Most of the time, the people who run the nation's big city school systems sum up their problems with one word -- money.

Without funds to pay teachers, buy materials and provide transportation, they say, the best programs and curricula won't make any difference.

So when Boston's acting superintendent Joseph McDonald sent about 3,200 dismissal notices to teachers, coaches and administrators at the end of April, he cited money as the reason: insufficient funds and Proposition 2 1/2, the stringent limitation on property taxes passed in November by Massachusetts voters.

But many educators, parents and teachers in Boston are not buying his explanation.

"Educational costs in Boston are exorbitant and must be brought under control," says Massachusetts Commissioner of Education Gregory R. Anrig.

Anrig and other critics do not deny there is a money crises in Massachusetts schools, resulting from heavy spending cuts necessitated by Proposition 2 1/2. As a result, Boston's schools may have to get by with $210 million next year, $31 million less than this year.

This school year, Boston's school authorities will overspend by $31 million the $210 million ceiling set by Mayor Kevin White. The schools remain open under a court order, but it was not until Friday that White promised to find money in the city budget to keep them operating after this week.

Yet more than earlier financial crises, this one has focused attention on the way big city school systems are operated and has raised a number of questions.

Are some school systems able to maintain adequate programs and instruction at much less cost per pupil than systems such as those in Boston, Washington, D.C., and Cleveland? Are these large systems too big and bureaucratic to serve interests of parents and children? Is there any hope for improving big city schools as long as school affairs are frequently used as a springboard for the ambitions of ward politicians?

And how much of the financial disorder can be attributed to mismanagement, bureaucracy, ward politics, the patronage system and corruption?

As long as money was flowing in from Washington, the statehouse and local taxes, these questions could be pushed aside. But as the reality of deep and possibly permanent cutbacks sinks in, this is becoming increasingly difficult to do.

Talks with parents, teachers, principals and present and former school officials in Boston produce little sense that the school administration is clear on its priorities for educating young people.

"The school committee [school board] has blamed [the crisis] on state mandates, the courts, the mayor, the unions, desegregation and almost every institution except the one most responsible -- the Boston School Committee, " Anrig said in a recent speech.

Anrig compared Boston's school record unfavorable with that of Springfield, Mass., which he praised for strong leadership and good results.

The Boston schools, he noted have one administrative position for every 73 students, compared with one for every 209 students in Springfield. It costs about $1,200 more annually to educate a public school student in Boston than in Springfield. And Boston school spending has grown 2 1/2 times as rapidly as Springfield's in the last two years.

Anrig acknowledged Springfield has less than half the number of students of Boston, but he said the two school systems were similar enough for comparison.

At least half the students in both systems are minorities. Both cities have sizable enrollments of children from poor families, and both desegregated schools under 1974 court orders. Enrollments have been dropping in Boston and Springfield at about the same rate.

Yet ninth grade blacks and Hispanics in Springfield scored higher on comparable reading tests than peers in Boston, and scores of all ninth graders in Springfield were 18 percentage points higher. Springfield's high school dropout rate is half that of Boston's and, despite lower costs, Springfield provides job and work education to a larger percentage of its students.

Boston officials accept only some of this criticism.

Deputy Superintendent Robert S. Peterkin acknowledges "there's no doubt that the school system is in need of management reform . . . we do a lot of business on the basis of past practice." But he said desegregation orders have placed heavier burdens on Boston than on Springfield.

These orders, in addition to requiring racial desegregration, also required costly new programs, such as "magnet schools" which draw children from all over the city.

Peterkin pointed out that Boston spends about $50 million a year providing "special education," such as remedial teaching and service to the handicapped, for 12,000 children.

"I don't regret that we err on the side of help for special needs," Peterkin said. "I bristle on that one, when you consider that we get no help from the state."

As Anrig has acknowledged, Boston also is burdened with an expensive pay contract with its teachers, who have a forceful union. The average yearly pay of Boston teachers is $4,428 more than in Springfield, which accounts for some of the difference in cost per pupil.

However, critics say these factors are not sufficient to explain the city's financial predicament.

In a sense, education in Boston divides into separate worlds. One is that of classrooms, teachers, parents and students. The other is the world of Court Street, headquarters of the school administration, where the ambitions of politicians and bureaucrats are played out.

"Our perception is that if the whole place [the headquarters] disappeared, except for the ordering of textbooks, it wouldn't make any difference, not a ripple," said a department head at one Boston high school. "They have a complex agenda there that doesn't center on kids and education."

From the earliest days of the Boston school system, the first public one in the country, ethnic and ward politics have exerted a strong influence.

As Irish and Italian groups maneuvered for power, school politics became a steppingstone for aspiring ward politicians. When desegregation occurred in 1974, school politics propelled antibusing zealots such as Louise Day Hicks into the national limelight.

Many of these traditions are carried on today. School committee member Pixie Palladino still uses any opportunity to keep the busing issue alive by boasting of her opposition to busing. And Anrig said despairingly in a recent interview that "in my tenure [as state commissioner], there has never been an issue of education raised in a campaign for school board . . . the only debate that has ever taken place has been over the yellow school bus."

Family ties continue to play a role in the ward politics of the schools. Joseph McDonough is acting superintendent. His brother, John, is a member of the school committee. And still another brother, Patrick, is president of the city council, which is now wrestling with Mayor White in a dispute over issuance of bonds to save the city financially.

A recent addition to the school committee is Jean McKeigue, who has emerged as a spokesman for parents. But McKeigue is, as another parent put it, "not your typical Boston mother." Her sister is Kathlee Sullivan Alioto, a former member of the school committee and wife of the former mayor of San Francisco. Both women are daughters of Billy Sullivan, president of the New England Patriots football team.

The seamy side of school politics came out last year with the conviction of school committee member Gerald O'Leary for attempted extortion from a company seeking a $40 million bus contract. O'Leary was sentenced March 11 to 18 months in prison.

Under the Boston system, three members of the five-member school committee can wield nearly absolute power over hiring and policy. There have been seven school superintendents since 1970.

Under court orders issued in connection with desegregation, blacks have moved into many jobs and some principalships formerly held by whites. School committee member John O'Bryant is black, as is Deputy Superintendent Peterkin.

However, whites still dominate the politics of Boston, and they have shown no inclination in the last few years to elect white community leaders with a strong commitment to improve a school system in which blacks make up two-thirds of the enrollment. Large numbers of children of Bostonians of Irish or Italian descent already attend parochial or private schools.

One by-product of the heavy politicization of the school system has been padding of the rolls with custodians, clerks, secretaries and nurses.

"What we're seeing is the results of 75 years of patronage," a white mother of three public school students said. "The system has run out of energy and leadership. It's a clash between the old white patronage system and the new black one, and competence doesn't play a role."

Much of the patronage system seems trivial. A principal, offered two tickets to a benefit sponsored by a member of the school committee, told of feeling obliged to buy them. His school will be closed next year, he will be up for a transfer and buying the tickets seemed the safe thing to do.

Such incidents contrast with the experience of principals and superintendents in schools that have a reputation for good management and quality education.

Newton school Superintendent Aaron Fink says he has never been approached by a school committee member on a patronage matter in 15 years, and Newton South High School principal Van Seasholes says that he has "never once had the school committee say I couldn't hire this person or that." "

In Boston, however, such incidents are common enough to "corrupt education," Commissioner Anrig asserts.

He says he is optimistic about the future only if there are basic reforms. He has announced he will ask the state legislature to place statutory controls on the Boston School Committee if action is not taken soon to correct "unjustifiable expenditures." And he has called on the citizens of Boston to form a "coalition for better schools."

The issue, he says, is leadership.

"This is a democratic system," Anrig said. "If people keep on electing people like they do in the Boston School Committee, then those on the outside -- from the state [government] and the press -- somewhere along the line are going to say, 'Gee, this is a disaster . . . Maybe we should intervene in the democratic process.'"

Until then, residents of Boston will be left with the school leadership they chose.