The war over the teaching of nuclear subjects in the classrooms of the nation's public schools is escalating. The principal target is a manual entitled "Choices: A Unit on Conflict and Nuclear War," which was prepared by the National Education Association in collaboration with the Union of Concerned Scientists.

"Choices," which was purchased by 2,500 public school teachers and taught in a pilot project in 35 states, has stirred the wrath of Albert Shanker, president of NEA's rival, the American Federation of Teachers. He called it "lopsided propaganda," and President Reagan's preferred periodical, "Human Events," characterized it as "extremely misleading if not false" in its presentation of the relative strength of the United States and the Soviet Union.

Now the administration has joined the battle by way of a blast from Deputy Undersecretary of Education Gary L. Bauer, who writes in the department's newsletter that the material from "Choices" clearly "panders to and encourages fear." He regards it as "leftist indoctrination aimed at turning today's elementary students into tomorrow's campus radicals."

Howard C. Ris Jr., a member of the Union of Concerned Scientists who worked on the book, insists that its only bias is "to prevent nuclear war" and that the views of such hard-line organizations as the Committee on the Present Danger are included. He says reports from the pilot program show that while a preponderance of students come out on the side of a nuclear freeze and de-escalation, a significant number were in favor of the Reagan policy of "peace through strength."

Besides, he points out, the administration is firing back with a manual of its own, aimed at schoolchildren from kindergarten through 12th grade and prepared by the Federal Emergency Management Agency (FEMA).

"Emergency Management Instruction" reflects the administration's upbeat view that while nuclear attack may be the most extreme type of disaster, it is still "a manageable disaster," Ris says.

The FEMA book has been pilot-tested in 22 states and, according to one FEMA official, the agency is awaiting an evaluation study from Far West Laboratories before fielding the manual in "nationwide deployment in public school by September, 1983."

Among the contentions that the Union of Concerned Scientists finds questionable:

"People who happen to be close to a nuclear explosion probably would be killed or seriously injured . . . . Most of the people in the fringe area would survive." (The fringe area is described as "a few miles from the blast.")

And, this description of radiation effects from the "Teachers' Resource Manual" that is provided in the FEMA curriculum:

"The result is somewhat analogous to sunlight . . . . Long-term exposure in one day can be harmful, while the same total exposure distributed over a few weeks produces a nice tan."

FEMA suggests such student activities as visiting a fallout shelter, emergency drills and visiting a nearby nuclear power plant.

Robert McClure of the NEA, who supervised the six teachers "of diverse viewpoints" who composed "Choices," says it is an attempt to "provide students with information." Of the Bauer attack, he says, "It is unfortunate that a high-level member of the Department of Education is so distrustful of teachers."

Bauer comes from a trade association rather than an educational background. He worked in the Reagan campaign on education issues and at the Reagan White House in the Office of Policy Development.

His anti-"Choices" newsletter was his idea and was "cleared through normal channels" in the department. He received several congratulatory calls from friends on the White House staff, and a Washington Post account of his views elicited an "incredible" reaction from the press.

He said over the telephone that he does not think nuclear war policies should be taught in public schools, which are not adequately teaching the fundamentals.

And what did he think of the FEMA pilot program?

Bauer said he had never heard of it. But he said he thinks that teaching children what precautions to take might be a good idea. He is "shocked" by people who do not agree with him that "civil defense is apple pie," something required of the government to "limit the damage if, God forbid, there was a nuclear exchange, accidental or otherwise."

His objection to "Choices" is that it increases the nuclear alarms of schoolchildren.

That the terror of a holocaust has hung over them with or without classroom instruction has been amply documented in several studies. Educators for Social Responsibility conducted a survey of 2,000 students in four states last fall, and it showed that 90 percent think there will be a nuclear war; 87 percent think they will not survive it.

But the administration plainly thinks that just talking about it is dangerous.