All D. C. teachers may vote Tuesday for a bargaining unit to represent them. A story in yesterday's Metro section incorrectly stated who is eligible to vote.

About 42 schools have been designated as polling sites throughout the District where teachers can cast their ballots Tuesday for their current official bargaining unit, the American Federation of Teachers's affiliate, called the Washington Teachers Union, or for the National Education Association's affiliate, called the NEA-D.C.

The WTU has represented D.C. teachers for more than 20 years. Members ousted its longtime president, William Simons, in an election last month. They elected Harold Fisher, an officer in the union, as its new president and swept in an entirely new slate of representatives, indicating considerable disatisfaction with the old leadership.

The WTU versus NEA-D.C. contest has been described by teachers as "intense." Some of the city's 5,700 teachers have called it a "teacher war" that either side could win. Others have expressed disappointment that representatives of the two groups did not debate each other in a public forum in order to establish their positions and intentions more clearly.

Representatives of both groups first campaigned quietly among teachers late last year when the NEA-DC started gathering petitions to force the election. By the end of February, about 2,000 teachers had signed petitions supporting the NEA effort to oust the AFT as their offical barganinig unit.

But in recent weeks representatives have been wooing teachers with activities before and after school and often during lunch-hour. Each group has spent thousands of dollars in radio ads.

The NEA-D.C. is led by James D. Ricks, 42, a former teacher and former member of the WTU, who ran against Simons for president several times without success. After losing to Simons in 1983, Ricks took an extended leave of absense from the school system to help the NEA establish a rival union.

Before D.C. teachers won the right to collective bargaining in 1967, the NEA represented them. The WTU defeated the NEA to become the official bargaining unit and served in that capacity without a challenge until this year.

In recent years in major cities across the country, AFT and NEA affiliates have been vying for teacher support in intense contests.

With 1.7 million members, the NEA, founded in 1857, is the larger and older of the two. Most of its bargaining units are in suburban and rural school districts in the Northeast, Midwest and the South, and more than 80 percent of its members are elementary and secondary teachers, an NEA spokeswoman said.

Most of the AFT's 610,000 members are elementary and secondary teachers who work in large northeastern and midwestern cities, including New York, Chicago, Detroit and Philadelphia. The organization was founded in 1916.

Ricks said, if it wins the election, "the NEA-D.C. will offer teachers top compensation, benefits and working conditions." He said, "Our prospects for victory are very good. It may even be a landslide."

"One of our immediate goals is to establish an educational instructional council . . . to work for teacher improvement, and stay on top of educational issues," said Ricks. "We want teachers to have better and more equipment, thereby giving students a better chance of achieving."

"We represent a new style, a new way and a new approach."

Fisher, 47, said the WTU offers "a new attitude and new energy. We're talking about physical energy, mental energy, creative ideas, creative approaches to some of our problems."

More than 800 teacher specialists, in subjects from foreign language to physical education instructors, have been lost as a result of reductions in force, layoffs and retirement, he said.

Increases in the teaching staff will enhance students' academic performances, he said. "It's all a part of what we hear about our children's test scores. Children learn better in small groups and lower class size. We need more staff people to give individualized attention to students."

Union members may vote between 9 a.m. and 3 p.m. on Tuesday, the teachers' last working day this school year.