The University of the District of Columbia has always had identity problems. Now, spurred by new trustee leadership, a budget squeeze and a year of scandals culminating in the forced resignation of President Robert Green, UDC officials are asking the broadest questions about that identity since the university was formed in 1977. Should they give up open admissions?

Open admissions, though philosophically a cornerstone of the UDC mission, is intimately related to many of the institution's most persistent problems; that administrators and trustees are willing to address it shows how intractable those problems have recently become. The main one is the catch-22 which UDC's existence embodies. UDC's unique "urban land-grant" mission is to serve those local students who can't get an education sewhere -- those who can't afford it, those who are immigrants or hold down jobs, those whose skills won't let them gain admission to other schools. That has been the purpose of land-grant colleges throughout the country and the century, and it is UDC's essential reason for existing.

And yet escalating money and image problems have showed that UDC cannot function at all unless it also attracts a fair number of the talented students who could go elsewhere -- students who will bring the school some honor and graduate to become prominent, generous alumni.

An internal "planning committee" on priorities, headed by acting provost Sam Sullivan, is looking carefully at ways to hold on to the school's small cadre of honor students, who leave in droves because the university doesn't offer them enough in the upper levels. The difficulty has worsened with UDC's image problems and, even more, with the increasing attractiveness of qualified minority students to selective colleges that are sensitive about their black-white student ratios.

"Those kids could really do good things for us," Sullivan says of the honor students, who comprise about 5 percent of the student body. Among his suggestions is expansion of the school's celebrated applied research center, which gives faculty and student researchers the chance -- and money -- to work on urban policy projects related to UDC's special status.

But open admissions also contributes indirectly to the recruiting problem. Under current policy, any high school graduate can enter UDC regardless of skills; if he doesn't pass placement tests in reading and math, he must take remedial courses at the "university college" before enrolling in college-level courses for credit.

The university college is thus the crucial link between open admissions and institutional viability -- but it is also perennially understaffed and overbooked, staggering from the floods of underprepared students who enter. In an internal eport done before accreditation in 1984, a UDC self-study committee noted the daunting statistics: of 16,000 students who took the placement tests between 1979 and 1983, 77 percent needed remedial work in reading and 91 percent in math. Almost 30 percent of these couldn't be accommodated. And with the university college failing to impart skills even to all the students it graduates, professors at the upper levels find it nearly impossible to insist on rigorous standards themselves.

Ending open admissions would be one way of stemming the flow, and the circumstances are ripe for such a controversial notion to have a chance. One reason is simple timing: the disastrous departure of Green in August coincided closely with the advent of strong new leadership for the board of trustees in the person of Dr. Joyce Payne. Payne's board, surveying the wreckage, has a mandate not just to pick a new president -- whose experience and interests will help determine UDC's direction -- but to rethink the university's entire role and function, and Payne is convening a blue-ribbon panel of high-profile outside educators to do just that. Such a commission's considered verdict could add valuable political ammunition and ballast in the political scuffle that would undoubtedly follow an attempt at major changes.

Another spur is financial. UDC reluctantly raised its tuition this fall, but is still fiscally strapped. The D.C. Council last year rejected its proposed budget for fiscal 1986, recommending that it find ways to "absorb internally" some $3.5 million in cuts. The council appended a list of areas to scrutinize for overstaffing and understaffing, including some -- such as the university college -- that it felt warranted much more money.

Sullivan, acting president Claude Ford, and the trustees must come up with a new budget by April. The effect on the committee, which is also involved in drafting the next five-year plan, has been Gramm-Rudmanesque; things are up for grabs that might never be considered otherwise. And Payne has made it clear, Sullivan and others say, that she is willing to look at the broadest of questions.

Could open admissions be dropped without the complete loss of the university mission? Previous attempts to address the problem as one of image have failed -- UDC's second president, the controversial Benjamin Alexander, proposed in 1983 that the university college simply be abolished because its "stigma" was scaring off able students. Outrage ensued, and the trustees vetoed the plan.

But "being open doesn't mean you have to have a complete and total free-for-all," notes Vijaya Melnick, director of the interdisciplinary Center for Applied Research and Urban Policy and a faculty appointee to Sullivan's committee. Melnick cites the University of Wisconsin, her own alma mater, as a state system that imposes grade or test-score requirements on entering students, but uses the two-year community colleges as funnels for those who don't immediately qualify.

If UDC were to pursue this line of reasonsing and officially no one has even thought that far ahead -- it could lead to another idea frequently floated among trustees and area educators, that of structurally separating UDC's two-year programs from the BA program -- bringing the institution closer to its ideal of "a state education system in miniature."

And yet, on another level, any attempts at conventional "competition" steer UDC back toward the same catch-22. The public university's unique "mission" is to fill the gap left by the other universities in the city, to serve those students for whom it is the only way up and out.

In an article tomorrow I will explore some of the ways UDC may be able to make itself attractive to the top students without forsaking that mission.