In one D.C. elementary school, a parent said, the children taking American history hadn't gotten past the Revolutionary War by the end of April.

In another school, a parent reported, one teacher regularly makes mistakes in arithmetic problems, marking right answers wrong and wrong answers right and getting upset with parents and students who try to correct her.

D.C. School Board member Conrad Smith, who represents Ward One (center city), said he has met many teachers who speak ungrammatically. On their blackboards, he said, there often are mistakes in spelling and syntax.

"All too often we have teachers who haven't reached the level of literacy that we need," Smith said, "and we have to do something about it."

How widespread these problems are among the 7,000 teachers in the Washington school system is uncertain, but last week the issue of teacher quality was underlined by the graduation of two students from D.C. Teachers College, even though from they failed their required courses in mathematics.

"Our students become teachers," said DCTC professor Joseph B. Thornton Jr., "most of them in the D.C. school system. How in the world are they going to teach what they themselves haven't mastered?

"When nurses make a mistake their patients might die. When teachers make a mistake their mistakes live on to multiply. That's one of the problems of the D.C. public school system."

Smith and other members of the D.C. school board say there is a serious problem of teacher quality that has become more severe since the city stopped giving examinations to new teachers eight years ago. Teachers now are hired solely on the basis of their college records, experience, and an interview.

School superintendent Vincent E. Reed said the number of poor teachers in the city school is small, a view that is shared by the Washington Teacher Union.

"It's just like any profession," said Harold Fisher, the chief field representative. "There are some people who aren't perfect in all the things they do, but I don't think there's a widespread problem. There's never been a profession where everybody is perfect. All you can do is help those (teachers) who need help through in-service training."

Smith angrily rejects this idea.

"The school system's duty is not to train teachers," he said. "We should be employing teachers who are already qualified, who can teach students well. We don't have the money to train the teachers we presently have."

Smith has proposed that all new teachers be required to pass a written examination before they are hired, and the school board rules committee asked Supt. Reed last week to prepare a plan one.

In addition, Smith said, he wants all current teachers to take "a tough literacy exam" every five years and to fire those who don't pass.

"We have a buyer's market for teachers (because of a nationwide surplus)," Smith said. "There are a lot of competent teachers who are unemployed . . . There's no reason to keep the ones with demonstrated deficiencies."

"I don't think it is too much to require our teachers to read and write and spell," said school board vice president Carol Schwartz. "If they feel threatened by that, it's too bad. I don't think we are wrong to demand some minimum competence. Our salaries are decent now."

(D.C. teachers' salaries now start at $11,040 and average about $17,000 for a nine-month school year.)

Fisher said the teachers union is not opposed to a written examination for new teachers provided it is fair and objective and clearly related to teaching skills.

"We're all college graduates," Fisher said. "What does that (sort of test) have to do with doing the right thing in the classroom?

"Everybody doesn't teach reading and math," Fisher continued. "Suppose there's an art teacher who does terribly in math, and he might do badly in English composition and the construction of a paragraph, but his art students do very well. Do you get rid of him because he can't pass your math and reading test?"

Smith rejoined: "If someone is an art or music teacher it doesn't mean she has a right to be illiterate. She should be able to talk to students clearly."

"I don't think we should rely on the validity of a college degrees," Smith said. "We have very poor colleges that are accredoted and very good colleges that are accredited, and even in the good colleges you can get a student who graduates without knowing very much."

Until 1969, Washington had a rigorous system for certifying new teachers that included the National Teacher Examination, which was widely used around the country, as well as its own local test, known as the Franklin exam. However, in the 1950s and 1960s, when there was a teacher shortage, not enough applicants passed the test to fill all of the city's teacher vacancies.

Many of those who failed were hired anyway as temporary teachers, and by the mid-1960s, about 45 per cent of all D.C. teachers were on temporary status, including some of whom had been teaching in the city for more than 20 years.

The National Teacher Exam also came under attack as being discriminatory against blacks because a much higher proportion of blacks failed it than whites.

Smith noted however, that there now is a large teacher surplus instead of shortage. He said the D.C. school board, which has an 8.3 black majority, is committed to using a test that is not discriminatory but does ensure that all the teachers it hires can meet high standards.

Under current board rules, teachers can be fired for unsatisfactory performance even with tenure, but last year, officials said, only 10 were terminated.

Reed said one reason why more aren't fired is the teachers union.

"Once a principal begins to rate a teacher unsatisfactory," Reed said, "the teachers union stands behind him, and the principal is put on trial (to defend his rating in grievance hearings). But that's the name of the game now."

George Margolies, an assistant to Reed, said many principals now are "gun shy" about trying to get rid of a poor teacher.

"Some principals will fight them tooth and nail," Margolies remarked, "but a lot of others will try to live with them, and have some peace in their schools."

Sometimes, he said, new principals will have serious problems when they try to get rid of a teacher they don't think is competent but has received satisfactory ratings in the past.

Fisher said the union defends every teacher who asks for its help, and has rejected arguments from Margolies and other administrators that it try to "weed out" poor teachers.

"We can't prejudge the teachers," Fisher said. "The board hasn't given us the right to hire and fire teachers, and they shouldn't ask to say who's good, bad, or indiffernt. We protect them like any attorney would. Everyone is entitled to his rights under the (union) contract."