A vote last week by the University of the District of Columbia board of trustees to raise tuition 29 percent next year has exposed a deep philosophical conflict within the board that encompasses far more than the approved increase in fees.

During 30 minutes of heated debate, five trustees -- including the student, alumni and faculty members -- argued that higher tuition would put the open-admissions university out of reach of the city's poor. But other trustees were equally vehement in saying the increase was crucial to offsetting a $5 million budget shortfall and advancing the university's snail's-pace march toward becoming an independent and self-sufficient institution.

"The question is much bigger than tuition," said former board chairman Ronald H. Brown, arguing for the increase, which finally passed by a 7-to-5 vote. "The question is who we want to run this university. We are about to be preempted as a board. If we don't start being serious, we are going to lose the independence of the institution."

Nowhere was the dilemma over the tuition issue better demonstrated than in the votes of Trustee Thomas A. Hart. On the first round he voted against the increase, saying the board needed to explore other options and to give students a chance to speak out on the issue. On the second round (after receiving an earful from Trustee Peter B. Edelman, who marched around the table to chastise him for his first vote), Hart abstained. On a recount, he raised his hand to be included with the majority in favor of the increase, which will raise undergraduate fees from $462 to $600 next fall.

The trade-off between tuition rates and political autonomy has been a delicate issue for the UDC trustees throughout the school's eight-year history. It has been particularly sensitive since 1982, when the trustees promised the District government that the board would prepare a multiyear tuition plan that would transfer more of the financial burden from the city to the university.

But over the years the combination of low fees and a student population that is one of the most expensive in the country to educate has placed UDC in the undesirable role of beggar. Few public universities depend as much on governmental agencies for sheer survival as UDC does on the City Council, the mayor and the Congress.

Although the tuition increase approved last week would account for only about $1.3 million of the school's projected $67 million budget next year, there is enormous symbolic importance attached to generating revenues internally -- that is, revenues that do not come to UDC via the District government.

While this has been a recurring theme for UDC administrators and the 15-member board during the school's short but tumultuous history, it has reached new proportions in recent months. The resignation of former president Robert L. Green in August, amid allegations that he misspent university funds for a host of personal items, brought to the fore new questions about the trustees' ability to manage the university and about the university's capacity for self-government.

The Green affair added insult to injury. Now the UDC trustees are under greater scrutiny than ever before by the City Council's Education Committee, which held a series of hearings this fall, and Mayor Marion Barry, who in picking the majority of board members retains enormous influence over the university.

It was clear at last week's board meeting that some trustees desperately want to prove to their District government benefactors that the university can raise some of its own revenues, pay some of its own bills and keep its own house in order.

"I have been a resister of tuition increases, but I will be voting for this resolution," said Trustee Lorraine Whitlock, who, with former chairman Brown, was attending her last meeting as a board member. "I see no alternative to a tuition increase. It is critical to the future of this university as a university."

Trustee Daniel I. Fivel, chairman of the board committee responsible for financial oversight at UDC, was blunt.

"You are taking a huge risk," he told fellow trustees after the board first voted against the tuition increase. " . . . The mayor will sock it to us. There will be a terrible reaction downtown. Where else is this money to cover the shortfall going to come from? I'm at a loss, even with this tuition increase, to figure out where the money will come from."

One of the board majority's fears is that the taxpayers' patience -- and thus the university's lifeblood -- may run out. The university has been through three presidents since 1976, has the highest administrative costs of any public university in the nation, and spends roughly twice as much per student as the D.C. public schools. Green's alleged misdeeds only served to confirm what skeptics already feared: that public money was being wasted at UDC.

"Somebody is paying the bills and they the taxpayers are beginning to ask questions," said Brown. "We have to face up to our responsibility."

The trustees who voted for the tuition increase said they remain committed to making higher education affordable for all District residents. Edelman and Board Chairman N. Joyce Payne said the lowest-income students will not be affected because they will still qualify for federal Pell grants under the new tuition plan.

"We're between a rock and a hard place," said Edelman, summing up the predicament the board faced. "We don't have the ability to make the choice [for keeping tuition lower] that we would really favor."