In simultaneous demonstrations at the South African Embassy and the Washington Convention Center, 58 teachers were arrested yesterday while thousands of other National Education Association school employes meeting here picketed and wrote post cards to their senators on behalf of legislation that would penalize the South African government for its policies of racial separation and white-minority domination.

The teachers, representing 8,000 NEA delegates meeting at the convention center this week, were arrested in what has been a weekday afternoon protest ritual at the embassy since Nov. 21.

"Our presence here today is a moral statement," NEA President Mary Hatwood Futrell told about 2,000 convention delegates who joined her in picket lines near the embassy. "We cannot and will not stand idly by and watch children suffer, to see their future be denied, simply because of the color of their skin."

Organizers said they would have bused in at least 5,000 protesters but for police requests that they not hold such a large gathering near the embassy at 3051 Massachusetts Ave. NW.

Another 6,000 NEA members held a support demonstration at the convention center, watched the embassy protest via closed circuit TV and wrote post cards to their senators.

Randall Robinson of the Free South Africa Movement said nearly 6,000 demonstrators have been arrested at the embassy or during protests in 26 other cities.