messing up completely," he says. His parents put him in St. Albans School for boys in Washington where he's now getting the attention and discipline that he needed to achieve academically.

Dugan and Donald are but two examples of an issue faced by tens of thousands of families throughout the area each year: whether or not to send a child to private school?

It is an issue that families agonize and argue over, often go into debt over, and it is frequently an issue with far-ranging consequences extending to success or failure in college admissions and even a future professional career.

Yet it is also an issue that eludes easy resolution. As the examples of Dugan and Donald suggest, while some students need the extra attention and guidance of a private school, still others can thrive equally in a public school.

"The kid who's really bright and self-motivated and has good study habits can do great things at any one of your good public schools, Walt Whitman, Langley, T. C. Williams McLean . . ." says Richard Jaeger, associate director of admissions at Dartmouth and a veteran of several years of dealing with Washington area schools.

"The kind of kid who flourishes at a private school and who might not elsewhere is your average kind of guy who could get lost in a sea of 800 kids at a public school. The private school will be able to give him a little extra time and attention."

By any standard, there are both public and private schools throughout the area with impressive records.

Bethesda's public Walt Whitman High School, for example, has 29 National Merit Scholar semifinalists - more than twice the number of any school in the area.

But in the private St. Albans, with 14 in a senior class of 62, has the highest per capita ratio of merit semifinalists in the nation.

Alexandria's public T. C. Williams has probably the most diverse curriculum of any school in the area and it has more students taking and passing advanced placement examinations than any other area school. The exams can mean advanced standing or credit in college.

With a vast array of sophisticated lab equipment, a planetarium and a highly trained science faculty, T. C. Williams offers a selection of courses in science that private schools simply cannot afford to match.

"I don't think one would send a son here who had pronounced scientific proclivities. If we have a bias it is towards the humanities," says Jack McCune, a history teacher at St. Albans.

"From the good public school districts we see students at the top of the class who are as well educated as we will see anywhere," says Tom Rawls, Princeton's regional director of admissions for the area that includes Washington and its suburbs.

"One can get a good education at an independent school and at a good suburban public school. And at some of the city schools. We see a lot of excellent candidates from Wilson. When you're talking about public and private schools, it isn't so much the quality of the education, but the approach."

Adds Robert L. Smith, headmaster of Sidwell Friends School in Bethesda and Northwest Washington:

"I guess, rightly or wrongly, the parent with a really bright child knows that child will do well anywhere. But most kids are not in that category and the parents are trying to see they get the best education possible."

Indeed, despite the availability of a first-rate public school education at no extra cost, parents in increasing numbers are paying up to $4,000 a year to enroll their children in private schools.

For some, it is a question of smaller classes in private schools and an ambience that puts a high value on academic vigor and scholastic achievement. Others need the individual attention and extra motivation that many private schools offer.

Many are looking for an insurance policy that they hope will buy admission to an Ivy League college. Still others are refugees from problems of drugs or discipline that plague some public schools. In Washington, many whites are looking for an escape from a predominantly black school system where their children would be in a racial minority.

With the exception of parish parochial schools, where enrollments are down, private schools in the Washington area are enrolling more students now than ever before and many are turning students away or have waiting lists.

The Association of Independent Schools of Greater Washington, which includes most of the better known schools in the area, counts almost 16,000 students among its members this year, a record number and up from 14,700 a year ago.

Even so, that's only a fraction of the estimated 70,000 children enrolled in more than 400 nonpublic schools in the Washington area when Catholic schools, other church-related schools and schools that are not affiliated with any association are counted.

"We have the advantage of being quite selective in our admissions, which means we can fill the school with a variety of kids who can learn from each other," says Sidwell's Smith.

Indeed, so selective is Sidwell's admissions policy that as many as 150 children compete each year for 24 spaces in the school's four-year-old kindergarten. They are examined, tested and observed by a team of psychologists and letters of recommendation are soliciated from nursery school teachers.

At the upper levels, competition for admission to Sidwell is even keener, and for many families whose children are admitted, says one Sidwell parent, the very fact of admission is considered "proof of success."

Some private schools base their admissions policies, in part, on the Secondary School Admission Test, others on interviews and grade records, but in any event many of the private schools start off with a collection of bright children. Not surprisingly, they have a high proportion of Merit scholars and they do well on college admissions tests.

For years, both black and white middle-class parents in the city have been opting for private schools for their children to escape what they perceive to be the chaos of an overwhelmingly poor, black urban school system. Now the trend has taken hold firmly in the suburbs.

"There has been a dramatic increase in the number of applications," said Hugh C. Riddleberger, headmaster of the private Landon School in Bethesda. Most of the applications are from the suburbs.

"Last year we had 48 applications for eight spaces in the seventh grade. We had 24 for the eighth grade and we had no vacancies. They're looking for a school that is hard-nosed enough to maintain standards and to have held to them through some difficult times."

Emphasizing the basics and sticking to the emphasis during the unrest of the late 1960s and early '70s when students were demanding their curriculum be "relevant" is now paying off, many private schools say.

While many school systems added such courses for credit as "bachelor living," most private schools continued to stress the basic academic subjects that appear on college entrance examinations.

"Monttgomery County (public schools) has to do what the people want. We don't," said one headmaster.

Increasingly, says the private schools, they are drawing their students from not only the rich but also from middle-class families who have to pinch pennies to meet tuition payments.

"We're extraordinarily middle-class and it certainly is a financial burden," says Mrs. Robert A. Hemmes of suburban McLean, the mother of a 10th grader at St. Albans.

The wife of a civil servant with the Bureau of Indian Affairs, Mrs. Hemmes said she and her husband ordinarily would have chosen public schools for their children.

But a few years ago their son, Robert, was assigned a teacher in the public schools who they felt was unsatisfactory. So they opted for St. Albans at just over $3,000 a year.

"They're very aware of each child as an individual. They get a fine education at St. Albans," Mrs. Hemmes said. "And there's one other thing. You know at that age peer pressure is so terribly important, and your're not a nerd if you get good marks at St. Albans."

"By and large, the independent schools each have a unique personality," say the Rev. Canon Charles Martin, headmaster at St. Albans. "They have a greater concern for the individual and are able to nurture him into his own uniqueness better than the large public school."

"We also tend to rely more on the basics. We are not so affected by the whims of change. In a world that changes rapidly and radically it is sometimes wise to hold onto that which is abiding, true and good."

Thus at St. Albans there is a mandatory dress code. The boys are expected to wear coats and ties. There are chapel requirements and prayers before and after lunch every day.

"The cannon is fond of telling parents that the school's real mission is not to see than the boys are admitted top the 'Kingdom of Harvard' but to see thaty they are admitted to the Kingdom of Heaven," says McCune, the St. Albans history teacher.

"Of course the cannon realy wants it both ways. The parents, naturally, would prefer the former," he added.

"Here if you have the intellectual capacity to do the work and if you want to go to Harvard, you can go to Harvard," say Bruce Meader, a St. Albans graduate who now directs fund raising and alumni relations for the school.

"You don't fell quite as safe at the local high school," continued Meader, an Arlington resident who sent his two children to private schools.

"I know that Wake field High does a good job for those kids who are very bright. But if you have not developed good study habits, you can get lost at a place like that. When you get lost a school like this, with a student-faculty ratio of 10 to 1, you can't sit in the back of the room and be obscure."

The kind of attention that such a student-faculty ratio can afford has paid handsome dividends for Carr Donald, the former Langley High student who was flundering academically.

"I'm usually at school until 6 or 7 at night. Then I go home and study until midnight. Here, all the teachers, everybody, knows you and they really care. At Langley, sometimes I felt like I was just a number."

Donald's schedule is not unlike that of many other St. Albans students, or, for that matter, student at the other highly selective private schools. After sports and study requirements, there is time for little else.

"For most of our student, this is their life at this particular time. Our program here is so demanding that for them to have independent lives in their own neighborhoods is just about impossible," said history teacher McCune.

While St. Albans and other private schools are often able to save students who flounder in large public schools, it is also true they have a high number of super-achieves.

Lyle Zimmerman, a student at St. Albans since the seventh grade, is one of the 14 National Merit semifinalists and he's aiming for Standford, Yale or Brown next year.

"You'd have to say that the faculty here is very good. They give you really thourough basic training as opposed to going off into esoteric fields," Zimmerman said.

"We have this guy out here named Mr. Ruge. He puts you through a semester of hell, but you really learn English. He really makes you work at it."

(Ferdinand Ruge, and English teacher, has been an institution at St. Albans for a half-century. At 76, he is semiretired but still teaches basic English composition to 10th graders and runs extra classes on a voluntary basis every Saturday morning for students who need them.)

Evan Westwood, another St. Albans National Merit semifinalist, transferred there two years ago when his parents moved to Washington from Cherry Hill, N.J. In New Jersey he'd been in public schools and the real difference of St. Albans is the atmosphere, he says. The academic workload was about the same.

"There were about 3,500 kids in my old school and a lot of them didn't want to be in school. Of course it was hard to teach them. Here there is just a much betterrelationship between faculty and students."