When more than 100 Alexandria public school teachers recently massed before the city's School Board to demonstrate their displeasure with a proposal to link pay increases to performance ratings, Superintendent Robert W. Peebles watched the protest in stoic silence.

After the School Board unanimously approved the measure, angry teachers stormed out of the board room muttering "the board is antiteacher" and "Peebles is a tired old man." The poker-faced superintendent was not moved.

It was the loudest protest that Peebles has heard since he took over the superintendent's job three years ago. But, unlike his predecessor, John L. Bristol, who sometimes seemed to enjoy confrontation, Peebles' style is to let it pass.

Peebles, 57, has learned to balance the difficult act of being both reformer and peacemaker and to work out potential points of contention in private. He says he would rather work with people than against them.

"I think it's silly to have a we and they atmosphere," he said. But he added, "I like being in charge . . . . Sometimes you have to say no. If you don't, you're constantly compromising and that doesn't speak of leadership.

"It's easy to get heady," he said. "I think I have a pretty good sense of myself and my limitations. I try very hard not to take myself too seriously, because I don't like it when I see it in others."

The quiet, almost detached demeanor Peebles shows in public during the board's twice monthly meetings is as deceiving as his soothing private charm. Peebles, say his associates, is a man driven by deep convictions who is determined to get what he wants and is not afraid of a fight.

"Some people are like eagles," said School Board chairman Lou B. Cook, "They soar away, make big, loud crying noises. They have sharp talons and swoop down on their prey, scaring the heebie-jeebies out of everybody.

"And then there are those who are like ducks, skimming along the water, looking like they are floating peacefully," Cook added. "But underneath, they are paddling like hell. That's Bob Peebles."

Peebles is widely regarded as a man who gets things done--quickly, quietly and smoothly, mostly because he defuses confrontations before they start.

His appointment calendar is filled with meetings with small groups of staff. He even holds a monthly news conference with local reporters--whether or not he has anything to say.

"He doesn't like to have people feel angry about things that are happening," said board vice chairman Judith A. Feaver. "On the other hand he is not afraid of confrontation."

Without dissension, Peebles reorganized his central staff so that administrators with overlapping responsibilities work cooperatively and he instituted a tough job evaluation procedure for administrators that, for the first time, denies pay raises to unsatisfactory performers. According to community leaders, he has restored the public's faith in the city's public schools in part by making numerous public appearances.

The son of a school superintendent, Peebles grew up near Boston and received his bachelor's degree from Boston University, a master's degree from Harvard and a doctorate from New York University, all financed by the GI Bill. Peebles took over the $64,260-a-year job as superintendent of the Alexandria school system in 1980. He came to Alexandria, which has 10,500 students, from a similar job in Stamford, Conn., where he was superintendent of schools for five years. The transition was not easy.

During his first month on the job in Alexandria, Peebles began to complain of chest pains, was hospitalized and the following month underwent triple-bypass heart surgery. He had suffered what he describes as a mild heart attack.

"I think I drove myself and I didn't know how to stop. I was running around like a 20-year-old," he said, living like his father, who, Peebles said, allowed the job to wear him out.

Eight months later, after his recovery from heart surgery, Peebles was struck by a car outside his home in the Rosemont section of Alexandria. He fractured his right elbow and left leg. Today, he still walks with a slight limp from the accident.

When Peebles was asked to come to Alexandria, board members were still smarting from problems during Bristol's tenure with school closings and turf disputes with the City Council, which has the last word on the school system's budget. Peebles was hired to be a fence mender and they say he has met that mandate.

Peebles, like all school administrators, says he also learned he would have to be something of an administrative acrobat, balancing budgets, improving the overall quality of education and cutting short the rapid decline in student enrollment. In all those areas fellow educators and community leaders have given him high marks.

This fiscal year, the City Council provided full funding for the school board's almost $50 million budget request, a 2.9 percent increase over last year's budget, which amounts to more than a third of the city's $147 million operating budget. Last week the National Commission on Excellence in Education named Alexandria's T.C. Williams High School as among the 144 best secondary schools in the country.

"What we have done is to establish credibility," Peebles said during an interview in the school system's administration building on West Braddock Road. He attributes his success to planning.

"It's preferable to plan what it is you're going to accomplish rather than respond to the job on a day-to-day basis, as many do and would argue is what should be done," he said.

"The day-to-day pressures are going to come invariably and if you don't take time to think about what it is you want to accomplish over a period of time, you're going to miss opportunities," Peebles said.

City Manager Douglas Harman said Peebles "came in with a different attitude than his predecessor. I think we work as colleagues rather than under some veil of suspicion that someone is going to get an upper hand. It has been a delightful experience."

This year Peebles says he has concentrated on improvement of employe and student performance and community relations. In line with that, Peebles has tightened procedures for evaluating employe performance; reviewed school curriculums and promoted a more open administration than Bristol, who was criticized for his reluctance to venture out of the school administration building into the community.

Peebles toughest battle came last month when the executive board of the Education Association of Alexandria, which represents 85 percent of the system's 770 teachers, turned in a vote of no confidence on Peebles and school board chairman Cook. The teachers said they were responding mostly to an unsatisfactory 3 percent cost-of-living increase and to the Peebles-inspired personnel policies that included the performance-to-salary measure.

"He got caught in a political situation," said EAA President Hazel Rigby, about the 3 percent increase, which was equal to the increase for city employes. "So he choose to come down on the side of the city and chose to satisfy the people who hired him. So I'm split on how I feel about Superintendent Peebles."

Those who work closely with Peebles say that when he is unable to persuade someone--such as the teachers group--of something he deeply believes in, he will simply press it to acceptance like an overly helpful host who won't accept no for an answer.

"He really insists when it comes to something he wants," school board vice chairman Feaver said.

As superintendent, Peebles also has drawn praise from the black community, whose children make up 48.5 percent of the city's public school enrollment.

"I'm impressed. The guy cares," says Lynnwood G. Campbell Jr., one of three black members of the nine-member school board.

In May, Peebles was invited by the city's Northern Virginia Urban League to be the keynote speaker for the group's annual awards dinner.

He took the opportunity to assail President Reagan's use of another report by the National Commission on Excellence in Education, a study that was critical of the nation's public schools.

"The president calls for tuition tax credits, a voucher system and the abolishment of the Department of Education in order to foster competition in education," he told the Urban League gathering. "Such actions in my judgment would not serve well the nation's public schools."

Peebles said Reagan's suggestions would encourage separation rather than competition and amounted to "playing politics."

Later, headlines in the local newspapers said the superintendent had taken on the president. But Peebles, ever avoiding confrontation, disagreed.

"I just feel strongly about these things," he said.