Virtually everyone connected with the University of the District of Columbia agrees that it should be an institution that has open admissions but not open graduation, that can attract the brightest graduates of the D.C. public schools while still providing a chance for a college education to those who enter with poor basic skills.

But how the university gets to that point from where it is now--a school where most students must enroll in remedial courses and where honors students complain that they are bored with many courses--is the subject of a wide-ranging debate at UDC, the city's only public university.

"What we do here in the next year will make or break the university," said Benjamin H. Alexander, who took over as UDC's second president last August with a mandate to improve standards and to change the university's image as a school of last resort.

Alexander has moved quickly to introduce changes. He and the university's board of trustees began enforcing a policy of suspending students who do not maintain a 2.0 or C average. Alexander also has proposed dismantling the "university college," which oversees remedial classes and offers students tutoring and counseling service.

"The students who cannot maintain a 2.0 average after they receive remedial training and other support services should be channeled into other career opportunities," Alexander said in part. "I believe all men are created equally, but not all men are created equally smart. Some are to be nuclear physicists . . . while others are to be automobile mechanics."

Others, including faculty members and trustees, say the main mission of UDC should be to continue serving the educationally and economically disadvantaged. They argue that even more remedial courses and tutoring services are needed.

"We have to create an environment where UDC becomes the institution of choice rather than necessity," said Ronald A. Brown, chairman of the board of trustees. UDC must do more recruiting in the public high schools and in private schools to attract better students, Brown said.

Marjorie Parker, former chairman of the board, said she believes the university should offer every area high school valedictorian a four-year scholarship.

Many of the problems the university faces today stem from its unusual history. UDC was formed five years ago from the merger of three institutions that had different missions and diverse faculties: Federal City College, a four-year liberal arts, open admissions school, Washington Technical Institute, a two-year vocational college with open admissions, and D.C. Teachers' College, a four-year school that had admission requirements.

Unlike most public universities, UDC serves simultaneously as a two-year junior college and a comprehensive university. In most state university systems, the two-year junior or community colleges provide whatever remedial work is required before students enter a four-year institution.

"One of the things that hurts us is that we're trying to do all things under one roof," said Wilmer Johnson, president of the UDC Faculty Senate.

Many university officials, including Alexander, agree that one of the school's central problems is the wide range of roles it must fill. But they are quick to add that too much effort and money has been spent in the past five years to change the university's structure now.

UDC has 14,115 students. This year 84 percent of the incoming students were placed in remedial mathematics and 63 percent in remedial English. About 52 percent of the students graduated from D.C. public schools. The rest are graduates of area public and private schools and foreign students. The average age of the students is 27. Wide Array of Services -

The university college is a focal point of the debate. It operates as a central point for students to receive a wide array of services, including testing and placement into remedial or honors-level courses, tutoring, and academic counseling.

The college also provides regular workshops on basic skills improvement and good study habits. The program here is similar to ones in operation at several other public universities.

Alexander, in his recent proposal to dismantle the university college and decentralize its functions, argued that its existence is a "stigma" that is preventing UDC from attracting better-prepared students.

The board of trustees established the university college in 1978 with the idea that the kind of students UDC attracts would need more intensive help and monitoring than that offered at most colleges. But Alexander maintains that not all first- and second-year students need the wide range of counseling and tutoring services now available through the college.

The number of students placed in the remedial mathematics courses has dropped in the past two years from 99 percent to 84 percent; the number in remedial English has dropped from 83 percent to 63 percent.

University college officials attribute that improvement to a refresher workshop they offer incoming freshmen before the mathematics and English placement tests are administered. They also say the university is enrolling more students directly from high school who are more familiar with the skills required on the tests than students returning to school after several years.

"If we work ourselves out of business, that will be fine," said Ewaugh Fields, dean of the university college. "But the fact is a large number of students still needs the services of the university college, and I don't expect things to change much in the next five years."

Some trustees, like former board chairman Parker, say the fact that close to 4,000 students have been expelled or placed on probation this past year for lagging academic performance is evidence that the services of the university college must be strengthened.

But Alexander takes a somewhat different view. "We regretted the necessity for both probation and suspension, but to do otherwise would be unfair to the students who are earning a grade point average of 2.0 or better," he said.

UDC does have some major strengths, like its low tuition, $330 a year. In addition, it offers a wide range of majors, like mortuary science, construction management and environmental science, as well as the more traditional liberal arts and business majors.

There are scarcely any records on what UDC graduates are doing in the world today. But approximately 75 percent of its nursing graduates in the past five years have passed the national examination to be licensed as registered nurses.

"We do have some very good students at UDC; not all are of remedial caliber," said John D. Butler, dean of the college of liberal arts. He cited a letter from a Veterans Administration hospital official calling Nelly Canar, a speech pathology student at UDC who had done an internship at the hospital, "one of the top two or three students I have seen in the past 17 years."

Alexander and other UDC officials say they are particularly concerned that the university is not doing enough for its above-average students.

The university does have an honors program, but it is limited to the freshman and sophomore levels. There are about 75 students in the program this semester--all having placed in the top 20 percent of high school graduates nationally, according to the scores they received on standardized English and mathematics placement tests that all UDC freshmen take. Honors Courses Differ -

What makes an honors course different is the level and quantity of the work. In Professor Renee Hausmann's freshman honors English class, for example, the students read several short stories and are required to write six papers analyzing three novels. They also do a final research paper on a fourth novel of their choosing.

In Hausmann's regular freshman English class, students write shorter papers on expository topics, like the effects of television, and much more emphasis is placed on grammar rather than literature.

Many honors students say regular-level courses bore them. Deneen Twyman, who attended a Prince George's County public high school, recalled how she "never read a page" of her freshman biology book, but got perfect scores on every quiz.

One of the proposals Alexander and his staff will soon consider is whether to keep students placed in remedial classes from taking regular-level courses until they have completed their remedial work.

"My freshman courses have no content. I must necessarily concentrate on teaching skills, like reading analysis, clarification of thought," history Professor William Haskett said. Haskett says he has students in his U.S. history class read essays on themes related to history to help them improve their reading comprehension.

"I find myself bored," Haskett said. "But what good would it do me to prepare a splendid course and teach it at the level it demands if I thought the students would be lost?"