John A. Murphy plunged into his job at the helm of Prince George's County public schools one year ago, a would-be missionary from a well-to-do school district in suburban Illinois.

He went from what he calls "fat city" to a county system beset by financial and legal problems, and he immediately took ownership of its troubles, packing his calendar with meetings five nights a week and ordering a car phone so he could do business on the road.

In 12 months, Murphy estimates, he has attended 700 meetings, visited all 175 schools, met about 7,000 parents and the majority of the county's 5,000 teachers.

That sustained activity in the Washington area's second largest school system has not been without sacrifice to his personal life. But it has brought him high marks, even from his adversaries, who acknowledge that he is a man committed to a system plagued by low staff morale and that he is a catalyst in bringing a longstanding desegregation dispute as close to resolution as it has been in years.

Murphy is now hoping that a controversial major magnet school plan he proposed early this spring will be successful in settling that legal squabble and making the school system a showcase for the nation. It's a high-risk gamble with a school system at a crossroads.

"If we can make public education work and work well in Prince George's," he is quoted as saying to a group of parents, "then the nation can be assured that public education will work anywhere."

"He came into a school system that is at best mediocre . . . . He certainly comes across as wanting to improve education," said Thomas A. Newman Jr., spokesman for the county NAACP, the plaintiff in the desegregation suit against the county. "He has certainly been effective in getting some movement in a 13-year-old desegregation suit."

Murphy's magnet school plan has been accepted by the local NAACP and by the presiding federal judge.

Also, Murphy has announced his intention to raise county test scores dramatically and will soon propose a top-level administrative reorganization.

His initiatives have been seen as both innovative and risky.

"He is a risk-taker, if it's something he believes in and he really thinks it can work," said school board member Doris Eugene. "He chooses his risks."

Now, as the county watches to see how well magnet schools will work in a school system that is 57 percent black and historically difficult to desegregate, Murphy acknowledges that his job security is tied to the success of the plan.

"If they [the magnet schools] fail, I'm gone," he said in an interview last week. "I'm the only one taking the risk. That's been my operating style."

Murphy, who comes from an Irish Catholic family in the Massachusetts Berkshires where his father worked in an electronics factory, presents a low-key veneer that belies a driven workaholic.

"My work becomes my avocation. It is my leisure time activity," he said. He does play golf occasionally, but he unwinds at the end of the day by reading historical biographies.

Murphy said he chose Prince George's for precisely the reasons that many superintendents would stay away: 500 square miles of urban-suburban mix; the large number of black students, many from single-parent and lower-income homes; housing patterns that since 1970 have led to resegregation, and, finally, the need for educational improvements in the face of financial limitations.

"I was in fat city and I was bored to death," he said of his previous assignment outside Chicago. In Prince George's, "There's a challenge to make it a far better school system."

He also sees his mission in terms of its effect on the county, how well schools can draw desirable development and high-tech firms. "The future growth of the county relies heavily on what happens to a school system," he said.

Others see Murphy's role in even larger terms: arresting a decline in educational quality as an aging population group without school-age children, both in the county and nationally, becomes less committed to funding education.

Alvin Thornton, a member of the Ad Hoc Committee for Excellence in Education, said that in Prince George's, "The old guard had been around for so long, you couldn't do anything about them. You could simply let the demographic changes take hold of the system and take it downward."

Thornton, whose committee was formed over the desegregation issue, said he will reserve judgment on Murphy's performance. "It's much too early to tell . . . . To the extent he has participated with others to bring [the desegregation issue closer to resolution], he has slowed the downward spiral."

The issue of funding schools has been a point of contention since 1979, when county voters placed severe limits on tax collections by approving TRIM, a property tax cap. That restriction was loosened last year, and the fiscal 1986 education budget of $349 million represents 4.7 percent growth. But per-pupil expenditure in the county, at about $3,100 for the system's 105,000 students, still falls significantly behind those in other area jurisdictions.

Murphy believes there is a fundamental connection between the success of the school system and the community's willingness to fund it.

"It's kind of a Catch-22," he said. "The reason money is a problem is that people are reluctant to support a school system if they don't have total confidence. Once we develop confidence . . . we'll get the financial support."

That confidence, or lack of it, is tied closely to a sense among many Prince Georgians that they must defend themselves against the perception that their county, or its school system, is inferior -- an "ugly sister" reputation that got its name from a newspaper headline years ago.

"It has to do with the image of Prince George's County . . . . The school system is caught up in that image," said school board member Eugene. "Because Murphy came from outside, he can get above that . . . . [He] brought a credibility from the outside."

Murphy was hired on a 5-to-4 vote, with the dissenters arguing that the new superintendent should come from inside the system. Murphy's backers won but suffered some anxiety over how the community would receive their new superintendent, who in 1981 resigned a position in Wake County, N.C., during an investigation of conflict-of-interest charges against him.

He had been charged with hiring a consulting firm for which he had worked and charging personal expenses to the school district. Murphy said he had acted with the knowledge of the local school board. Also, an investigation by state and county officials concluded that there was no evidence of criminal misconduct.

Whatever damage that incident may have done to Murphy's record, it has stirred little interest since his arrival in Prince George's. And there has been no attention paid to the breakup of his marriage since he became superintendent.

Murphy confirmed that his wife Ruth left Prince George's four months ago to return to North Carolina. He said he assumed, but was not sure, that the separation would lead to a divorce. A 10-year-old son, Sean, remains with Murphy, who blames his work schedule only partially for his marital problems.

There's another personal toll he assigns to work: "I could be 20 pounds lighter if I had more time to exercise," he said.

When Murphy is assessed by those who have worked with him, they most frequently mention his personal style.

"He exudes an upbeat confidence," said Jeanne Washburn, president of the County Council of PTAs. "That's been very good for the system, because for a number of years spirits were down."

That confidence is reflected in the ambitious objectives Murphy has publicly announced: for example, moving countywide test scores from near the national average, where they are now, to at least the 75th percentile in four years. He hopes to advance toward that goal by sharpening accountability through a major reorganization that will divide the county into six districts, rather than the present two.

Murphy has overseen the implementation of a strict policy requiring students to maintain a C average in order to participate in extracurricular activities. That policy was approved by the school board before Murphy was hired, but it typifies a hard-line emphasis on academics and discipline that was manifested in his budget, including a proposal -- ultimately stalled by the board -- that students with discipline problems be placed in an alternative high school.

It was Murphy's communication skills and willingness to talk, many say, that pushed negotiations in the desegregation dispute to their present state of understanding.

Murphy says he has opened communications with the staff and, as a result, he says, teacher morale has improved during his year in office. A recent survey conducted by the county teachers union, however, indicates that 47 percent of the 4,350 educators who responded want out of their profession because of low pay, high stress, large classes and discipline problems.

"We shouldn't paint too rosy a picture," said Paul Pinsky, president of the Prince George's County Educators Association, the union. "He has gone out and sought contact with teachers, and they appreciate that. A lot of people are waiting to see what changes he'll bring to their day-to-day experience in the classroom."

Murphy is also known as a slick public relations man. He is planning a pep rally for all school employes Aug. 22 at the Capital Centre, an event that has been met with enthusiasm and cynicism by teachers.

His public relations skills were also evident this spring, when a court-appointed panel called for extensive busing and school closings as a means of desegregating schools. Murphy put together a traveling slide show highlighting the unpopular recommendations and took his show to parents, government officials and community groups. In the meantime, public outcry grew against the report by the "Green panel," headed by Robert L. Green, president of the University of the District of Columbia.

"The school board took some cheap shots at the Green Report, and I wish Murphy had prevented that," said Robert L. Crain, a member of the expert panel. "But that sort of thing is so common in desegregation cases that no one should take it very seriously.