Many people assume that private schools get much better results with their students than public schools, and it stands to reason that they would. Private schools don't have to worry about bureaucratic regulations. They don't have to take students they don't want and are free to kick out the ones who aren't working or who cause trouble. Private school parents make more money and are better educated than public school parents, and both of these facts influence student achievement. We hear, too, that teaching is much better in private schools because there are no teacher unions or collective bargaining or tenure. So it's shocking to look at the results of the recent National Assessment of Educational Progress (NAEP) math exam and find that, when private school students graduate from high school, they do almost as poorly as kids graduating from public schools.

How can this be so? I've already suggested one possibility in a recent column: Our students don't know very much because they don't work very much. High school students quickly discover that they will graduate from high school no matter how little they do. They also know that a high school diploma will get them some job or admission to some college, even if they are illiterate and innumerate. Since they can get what they want without working, it's no surprise that youngsters in both public and private schools do very little work and achieve at very low levels.

But there are other possible explanations that need to be examined. Private school supporters often paint an unflattering picture of teaching in public schools, where teachers are, they say, immobilized by regulations and teacher unions. Private schools, on the other hand, are said to be more like freewheeling, scholarly academies where teachers can live the life of the mind.

Now, the National Center for Education Statistics of the U.S. Department of Education has produced a study, "Characteristics of Stayers, Movers, and Leavers: Results from the Teacher Followup Survey, 1988-89," that allows us to take a closer look at some of these notions, about public and private school teaching.

Contrary to what we might predict, there is much greater teacher turnover in private and parochial schools than in public schools. Between 1987-88 and 1988-89, 5.6 percent of public school teachers left teaching in comparison with 12. 7 percent in private schools. That 12. 7 percent, if consistent, would give private schools an attrition rate of over 60 percent in five years. In any case, it's more than twice that of public schools.

But how different are public and private schools? One way to find out is to ask teachers who've worked in these schools, which is what the survey does. And while there are differences, the degree to which public and private school teachers agree in their complaints is striking. Take the teachers who gave "dissatisfaction with teaching" as one of their main reasons for leaving the profession:

• 26.4 percent of public school teachers and 22.2 percent of private school teachers complained about inadequate support from the administration.

• 8.0 percent of public and 6.4 percent of private school teachers said there was not enough opportunity for professional advancement.

• 7. 6 percent of public and 3 .2 percent of private school teachers spoke about a lack of influence over school policies and practices.

• 1.3 percent of public and 2.8 percent of private school teachers questioned the professional competence of their colleagues.

• 3.6 percent of public and 7.7 percent of private school teachers complained about generally poor working conditions.

• 2.9 percent of public and 2.6 percent of private school teachers said classes were too large.

It's no surprise that a much larger percentage of private school teachers than public school teachers cited dissatisfaction with salaries-7. 3 percent public and 16 .1 percent private. But the figures on student discipline are surprising: 7.5 percent of public school and 16.5 percent of private school teachers called this a problem.

When people think about the differences in atmosphere between public and private schools, they usually have in mind a contrast as stark as the one between a diploma mill and Harvard University. Public schools, they assume, are bureaucratic, rule-oriented places where no one cares what happens; private schools are institutions where learning is truly valued and teachers are treated like scholars in medieval universities. This survey indicates that, when you question public and private school teachers who have left their schools or left the profession, their complaints are not all that different. 

When people talk about private school choice, there's often all unexamined assumption that private schools are far superior to public schools. The first shock was that NAEP test scores don't bear this out. The second one is that the complaints of teachers who quit or switched schools don't differ significantly between public and private schools. Before we base any important decisions on the presumed superiority of private schools, we need to look at it more closely; it could turn out to be largely imaginary.