It was the first Arlington County School Board meeting in September, only the second official meeting for Superintendent Arthur W. Gosling. School Board Chairman Gail H. Nuckols looked almost apologetic as the board rejected a recommendation from the new superintendent and his staff about moving a school bus stop.

Gosling caught her glance. "Madame Chairman, may I say something?" he said with a broad smile. "The staff has thick skin."

Seven months later, some in the school community remember the moment with laughter and say it is typical of Gosling, a man they describe as a self-confident manager who approaches his job with conviction and research in one hand and pragmatic humor in the other.

Gosling's initiatives thus far -- including proposals for minority achievement programs, teacher incentives such as sabbaticals and the continuation of open campus for seniors during lunch -- have won him both vocal supporters and opponents in the community.

But even those who take issue with his ideas agree that Gosling, who is paid $70,000 a year, is a superintendent who does his homework.

"You don't hold your breath when he speaks in public," said School Board member Dorothy H. Stambaugh. "He's thoughtful; he's absorbed an incredible amount of knowledge about the school system; he can handle the off-the-wall questions and the complicated questions. You respect the way he comes to his decisions, even if you don't agree."

Gosling "seems to do his homework," said Conchita Mitchell, president of the County Council of Parent-Teacher Associations. "He's not defensive. If he doesn't know, he'll readily say, 'I don't know.' "

"I don't like surprises. I don't like to be surprised myself and I don't like other people to be surprised," Gosling said in a recent interview. "Diligence and sweat is the name of the game."

In a county in which 80 percent of the adults do not have school-age children, Gosling said, one of his goals is "to make us as visible as we can be."

Gosling, 49, came to Arlington from Fairfax County, where he was superintendent of Area IV in the southwestern section of the county, a place markedly different from Arlington. The school population of Area IV is twice the size of Arlington's and is about 90 percent white; Arlington has a 45 percent minority enrollment.

When Gosling was appointed, the School Board agreed that he could continue to live in Fairfax until his youngest daughter Laura graduated from Oakton High School this June. Gosling said he and his wife Carolyn sold their house in Herndon last month and are "actively looking" for one in Arlington.

Gosling's predecessor, Charles E. Nunley, was a controversial school leader whose critics said he was not well prepared on issues and remained out of sync with Arlington's activist community. He announced in September 1984 that he would not seek a second four-year term and left the superintendency last June.

In contrast, School Board members, parents and teachers praise Gosling's efforts to reach all parts of the community and the ethnically diverse student body of 14,500.

His entrance into the Arlington community has followed some traditional paths: He serves on the Chamber of Commerce board of directors and the local United Way executive committee and attends the meetings of numerous advisory groups, churches, civic associations and PTAs.

Gosling also has tried some less conventional approaches. In an effort to improve communication -- literally -- with the Hispanic community, he arranged to be tutored in Spanish by the director of the English-as-a-Second-Language program, though he admits the lessons have been "erratic" in the past few months.

In a project begun last month, school officials invite an array of residents -- librarians, PTA presidents, Chamber of Commerce members -- on bus and walking tours of several schools and their grounds. "It seems to me he's acknowledged early on that Arlington is more than the people who come to School Board and advisory committee meetings," said Marjorie McCreery, executive director of the Arlington Education Association.

Members of the Committee of 100, a coalition of civic and school activists, and the Civic Federation said Gosling was candid and thorough in speeches to them, giving frank answers to even the sticky questions on subjects such as the lag in minority achievement test scores.

"If someone says, 'Will you come and speak to us?' I say yes,' " Gosling said. "I usually try to focus on: 'Here is a good school system, and here's why; but we have some problems, and here's what they are.' "

Gosling recently showed he will not hesitate to make a decision that angers the same community groups he is trying to befriend, if he believes it is the right thing to do.

Despite vigorous criticism from residents who said giving seniors open campus privileges at lunchtime would aggravate delinquency, drug use and neighborhood vandalism, Gosling recommended that the board alter a 1983 decision and allow the seniors to have open campus next fall. On March 20, the School Board voted 4 to 1 to follow his recommendation.

"We tried to look as carefully as we could at the gains and the losses. Either way we go, we're going to have some for us and some against us," Gosling said in an interview before the vote.

"We had to ask, at bottom, what is our belief system about what's best for kids . . . . It has to be more than what can you sell, what can you get away with. I personally believe it's appropriate for us to support a senior privilege system," he said.

That decision has earned Gosling some critics, including board member Margaret A. Bocek, who voted against the open campus plan. "Despite the fact that we had serious community opposition to open campus, in the face of all that, he recommended it," she said.

"The community had a deep, strongly spoken concern," said Ed Hilz, chairman of the schools committee of the civic federation. "I'm not sure how much weight he gave to that comment."

Several of Gosling's proposals show his preferred style of management as well as his objectives for the classroom.

For instance, his budget included $130,000 for minority achievement programs but did not specify what those would be.

The details, he explained, will be developed later in cooperation with principals, teachers, parents and staff members.

A proposal to launch guidance counseling for elementary students will work in a similar way, with several schools trying various ways of providing that counseling during a year-long pilot project.

"What I resist is saying, 'Okay, we're going to develop the program in the central office and send our wisdom out to the others,' " he said.

Minority achievement will remain a crucial concern in the next several years, Gosling said, as well as improvements in some school buildings and the continuing cutbacks in federal education funding. He said he wants to make sure that "special" programs such as the performing arts and those for refugee students and the handicapped remain intact. "When facilities get pressured and funds get tight, it's frequently the performing arts that suffer."

While Gosling is emphatically realistic before the School Board -- frequently reminding board members that tests are not perfect, that people are fallible, that no plan can please everyone -- he holds his own work to perfectionist standards.

"I'm not a wilting flower," he said. "I think you have to be aggressive, you have to go after stuff, but in a way that mobilizes talents you have in the system."

What is difficult sometimes, he said, "is finding a way to accept the lack of perfection; it frustrates me when we don't do things the right way. For every question that comes up, I want us to be able to have an answer that's not off the top of our heads. But I know we're not able to do that every time."