APRIL IS THE busiest, if not the cruelest, month for high school seniors. For Kevin Reinstein and Sherri Lykes, each 17, it means finishing up the design of their science experiment, which believe it or not will be carried aboard a NASA space shuttle mission later this year. Meanwhile, their classmate Elbert Harrison, also 17, is pondering the effect of caffeine on the breeding habits of Drosophila melanogaster ("fruit flies," he explains).

Reinstein, Lykes and Harrison all attend the Science and Technology Center at Oxon Hill High School. They are among a growing number of talented American youngsters enrolled in rigorously academic public high schools many of which specialize in mathematics and science.

Fifteen years ago such schools were derided as "elitist" by their critics. They now appear to be a growing fashion -- with two new ones opening in the Washington area next fall, one in Fairfax County, another in Montgomery County. Interest in selective public high schools is so high that officials at the North Carolina School for Science and Math, a state-run boarding facility in Durham, report inquiries from more than 30 states where such schools are under consideration.

Among the states planning or studying the feasibility of selective high schools for math and science, either on the state or local levels, are:

* Virginia: Four regional magnet schools for science and technology are being set up in Fairfax County, Hampton, Lynchburg and Roanoke. Although the schools are being planned locally, the state is providing more than $625,000 in start-up money for the four schools, according to Callie Shingleton, administrative director of general education for Virginia's education department.

* New Jersey: The state is helping finance a science and technology high school in Bergen County, which will open September 1986, and if successful, will be followed by two similar schools downstate.

* Illinois: Gov. James R. Thompson has proposed that $500,000 in fiscal year '86 be earmarked for planning three special residential high schools: one a science/math academy to be located west of Chicago, close to the Fermi and Argonne laboratories; a similar high school specializing in biotechnology in Chicago; and an agriculture high school in southern Illinois. Getting the math/science academy underway is top priority, according to the governor's office. As a selective school for 10th through 12th graders, it will be a flagship for the state's efforts to improve math/science instruction.

* Indiana: A $50,000 study, proposed this spring for a governor's summer school for gifted students, will be, state educators hope, the first step toward establishing a year-round school for gifted students.

* Texas: Gov. Mark White is supporting a $60,000 study for establishing a residential school to augment special high schools for talented students already operating in several urban districts throughout the state. Rigorous Entrance Exams

These new schools are to be distinguished from such famous public college preparatory high schools as Boston Latin, or Philadelphia's Central High, which have been catering to the needs of academically talented students for many years (Boston Latin was founded in 1635). Neither are they specialty "magnet" schools, open to anyone with the particular interest stressed by the school. They instead have rigorous entrance requirements -- examinations, grade-point standards, and often interviews -- and are designed to serve the very brightest students who have a clear aptitude for math, science or engineering.

Their current fashion, say those who are planning them, is partly a reaction to the reports criticizing mediocrity in American secondary education; a greater interest in improving services for gifted students; and a perceived need to beef up American education in technical fields.

"It is now evident that the scientific and technological preeminence long enjoyed by the United States is threatened," warns a pamphlet about the North Carolina Governor's School. "Unless we act quickly and decisively, the next generation of Americans will lack the educational means to participate competitively in the world of technology they will inherit."

The science/math high school is "an idea whose time has come," says Callie Shingleton. "Now is just the beginning of a trend." Finding Role Models

THE SCHOOL WHICH serves as a model for many of the new institutions is Bronx High School of Science, founded in 1938 and serving a student body of 3,150. The alumni list includes three Nobel laureates, and over the years the school has produced 95 finalists in the Westinghouse Talent Search, a bench mark of any school's excellence in science. BHSS, which boasts the most racially and ethnically varied (16 percent black, 19 percent Asian) student body in New York City is presided over by Principal Milton Kopelman, who came to the school as a substitute teacher in 1949 and went on to become the biology department head before being named principal five years ago.

Kopelman is visited in his pine-paneled office, which is stuffed with trophies his students have won in everything from debating to soccer (they were Bronx champs last year), by emissaries from other states and even foreign countries seeking to emulate his school back home. Already he's had visits this year from British, Filipino and Korean educators.

And he's an enthusiastic salesman for the kind of education Bronx High School offers.

"When the kids are selected as they are here (by examination and principal's recommendation), you get a synergistic effect where the whole is greater than the sum of the parts. Things happen in the classroom that are tremendously exciting," he says. The curriculum, which requires a core of science (biology, chemistry, physics), math (four years), English (four years), social studies (four years) and foreign language (three courses), also features a wide array of advanced electives such as robotics, human genetics, telescope making or plant physiology.

"To get it all in, we have a nine-period day," says Kopelman. Some students skip lunch and have a 10-period day. "They may eat a sandwich in the lab or in math club. All they need is a note from home to eat on the fly. So the place is a mess," he shrugs. "We have a few roaches. We call the exterminator."

It's all part of being a school popping with intellectual vitality. As the quotation from John Dewey inscribed in a huge mosaic at the school's entrance says, "Every great advance in science has issued from a new audacity of imagination." Gaining Community Support

PERHAPS ONE REASON for the current popularity of science/math high schools among educators is the support these schools have from their communities. James Hunt, the governer of North Carolina who pushed hard to establish the state boarding school for math and science, encountered little opposition to the idea of a school which costs state taxpayers $8,000 per student, or $3.2 million per year to run. And Fairfax County's Thomas Jefferson School for Science and Technology, when it opens next September, will have been the beneficiary of over $1 million donated by county businesses. AT&T Communications, for instance, is the main sponsor of a telecommunications laboratory at the school, while Hazleton Laboratories is the prime sponsor of the life sciences and biotechnology laboratory. Both companies are part of a business coalition responsible for most of the school's fund raising.

In Norfolk, the High school for Science and Technology which will open next September, has been adopted by NASA, and the North Carolina school owns an electron microscope donated by Duke University, which is only part of the $8 million in money and equipment from universities and businesses in North Carolina. It's hard to conceive of that kind of support for, say, a high school for English and history.

In many of the schools, the courses offered are tailor-made to the needs of research and high-tech industry. Fairfax County's school, when it is fully established, will include 12 laboratories in high-tech fields including electro-optics/fiber optics, telecommunications, computer system design, and computer-assisted drafting. Prince George's County science and technology centers at Eleanor Roosevelt and Oxon Hill high schools both emphasize the hands-on skills needed to handle techical development. Students there must take courses in "exploratory technology," a sophisticated version of "shop," in which they manufacture objects from various materials. A similar course exists at Bronx High School of Science.

Of the states where selective high schools are in the pipeline or recently established, Louisiana is notable for emphasizing the arts along with science. (Fairfax has no specific plans for the arts in its school but will wait to see what students want). The Louisiana School for Mathematics, Science and the Arts was established in 1983 in Natchitoches. Director Robert Alost, who had a hand in planning the curriculum, says he visited 18 different selective high schools. "We wanted to present the total curriculum. And we have students who excel in all three areas." Who Goes to the Schools?

THE COMPETITION for admission to these special schools is nearly as fierce as the fight for entry to an Ivy League university. Fairfax County had nearly 1,200 applications from eighth graders last fall for about 400 freshman slots at its new science and technology high school. Prince George's County receives about 2,000 applications a year for 475 ninth-grade slots at its two science and technology centers. And North Carolina has about 800 applicants for the 200 places open each year in its residential School. The competition to teach these gifted students can be even stiffer. When Louisiana opened its school, 2,600 teachers applied for 40 faculty positions.

Admission is usually based on a combination of test scores and grades. Louisiana administers the Scholastic Aptitude Test (the average score for those admitted is 1100) while North Carolina has developed its own mini-SAT. Both Fairfax County and Prince George's use the Differential Aptitude Test, a national standardized test. The North Carolina school invites the first cut of applicants (usually 400) to come for an interview as well.

But there are other factors besides test scores and grades, and most selective high schools make an effort to admit disadvantaged students. Milton Kopelman at Bronx High School of Science is especially proud of the school's Discovery Program, which identifies each year about 100 students, who have come within five points of passing the entrance examination and are on welfare or have English as a second language, and have been recommended by their school principals. They are given an intensive summer program at Bronx High in math, English and library skills.

"Then they are mainstreamed," says Kopelman. "No one ever knows who they are but me."

A few drop out, but most survive, he says. "And one," he says proudly, "was a semi-finalist in the Westinghouse Talent Search this year."

Charles Eilber, director of the North Carolina school, says there is no quota system for minorities or disadvantaged students. "We refuse to bring in non-qualified students just to say we have such and such a quota," he said. "But we do have an informal effort to encourage students, especially in rural areas; we enlist the aid of ministers, teachers, community leaders to help us. And we have private funds to finance transportation when it's needed." The school currently lists its minority population at 20 percent, which includes black, oriental and hispanic students.

Those who do make it into selective high schools find it opens many doors to opportunity -- jobs, college admission, financial aid. The 180 students who will graduate from Louisiana school in June already have won $1 million in scholarship money from colleges across the nation.

"Another of the big advantages of being here is the summer jobs," says Mary Anne McLean, a senior at Oxon Hill High's Science and Technology Center, who has worked as a technician at Goddard Space Flight Center. Her classmate Sherri Lykes, who wants to be a veterinarian, landed a job at the Beltsville Agricultural Research Center, working with sheep. A New Elite?

THERE ARE those who question the desirability of segregating bright students from their more average peers and pushing them to their academic limits. It's a concern that champions of selective high schools are used to hearing. "There are principals and teachers who complain that it skims off the cream. The question is what's best for the students? That depends on whose ox is being gored, " says Donald Horrigan, director of the Science and Technology Center at Prince George's Eleanor Roosevelt.

Whatever the criticism leveled at selective high schools, they appear to be universally loved by those who teach and learn in them. Ethel DuBois, a chemistry teacher at Oxon Hill High School, who teaches several sections filled with "Techies," as the Science and Technology Center students are known, says she particularly enjoys their wit. She wears a lab coat decorated by the students with Magic Marker. Across her back is written, "Caution, Break Dancer."

"They're normal, just brighter, and more motivated than most students. Also, they have more parental support. I've seen more parents in the three years that the tech center has been here than in all my previous years of teaching put together."

"I thought it would be great to be with a lot of people who have the same interests I do," says Bertha Kao of Metairie, Louisiana, explaining why she applied to the school in Natchitoches. Kao, after juggling a "triple major" in math/science, humanities and the arts (she is an accomplished pianist and singer), must now decide whether to continue her education at Boston University, MIT, or Northwestern, all of whom are courting her.

But perhaps Mary Anne McLean a 17-year-old senior at Oxon Hill, best puts her finger on the attraction of such a school. "You don't have to hide your head if you set the curve on a test," she said smiling.