Matthew Fraser was a 17-year-old high school senior in a farming town near Tacoma, Wash., in April 1983 when he gave a one-minute speech that he thought would grab students' attention.

It did, and then some.

When administrators at Bethel High School heard what Fraser had to say in his brief plea on behalf of a candidate for student-body vice president, they suspended him. On Monday the Supreme Court will hear oral argument about whether officials at the Scanaway, Wash., school violated Fraser's First Amendment rights when they suspended him for the speech, which contained crude sexual allusions.

The case, Bethel School District No. 403 v. Fraser, puts the justices once more in the midst of a national debate over the proper role of public schools in shaping students' values and controlling their activities. The Reagan administration, in a friend-of-the-court brief, has asked the court to give school officials broad power to limit student speech in order to maintain "an atmosphere of civility" or to transmit "basic societal values."

Fraser's six-sentence speech on behalf of his friend Jeff Kuhlman was rife with sexual suggestion, but contained no profanity.

"I know a man who is firm -- he's firm in his pants, he's firm in his shirt, his character is firm -- but most of all, his belief in you, the students of Bethel, is firm," Fraser, a champion debater, said to the accompaniment of hoots, cheers and lewd motions from his classmates. "Jeff is a man who will go to the very end -- even the climax -- for each and every one of you."

Fraser, now a junior at the University of California at Berkeley, says he used the suggestive approach in his speech, which he dashed off at the last minute when he was called in to replace a sick friend, because "I thought it would get him elected. I thought the kids would find it humorous . . . daring to do it publicly."

Within 20 minutes of making the speech, Fraser was summoned to the principal's office. The next morning, administrators told him his speech had violated a school rule against "disruptive conduct," suspended him for three days and removed his name from the list of candidates for graduation speaker (he won the honor on a write-in vote).

Such controversy was not new to Fraser, who had been battling school administrators since his junior high days, when he published an underground newspaper.

He sought help from the American Civil Liberties Union and took his case to federal court. The 9th U.S. Circuit Court of Appeals agreed with the lower court that Fraser's constitutional rights had been violated. He was awarded $278 in damages plus legal fees.

Bethel asked the Supreme Court to hear the case because, in the words of its lawyer, William A. Coats, "part of the duty of a public school district is to educate students about morality, respect for others, decency and other things, and if the 9th Circuit's decision were upheld, I do not believe the school district would have the tools to do that."

In 1969 the high court extended constitutional protections to high school students disciplined for wearing armbands to protest the Vietnam war. But Coats sees no similarity between the two cases.

"We're not talking about the marketplace of ideas here," he said. Fraser's lawyers "are trying to say the First Amendment protects what is essentially a dirty joke." While that might be true outside an educational setting, Coats said, schools "have to be able to control more than hard-core pornography."

In his brief, Coats warned of the danger of "unelected federal judges destroying the public's expectations of decency and civility in the public schools by placing offensive student speech beyond" the schools' control.

Fraser's lawyer, Jeffrey T. Haley, contends that his client's speech did not "materially disrupt" the educational process and contained language no more ribald than that which students hear daily on television or can read in such classics as "Romeo and Juliet."

Giving schools "open-ended power to ban speech merely because it appears 'inappropriate' to someone in authority," he argued in his brief, would constitute censorship barred by the First Amendment.

"In their zeal to impose on teen-agers Victorian canons of taste . . . the school inadvertently would teach an ugly lesson -- that those in power can suppress the expression of those with whom they disagree," Haley's brief said.

In an interview, Haley said he thinks that there is a proper role for federal courts in such disputes. "If the courts do not on occasion get involved . . . , administrators will have unfettered discretion to suppress the speech of the students any time, any place, any subject," he said.

The Supreme Court's decision to hear the Bethel case may be a reflection of its interest in outlining -- and, some say, expanding -- school boards' powers over students. In a recent example, the court last year gave school officials broad authority to search students suspected of carrying weapons, dealing drugs or violating school rules.

"What you're seeing now is a retrenchment" from the court's views under the late chief justice Earl Warren, said Michael D. Simpson of the National Education Association, which has filed a brief supporting Fraser.

"The attitude that permeated the Warren court was that one of the lessons to be taught to students is that . . . students as well as adults enjoy constitutional rights -- on school grounds as well as off," Simpson said.

"The Warren Burger court, by contrast, views students as something less than full citizens and sees a greater societal interest in restricting the speech and activities of students . . . . "

Others view the case as a chance finally to free school officials from the threat of being hauled into court every time they discipline a student.

Fraser, who has a head start on his planned legal career by virtue of reading Supreme Court rulings on free speech, said he would give his speech again if he had it to do over. "The purpose of the speech was to get him elected, and it worked," he said of Kuhlman, who won by a large margin. Besides, added Fraser, who plans to attend the oral argument, "it's been kind of fun" watching the case progress through the courts.

Bethel administrators also remain convinced that they were right.

"It became an an issue of who controls the curriculum of the school," said Superintendent Gerald Hosman. "Children are sent to school with some expectations from the community. We have a grave concern that the public street corner has been equated with the public school."