The Washington school system has fired a 62-year-old junior high school mathematics teacher for using corporal punishment on his students even though parents of five of the seven students involved had urged that he be allowed to keep his job.

The fired teacher, Joseph D. Horton, of Stuart Junior High at 4th and E streets NE, acknowledged "touching" two of the students on the back with a stapler. But he vigorously denied hitting or hurting any of them.

In turn, Horton said that many teachers in the four junior highs where he has taught since 1972 do use corporal punishment despite a D.C. school board rule against it and denials by school officials that hitting students is widespread among the city's 6,8000 teachers.

Since September, 20 parents have signed formal complaints with the U.S. attorney's office, charging teachers with assaults on D.C. school children.

Many of the cases have no merit, said Assistant U.S. Attorney James N. Owens, chief of the misdemeanor section in D.C. Superior Court. Some of the teachers, he said, "in some fashion admit their guilt."

"Mostly, these are teachers who are pressed beyond endurance." Owens said, "and being very human they just lash out. It may have been a child calling them all sorts of vile names or being very provocative.

"I don't charge them," Owens continued. "I understand the circumstances, particularly if the teachers come in and admit guilt . . .As a general rule, the parents don't want the teachers locked up. The teacher makes an apology, and that's it."

Owens said that in the fall of 1975 he had one teacher arrested "for the first time in recent memory" for striking a 16-year-old student in the eye.

Eventually, the chargewas dropped. Owens said, after the teacher took part in a pretrial diversion program for first offenders.

Although there was no publicity, Owens said the Washington Teachers Union "got the word out," and assult complaints by parents dropped from about 50 a year to almost nothing.

"The teachers just kept their hands off the kids," Owens said, "Through the spring of 1976. Now it's creeping up agains."

On one of the charges against Horton, Owens held an informal hearing after a parent's complaint, and found "probable cause" that the teacher "did willfully strike (the student) on the hand with a round stick of indeterminate length,"

But Owens said he decided not to prosecute "in view of the nonmalicious nature of the offense" and because there was no physical injury.

After Horton was fired last Wednesday, Mary Yarborough, the parent who brought the charge to the prosecutor's office, said she was "sorry" the firing occurred.

"I told them (at the school) that I didn't want him to lose his job," Yarborough said. "I wanted him to know that he's not supposed to hit my child . . . I think it was a misunderstanding between my son and Mr. Horton. Since then things have changed and they get along just fine. I don't have complaints about him whatsoever."

Horton has taught in Washington for the past five years after 32 years of teaching in Easton, Md., and Baltimore.

"I'm sorry Mr. Horton got fired," said Hoyt Smith, whose son was one of those Horton was accused of hitting.

"My son said Mr. Horton hit him, but it wasn't anything to get fired about. It didn't hurt him any. My boy said he was throwing some paper.

"I know you aren't allowed to beat them in school any more," Smith continued, "but some of these children need it. I think it should be like when I went to school (in South Carolina): "Whip 'em a little bit with a switch but don't hurt 'em.'"

However, Conrad Smith, president of the Washington School Board, said the rule against corporal punishment here, which dates back to 1918. Should be strictly enforced no matter what some parents are willing to let teachers do to their children.

"What the parents want is irrelevant," Conrad Smith said. "I don't think corporal punishment is necessary to maintain order in school, and I don't think it is necessary to inflict corporal punishment to inspire youngsters to be interested in the learning process.

"The parents have the right (to hit their children," Smith continued. "The problem is that parents have been derelict in their duty and have allowed their kids to come to school as discipline problems.The solution is not to allow the teacher to hit the child. The parents should discipline the child."

In a letter to Horton, announcing that he would be fired, assistant superintendent William H. Brown said that after a conference, he was "not at all satisfied with your explanation as to how these incidents occured."

"In each instance," Brown wrote, "there was some violent movement, involving an instrument, stick, chairs, (or) pounding of tables and chairs. None of these actions seem appropriate in an effort to control children."

In a letter April 11 rejecting Horton's appeal of the decision, Brown said the support the teacher had from parents "does not alter the charges agaist you."

Horton said he now intends to ask city school Supritendents Vincent Reed to reinstate him under grievance procedures in the school board's contract with the teacher's union. Even though firings are kept secret under terms of the contract, Horton telephoned The Washington Post and said he wanted publicity about his case because he had been the victim of "trumed-up charges."

Teachers' union president William H. Simons said the union had the case "under consideration" but had not decided whether to help Horton make his next appeal.

"We tell teachers that there is no defense for them in cases of corporal punishment," Simons said. "There is for self-defense, but when a teacher hits a child, there's no defense."

Prosecutor Owens said almost none of the assault charges field aginst teachers involve "the old-style corporal punishment where children bared their buttocks."

"It's things that happen in a rage after a provocation by students," Owens said. "Generally, it's in the elementary schools - a lot of fourth and fifth graders. They're mostly small kids, the kind who can torment a teacher."

George Margolies. legal counsel to Superintendent Reed, said the school system keeps no central records of how many teachers are firedsuspended or transferred because of corporal punishment.