Asked what new songs she had learned in school, a Montgomery County student quickly broke into the following ditty, to the tune of "Battle Hymn of the Republic":

We are here for the burning of the school, We have tortured every teacher, We have broken every rule, We have set the school on fire, We have killed the principal, Our truth is marching on !

The student is in second grade.

A senior at Fort Hunt High School in Fairfax County, where arson caused $4.5 million in damages and forced the transfer of 1,750 students, told a reporter last week that vandalism is "the only way" to get back at a school administration that treats him "like a child."

Public school vandalism -- behavior born of the bean shooters and spit wads of grade school children -- has grown to national proportions, linked by sociologists to the complex, often violent ways American students react to school authority.

A Senate report issued by Sen. Birch Bayh (D-Ind.) estimated that public schools in the United States lost $590 million to vandalism in 1977, 40 percent of it by arson.

School-age vandals strike in poor and affluent communities alike, leaving students and parents to chuckle at pranks like simultaneous toilet flushes, but bristle with anger when criminal acts occur close to home.

The burning of Fort Hunt, which led to the arrest of two 18-year-old Fort Hunt students and one 19-year-old Fort Hunt graduate last weekend, outraged both students and adults at the school. Some have threatened revenge against the suspects.

On Tuesday, more than 1,000 Fort Hunt parents crammed into a meeting room designed for 300 and yelled at school administrators who wouldn't promise to rebuild the school. Most residents of the Mount Vernon area, where Fort Hunt is located, remain puzzled about why any student would want to destroy a fine school with an excellent college-placement record.

But according to police and school aofficials, the early morning fire that gutted much of Fort Hunt was not an isolated act of vandalism.

Since last spring, vandals have slashed the tires of a police car in the Fort Hunt parking lot, broken into the library and painted drug graffiti on the walls, ripped the front gates from th school, mashed windows, ruined a carpet with glue, exploded a "cherry bombc in a smoking area, snipped gaping holes in the schoolhs cyclone fence, poured motor oil on a school hallway and cut down the school flagpole with a pipe cutter and rammed the pole through a window in the principal's office.

All of these acts of vandalism, which have perplexed and frustrated Fort Hunt parents, defy easy explanations even by people who have been years studying schools and school violence.

Fort Hunt principal James J. Manning said he noticed that the Vandalism started, soon after the county school system moved last spring to crack down on drug abuse in the schools.

Manning said he has attempted to stop students from smoking marijuana at the school and that the vandalism that has occurred since was caused by student "venting their anger" at the policy.

His reasoning is rejected as simplistic by an American University sociologist who has studied school violence in the Washington area for three years and a social psychologist who works in the Mount Vernon area. They said this week that the Fort Hunt fire can be explained only by examining the national trend of school vandalism and the sometimes confused lives teen-agers lead in the affluent and transient Fort Hunt community.

Sociologist Robert I. David, who has interviewed more than 100 Montgomery County students from kindergarden through 12th grade, said all students understand the power that public schools have over their lives and all -- to some extent -- resent it.

"If a student thinks he is a victim of institutional power, one of the things he can do is fight back,c said David. This fighting back, according to the sociologist, can take the form of passing notes in class, giggling at the class clown, refusing to "fink" (tell) on classmates or vandalizing the school.

David said that student bandals who place tacks on teacher's chairs, make flatulent noises or ram flagpoles through the principal's window do not see their acts as crimes, but rather as "pranks."

When they are outside school, students, especially in affluent suburbs like Montgomery and Fairfax counties, have too much of what David calls "hanging out time."

"The fact that they are the only members of society that can hang out in a parking lot and be rowdy, demonstrates to the students that they are different from everybody else," the sociologist argued. "Students are not expected to be capable of independent thought or action; they are told what to do all the time."

The principal of Lee High School in Fairfax County, William E. Jackson Jr., agreed that public high schools often treat students like children.

"I guess our regimentation can be interpreted as treating the students as children, but then you are left with a puzzle. How else can you control 1,875 students?"

The answer, Jackson said, is to try to create a sense of community in the school, so that a student feels the school has an interest in preparing him for the future and not oppressing him because of his adolescence.

In the Fort Hunt area, where school figures show that one-fifth of the school-age population moves in or out every year, there is no clear set of common values or of community identity, according to Dr. Robert A. Weigl, a social psychologist at the Mount Vernon Center for Community Mental Health.

"Many of the families that have come here came for federal jobs, leaving their roots behind them in New York City, Des Moines, Texas and San Francisco. There is a sense here that outside of their school the kids have nothing in common to react to," Weigl said.

Principal Manning disagreed. "The great majority" of Fort Hunt students share "the same American ideals that have been transmitted from parents to children for years and years..."

A community study, which involved interviews with 117 leaders in the Mount Vernon area, however, indicates many families in the area are over-extended financially, that there is little sense of common values among neighbors and that students have few opportunities to do any work outside school.

"The study shows many students who are too old to babysit and too young to work at anything else," Weigl said.

Students attending Fort Hunt High School may have little affection for the school if they are not interested in academics, according to Weigl.

Manning said the problems at Fort Hunt are not caused by any sense of rootlessness among the student body. It is a product of the "three percent (of students) who you always find fo not want to obey and respect authority," he said.

'If a student thinks he is a victim of institutional power, one of the things he can do is fight back.' It can take the form of passing notes in class, giggling at the class clown, refusing to 'fink' (tell) on classmates or vandalizing the school.