The Washington school system has been ordered by an arbitrator to reinstate a 63-year-old mathematics teacher who was fired last spring on charges of using corporal punishment.

But a school official said yesterday that the teacher, Joseph D. Horton, won't be coming back to the classroom because he was a temporary employe whose contract expired last June.

In a 23-page opinion, filed Dec. 4, arbitrator Louis Aronin ruled that Horton's firing in April was not for "Just cause," as required by the board's contract with the Washington Teachers Union.

Aronin said none of the seven students involved in the incidents at Stuart Junior High School, Fourth and E streets NE, had been injured by Horton. In five of the cases, Aronin said, no physical contact took place, even though Horton had banged chairs on a desk or pushed them toward students who were unruly.

One student later withdrew his charge and said Horton did not hit him, Aronin found.

In the last case, Horton acknowledged "touching" a student on the back with a stapler, but Aronin said this did not amount to using force, which is prohibited by board rules.The stapler was used "merely as an extension of (Horton's) arm," Aronin said.

Yesterday, however, George Margolies, legal counsel to Supertintendent Vincent Reed, said that even though the incidents were "not enough to get (Horton) fired, any one of them would be enough not to rehire him after his contract expired in June)."

Margokies said the school board would give Horton the pay he missed up to June 30, as required by the arbitrator, but nothing more.

"We don't think he has any greater right (to be rehired) because of the decision of the arbitrator than any other temporary teacher," Margolies cantinued. "A lot of temporaries aren't rehired, so if it's questionable in any way, why give him another year in the classroom?"

Before he was fired by an assistant superintendent in Apprill, Horton had taught mathematics at four Washington junior high schools in the previous five years.

He said he had taught for 32 years in Easton, Md. and Baltimore and was fully licensed in Marylandl. Horton said he worked in Washington only as a temporary teacher because he lacked two courses that the Washington school system requires for certification. His salary in Washington was $16,000, Horton said.

He said he has been unemployed since he was fired, and has been collecting unemployment benefits of $160 a week for moslt of that time.

Just before Horton was fired in April, parents of five of the seven students involved urged that the teacher be allowed to keep his job. William H. Brown, the assistant superintendent who made the decision, which Reed later affirmed, told Horton their support "does not alter the charges against you."

But Aronin said the parents' letters should have prompted Brown to investigate further.

In their objection to Horton's appeal, school offcials contended the teacher had loslt his right to use the school system's procedures for binding arbitrarion because he had telephoned The Washington Post to publicize his situation. But Aronin ruled that Horton did not lose anny rights as an employe by publicising his case.