THIS BOOK IS a nostalgic sequel to Nat Hentoff's earlier work, Our Children Are Dying, an excellent profile written in the 1960s, of a scholarly and saintly man named Elliot Shapiro, a Harlem slum teacher and schoolmaster with some of the most impressive characteristics to be found in any active educator of the past hundred years.

The present book, while inevitably less moving and less unified in its scattershot approach (the book deals with several decent and enlightened versions of Shapiro - only to wind up with the original Shapiro once again), is nonetheless a very important book on inner-city education and, in particular, the crisis of the New York schools, more than a decade after Hentoff's first attempt.

It will be read - and must be read - by anyone who, in Hentoff's words, does "give a damn" about the desperation of our urban schools.

The book deals with specific schools, specific children and specific bold and charismatic teachers or headmasters. By so doing, Hentoff is able to sidestep in one stroke both the historic (and inherent) problems of the total syndrome of an institution such as public schools, and also to avoid such pressing current issues as desegregation by court order in the Northern schools. This basic decision, on the author's part, proves at once to be his weakness and his strength.

The weakness emerges from Hentoff's refusal to recognize that public schools do not become "bad places" because of "more bad people," anymore than they become heroes such as Elliot Shapiro. Segregation is an institutional factor which destroys and undercuts all serious efforts on the part of even the most impressive men and women whom Nat Hentoff may discover and portray.

Again, institutional patterns of classistratification ("tracking"), assigned to our schools a century ago by no less a pedagogue than Horace Mann, cannot help but render the most vigorous efforts even of the most courageous teachers present in this book at once heartbreaking and naive.

These reservations notwithstanding, Hentoff has produced a book of obvious pragmatic value by his skillful observation of the way schools really "work" in New York City and of the way that certain limited numbers of inventive and unbroken human beings do have the power, if only for short periods of time, to battle against those age-old evils that we know, by now, only too well - thereby to salvage thousands of young lives.

If these people are exceptions, nonetheless they are delightful and remarkable exceptions. Luther seabrook, for example, a New York City principla (now a district superintendent) gets a good deal of meticulous attention here, and comes across - by contrast with his peers - as one of the most brilliant, biting, humorous and ingenious school administratorsever to be hired by the New York Board of Education to subvert its orders and undermine its hopeless patterns of destruction.

Seabrook, whom I used to watch with wonderment in Boston when he led one of the finest free schools in the East, now has enormous power in the New York system and performs - within that system - like a roguish, smiling and nonviolent version of Ernesto Che Guevara; charming, tactful, clever and unceasingly insidious in his efforts to defend the rights of kids against their would-be benefactors.

Above his desk, at IS. 44, on the westide, Seabrook used to post six lines from an unyielding piece of verse by Yevtushenko:

Telling lies to the young is wrong

Proving to them that lies are true is wrong.

Telling them God's in his heaven and all is right with the world is wrong.

The young know what you mean.

The young are people.

Seabrook is a "person" too, rare to find within an urban public school, and rarest of all within the system that still cowers beneath the thumb of New York's unforgiving - and unforgivable - union boss, Al Shanker.

In spite of all, Seabrook manages to keep hold of his optimism, wit and ethical passion the midst of red tape and archaic customs. So too, in this immensely useful book, does Seabrook's sensitive friend within the press, Nat Hentoff.

If there are some words of reservation and of criticism here, they are nonetheless the words of a profound admirer of Hentoff. This is not his best book, and by no means equal to his own best insights into public schools. It is, for all of that, an eloquent and a practical book which every teacher and all conscientious parents will ignore at their great cost.