Defense Department officials and state educators are joining forces to encourage people soon to be mustered out of a downsized military to reenlist in the nation's teacher corps.

Education officials from several states are counting on recruits from the military to counter a shortage of mathematics, science and vocational-technical teachers. Many military personnel have scientific or technical backgrounds and have experience teaching in training programs.

Christopher T. Cross, the Education Department's assistant secretary of educational research and improvement, said the programs would be geared to noncommissioned personnel as well as officers. Nearly all military officers have a bachelor's degree, a prerequisite for public school teachers.

"A terrific match," said Cross, who has helped bring educators and Pentagon officials together to discuss career transition programs.

To the extent that the match gets made, the Defense Department stands to soothe the resentment of thousands of troops facing "involuntary separation" from the military, an issue Pentagon officials are reluctant to discuss.

"A lot of these people are angry," said Jim Pirius, a Florida education official.

Florida, home to 32 Navy and Air Force bases, has the most developed plan for placing ex-military people in the classroom. The state is scheduled to sign a formal agreement with the Army later this month. Other states talking about similar programs are California, Texas, Indiana, Alabama and New York.

Lenore Saltman, deputy director of education policy at the Defense Department, said her office would soon send a list of state teacher certification requirements to military installations worldwide. "What we would like to do is get more information to service members . . . make them more aware that there might be opportunities in teaching," she said.

Saltman also said it was possible that the military services would expand education courses offered by colleges at some bases. These existing programs, which date to the 1980s, have been geared toward military personnel who are about to retire, often in their mid-40s, and who plan second careers as teachers.

The limited evidence available about these programs suggests relatively small numbers of ex-service members can be expected to become teachers, in part because they discover schools to be quite different from military posts.

"We're not estimating huge numbers of persons here. . . . We're talking about numbers that may be in the hundreds," said Gordon Ambach, executive director of the Council of Chief State School Officers. "But every new math-science teacher who is qualified is going to make a difference at that school."

Jay Shotel, an education professor at George Washington University, said its teacher education programs in Crystal City and Hampton, Va., have prepared 40 to 50 retiring military personnel for the classroom since 1985.

"The culture of the military is very different from the culture of the school. . . . It's a tremendous transition," Shotel said. "The discipline factor is different. You're not obeyed because you're of higher rank."

Shotel said the program's first course requires students to spend 30 hours in schools, and some prospective teachers drop out then because they are turned off by students with "spiked hair" and other nonconformist behavior.

In September 1986, then-Education Secretary William J. Bennett and then-Defense Secretary Caspar W. Weinberger announced a joint initiative to encourage military retirees to pursue teaching careers. Education Department officials said more than 9,000 copies of a brochure, "A Second Career for You," were sent to military bases and individuals in response to inquiries. But no follow-up has been done to find out how many retired military people have actually entered the teaching force.

State education officials are hopeful their active planning in anticipation of the military's downsizing will prove more fruitful.

Pirius said Florida's education department has already referred about two dozen military personnel to various school districts with job openings. He said the Florida project recorded its first hire on July 30, when David McDowell, a former Army captain and a math major in college, signed on to teach emotionally handicapped pupils in Nassau County near Jacksonville.

While Pirius conceded the project to recruit ex-service members would not solve the state's shortage of math and science teachers, he said that "down the line, it could have considerable impact."