Public high school principals across the nation say their schools have turned a corner and are doing a good job of educating America's youth. The public at large sees the schools as essentially undemanding and problem-ridden, but still managing to prepare young people decently for later life.

Principals contend their schools have tightened standards for discipline and academic performance, but the public continues to feel that schools are beset by drug use among students and other disciplinary problems. About four in 10 parents of students of high school age or near high school age criticize educators for grade inflation, for having unmotivated teachers and for offering a pass-through education.

At the same time, however, despite such complaints, three of every four parents give the high schools favorable ratings for preparing students who go on to college, and two in every three say the schools are doing a good or excellent job at preparing students who go on to jobs after high school graduation.

These are among the key findings of a Washington Post-ABC News poll on education in the nation's public high schools, in which a random sample of 303 high school principals and 1,501 other adult citizens were interviewed.

When high school principals express concern over education problems, they largely refer to budget cuts that have forced them to lay off teachers and eliminate or cut course offerings. The public expresses some concern with cuts in spending, but focuses more on problems associated with discipline.

Differences between the public and the school establishment, as personified by the principals, are often extreme. Asked to grade their own high schools, only one in 16 school principals gives a grade lower than B. But half the public, asked to grade their local high schools, assigns them marks of C,D or F. Eleven percent give an A and 29 percent a B.

The principals tend to blame the public and not the schools for whatever problems exist. Aside from budget cuts, many principals are frustrated by what they see as public indifference to education. More than one-third cite parental or student "lack of interest" as a major problem in their schools.

One expert on education, Harvard Prof. Stephen Bailey, a former president of the National Academy of Education, says that the true story of the public high schools in the United States lies between the views of the public and the school principals.

"I agree with the public that a hell of a lot more needs to be done in the schools, particularly on the standards issue," Bailey said. But, he said, the public has a heightened fear of conditions in the schools that has been "hyped by the media," and the school principals "have inevitably a sense of protection, where they do not want to admit the problems that really exist."

In the Post-ABC News poll, principals downplay problems associated with violence and lack of discipline. They say their schools have established an orderly learning environment where those problems barely exist.

But the public high school system viewed by many Americans is one in which drug use and other disciplinary problems are common. One poll question was this: "What do you think is the biggest problem with which your local public high schools must deal?" Almost half the public names drug use, violence, or the lack of discipline. In striking contrast, only one in 25 principals cited those problems.

Post-ABC News interviewers read a series of statements to principals and asked them whether or not each statement described their school. Parents were read the same statements and were asked if they described the high school closest to them. Again, the differences in perceptions are often stark.

One statement, for example, was this: "Most teachers at that school lose their dedication to their profession and their students after a few years of teaching." Thirty-six percent of the public agree, but only 4 percent of principals agree.

Have the high schools gone back to the basics? The principals say yes, overwhelmingly. Eighty-five percent of them hold that there has been increased emphasis on English and math at their schools in the last few years.

But parents, by 47 to 34 percent, say the high school closest to them has not moved back to basics, and half the parents complain that the high schools are not giving English and math the attention they deserve.

Many parents feel that the high schools have become babysitting institutions where students are sentenced to spend four years. Four in 10 agree with the statement that "too many students are allowed to graduate from that school without learning very much." Only one in 10 principals agrees with that criticism.

Scott Thompson, executive director of the National Association for Secondary School Principals, maintains that schools are improving but that a "communications lag" is slowing public recognition of high school improvement. "It takes a while for the public to understand that the schools are moving in a new direction and putting more emphasis on academics," he said.

Columbia Teacher's College Prof. Dale Mann, who has written on how principals relate to the community, takes the same position. "Schools are suffering a hangover from the heavy duty criticism of the 1970s. It is increasingly out of sync with reality."

While citizens say discipline in the schools is not strict enough, few give school administrators the blame for that. By a 5 to 1 ratio, the public said parents are more to blame than high school officials for a lack of discipline.

But that frustration pales compared to the principals' outcry over money. Inadequate funding is their No. 1 concern, dwarfing other problems. The overwhelming majority report having been forced to make some budget cut in the last five years, with three in 10 saying that cuts have significantly affected the quality of education at their schools. Parents are just as upset by budget cuts.

A substantial minority of principals and parents agree that "it's almost impossible to fire incompetent teachers," but they disagree over a proposed remedy. A 2-to-1 majority of parents say high school teachers "should be required to pass competency tests every few years in order to continue teaching." But principals reject that proposal by 3 to 1, although 23 percent of them say that "difficulty in getting rid of bad teachers" is a major problem at their schools.