The way D.C. School Superintendent Vincent E. Reed envisions it, the students who graduate from his proposed model high school would have taken more math, science and social studies courses than most students in the school system. They would get a working knowledge of at least one foreign language and a classical language.

They would know what it's like to take college-level courses, since several advanced courses such as fifth-year calculus and chemistry would be offered.

The youngsters also would be expected to devote their after-school time not to athletics or other extra-curricular activities, but to working late in the school's science labs and library, or working at a school-related job in the community.

The model high school is Reed's way of helping public school students he believes are bright and motivated but may not be sufficiently challenged by the current high school cirriculum. Reed hopes it will also stem the flight of city youths to private or parochial schools.

"For years . . . we haven't been doing anything for our bright kids," Reed said in an interview.

Reed said he hopes the additional emphasis on math and science would help students achieve high scores when they take their college entrance exams. Last year, District students had the lowest college board scores of any Washington-area school system and placed in the bottom 20 percent among all students taking tests nationwide.

Such statistics have driven many middle-class youngsters to private schools. About 17,500 city students attend private schools and parochial schools. The enrollment in public schools in 113,050.

This is the second time in two years that Reed has promoted the idea of a special academic school that would offer a more rigorous academic curriculum and serve as a sort of college prepartory school.

But the proposal proved unpopular the last time with the parents of good students who felt it would drain neighborhood schools of their brightest students. Parents from the city's low-income neighborhood branded the proposal as "elitist."

Much of the proble with the first proposal stemmed from the location that school officials had selected for the academic high school -- a generally wealthy, white neighborhood in upper Northwest.

Students were to gain admittance to the school on the basis of their test scores. Youngsters living in the area of the school were to be given preference over those from other parts of the city. Several parents from the upper Northwest corridor worked on the proposal with school officials.

Some of the same arguments against it have cropped up again.

"I just wonder what a proposed model high school means with respect to the other high schools in the city," said board member Eugene Kinlow. "How soon will we have to wait until all other high schools become model schools?"

He said he is not opposed to having special academic programs within existing schools, such as the advanced math-science program at Ballou High School in Southeast and the Ellington School for the Arts in Northwest.

"We are so afraid in this city of providing for excellence that we don't do anything. We're so afraid of being called elitist," countered school board member Carol Schwartz.

High school principals in the city also are divided over the concept.

"It can't help but take away some of our good students," said Otis Thompson, principal of Calvin Coolidge High School in upper Northwest.

"I like the idea," said James C. Queen, a vice principal at Woodson High School in far Northeast. ". . . A lot of times, high academic students are intimidated by students who just want to do the minimum." He said he would not expect to lose any students to a new school unless it were placed right in the vicinity of Woodson. It takes Woodson students more than an hour to travel by public transportation to most other sections of the city, he said.

The model school would be different from the "School Without Walls," an alternative high school program within the city's school system.

The academic school would offer a more structured curriculum, with students taking mostly the same courses with few electives. School Without Walls permits students to concentrate on subjects in which they are most interested and allows them personal freedom in choosing, the ways they want to learn.

For example, students at the School Without Walls sometimes participate in local dance companies or take art courses at the Corcoran Gallery.

This time Reed has tried to cast a proposal that would please both sides. The model school, he said, would have to be as centrally located as possible and easily accessible to public transportation.

While some school officials have said the model school would be for "average and above-average students," Reed said he would be willing to accept any student who shows high motivation and is already working at grade level or above in reading and math.

Once in the school, the students would be required to maintain a certain grade average or they would be asked to leave, the superintendent said.

Reed said he is concerned about the number of electives that high school students are now permitted to take. That is why, he said, the model school will offer fewer electives, and will require at least two years of mathematics and science, and four years of social science instead of one year for each of those subjects.

Students also would take three years of a modern language and three years of a classical language, such as Latin. There are no language requirements in city high schools.

The model school probably would be located in an existing school building that is not now being used. It would serve from 700 to 900 students, Reed said.

Students who apply for admittance to the school would write an essay on why they want to attend that school; submit three recommendations, undergo interviews with a peer group and the school's staff; and sign a "contract" stating their willingness to participate in the entire school program.

The youngsters also would be required to work part time in their community or the shool to relieve "the obvious boredom, potential for destructiveness and pent-up energy of teen-agers," the proposal says.

Over the years, the school system has had difficulty steering its best students toward advanced or accelerated programs because of a 1967 court decision that ordered the dismantling of a "tracking" system, based on test scores, that rigidly separated students according to ability.

Reed insists that the model school would not, in effect, result in the "tracking" of bright students to the best programs. He said this is because the school would be open to any student who has demonstrated a certain level of achievement in classwork and wants to participate in a more rigid academic program.

"I say let's get this school going and once we do, we can take elements of this school and maybe set them up in other city schools. Or we could have students from some other city schools attend certain classes at the model school," Reed said.

A few years ago, school board member John E. Warren recommended increasing the number of required courses high school students need for graduation. The shcool system is now considering such a proposal, Reed said. g