When a handful of parents, teachers and administrators gathered in Arlington's education center last week to describe the kind of school superintendent they were looking for, the session turned into an educator's wish list:

"We need a superintendent who regularly is open to the public to come in and talk," said one woman.

"A person who has strong employe relations skills," advised another.

"Somebody who can take direction from the board, but still be strong in leadership."

"He ought to be a fantastic PR person."

Later, School Board member Frank K. Wilson agreed that the superintendency of Arlington's 15,000-student system -- a racial and ethnic smorgasbord of students speaking 60 languages -- is a tough spot to fill.

"Maybe the person we're looking for hasn't been born yet," he said.

But amid the varied, and perhaps unrealistic, demands that teachers, parents, students and administrators have expressed for their superintendent, one sentiment keeps bubbling to the surface: Arlington's new schools chief should be comfortable with residents well known for asking pointed questions, seeking detailed information and wanting a role in guiding the schools.

Superintendent Charles E. Nunley, 55, who announced in September that he will resign June 30 at the end of his four-year term, has been criticized by some parents, teachers and School Board members who say he never really learned to welcome Arlington's unique style of school activism.

While they say that Nunley has excelled at some items on the wish list, citing his budget skills and efforts to enhance the schools' reputation in Arlington's business circles, they claim these successes have alienated other groups and left facets of the school system floundering.

"Dr. Nunley has some wonderful attributes in terms of management. He's done some wonderful things in terms of the fiscal side of the school system. However, there's more to education than that," said Wilson. "He's not the instructional leader we need for our school system."

"I think I know what his basic philosophy of education is, and I think it's back to basics. But I don't know how he's going to go back to basics. I don't know where he thinks Arlington falls. I don't know any more than that about what he means," said another School Board member, who declined to be quoted by name.

Nunley declined to be interviewed and would not answer specific questions or respond to his critics' charges. Asked to discuss the accomplishments and problems of his administration, he repeated words of Abraham Lincoln: "I do the very best I know how -- the very best I can; and I mean to keep doing so until the end."

Some of the tensions that have marked Nunley's term are played out in public board meetings. At one recent meeting, he objected to a board member's suggestion that a report on the seven-period day be sent to the teachers' association for comment.

Board member Dorothy H. Stambaugh replied, "But Dr. Nunley, you yourself recommended that we refer it to other community groups. Now they teachers certainly are a community group."

"If you want to classify them that way, you may," Nunley responded. "I wouldn't."

Later, Nunley ended a discussion of the seven-period day by saying, "My kid's already out of school , so I don't really have too much to worry about on this thing."

Nunley later said he meant to express his lack of a personal stake in the board's decision. But to teachers, comments such as those typify a "flip discarding of opinion" on important issues, said Marjorie McCreery, executive director of the Arlington Education Association, which represents most Arlington teachers. In June, an AEA delegation voted "no confidence" in Nunley's ability to manage the school system and treat its employes fairly.

Nunley's remark about not classifying teachers as a community group drew some gasps at the School Board meeting and strong words later from Stambaugh. "I think his comments about the AEA and teachers have been inappropriate. I do not know how relations between teachers and Nunley got to this point. There is antipathy on both sides. Since he is the superintendent, I think it is his role to refrain from exacerbating the situation," she said.

When Nunley was hired by a Republican-dominated School Board in 1981, enrollment was dropping, inflation climbing and Arlington, along with the rest of the country, was beginning to lean toward a back-to-basics style of education.

"There was a feeling in the community that we ought to slow down and assess what we had done," said former Democratic School Board member Ann S. Broder, whose term ended before Nunley was chosen.

In many ways, Nunley fit the philosophical bill. Under his superintendency, the board approved a no-smoking policy, tightened graduation requirements and started to end open campus in the high schools, although some board members say the national current toward rigor in the schools would have brought such changes anyway.

His supporters point out that Nunley initiated monthly meetings with principals and regularly attends meetings of the County Council of PTAs. Several parents who are active in PTAs say they have found him responsive to their requests, even when he disagrees.

Nunley's efforts to court the business community flowered in the popular Adopt-a-School program, in which local businesses agree to sponsor a school, helping with funds and as volunteers.

"It's important to build those bridges," said board member Margaret A. Bocek. In a community in which only 18 percent of Arlington adults have children in the schools, "It's important for the business community to understand the budgetary needs of the school system and the effectiveness of the money that we have," she said.

Others say some Arlington residents, such as parents who do not attend board meetings or belong to Rotary clubs, feel cut off from the superintendent.

"I don't think Dr. Nunley's been visible enough throughout the community to let them know he's concerned about them," said board member Wilson.

Bob McClendon, who ran for the School Board last spring, said, "I don't think he was ever successful in engendering trust in the minority community. That's 99 percent of working with any community."

But "Dr. Nunley did what he was asked to do," McClendon added. "The needs, the mandate and the expectations of the community have changed over the last few years."

With that change has come a different portrait of the person needed to lead the schools. The wishes of various groups that surfaced last week point to a person with wide experience rather than someone to complete an isolated task.

"We are not looking for someone to do a specific job. We're looking for someone with a broad instructional leadership capability," said board member Stambaugh. "We're all looking for the ideal."