IN 1971 39 percent of all graduating high school students in New York City were admitted to four-year colleges, and 23 percent went on to two-year colleges.

However, according to a study which broke down these statistics by economic class, the figures were less cheerful than they appeared: Of students with family incomes over $15,000, only 12 percent were tracked into the two-year schools. Of students with family incomes under $3,700, the comparable figure was 41 percent.

That study confirmed what a number of scholars have been telling us now for several years. The public schools are by no means those vehicles of social mobility and of soci-economic fair play which our myth-makers purvey. On the contrary, public education by and large continues to guarantee the economic privilege and power of the children of the affluent, while channeling children of poor people into thse very same lower-paying economic slots which will be vacated by their parents.

David Nasaw confronts head-on this problem of tracking and class stratification in an interesting new Book, Schooled To Order. The work does not break substantially new ground but assembles in an effective manner the piecemeal arguments of those who have written on this subject before him.

The book belongs to the new and broadening genre of class-oriented scrutiny of our public schools. (Samuel Bowles and Herbert Gintis, Colin Greer and Michael Katz are the most prominent examples.) Nasaw draws, in his earlier chapters, upon the words of those who were the founding fathers of the U.S. public schools, Horace Mann foremost among them. Mann's good and idealistic goals are skillfully contrasted with his cynical compromise (perhaps "collusion" is more accurate) in seeking support for his ideas from bankers, brokers, corporate leaders, and those other men who then, as ever since, held virtually unquestioned power in the Massachusetts public schools.

The real advantage of public schools, from the point of view of business, Mann maintained, was that "schooled workers" rapidly learned the necessary habits of "docility and quickness in applying themselves to work," "personal cleanliness," "the economies of housekeeping" - above all, "punctuality and fidelity in the performance of duties."

Business leaders, according to Nasaw, were unanimous in recognizing the accuracy of Mann's predictions. Workers who had been correctly disciplined in the various degrading rituals of public school were both "more orderly and [more] respectful in behavior, "more ready to comply with the wholesome and necessary regulations" of a factory.

For all the radical upheaval of the 1960's, public schools today appear to carry on the function allocated to them in the early 1900s with unbroken stride.

"In 1971," says Nasaw, "42 percent of private university students came from families with incomes over $20,000, but only 11 percent . . . from families with incomes under $8,000."

The public schools emerge, from Nasaw's overview, as not entirely inyidious institutions but rather as curious hybrids: "They do not belong to the corporations . . . . Neither do they belong to their communities." Nasaw's final statements assert that public schools cannot become "truly egalitarian educational institutions without at the same time effecting radical changes in the state and society that support them."

He writes as if he view the latter possibility as unlikely.

The book's chief failings - and neither is sufficient to discredit a significant piece of work - lie in two areas.

First, the author fails to go beyond those whose pace-setting books he quotes repeatedly and, therefore, he adds little to the sense of leverage that we already possessed in 1970. He tells us in an orderly fashion all that we knew before, or else could readily learn from any one of the major books, published in the previous 10 years, to which he constantly alludes.

More important this, however, is the passive, static and acquiescent manner of his own conclusion. He does not extract, from the impeccably accurate history he draws, an urgent mandate for the future. He tells us what it's like but does not choose, or dare, to tell us what might be done to make it different.

In his last words, he says that the public schools continue to be the arena "where the tension is reflected and the contest played out between the promise of democracy and the reality of class division."

He is courageous to close his book on these two frequently verboten words; but no one who has suffered through these struggles for a decade can fail to be disturbed that he does not end up with less exquisite, and more active language. After so many books which tell us of this "class division," it would be nice to find a writer who is willing to take sides.