Twenty candidates, including four incumbents and several well-known Democrats and community activists, filed petitions yestersay to run for seven seats on the District of Columbia School Board in the Nov. 8 general election.

The largest group of candidates - five - filed to run for the two at-large seats. Incumbent Therman Evans, the board's current president, has decided not to seek re-election to his at-large seat. Barbara Lett Simmons, the other at-large incumbent, does plan to run again, and she filed petitions yesterday.

Also running for one of the two at-large seats is Frank Shaffer-Corona, a free-lance writer and consultant who has been active in the city's Democratic Party. If elected, Corona, a Mexican-American, would become the first Latino to serve on the school board.

Anton V. Wood, 28, an active member of the D.C. Statehood Party who ran unsuccessfully for the ward six school board seat in 1975, is running at large this time. The other two-at-large hopefuls are Stuart Rosenblatt, 26, director of the Washington local affairs office of the U.S. Labor Party and Afrodita Constantindis of New Hampshire Ave. N.W.

Three persons have filed petitions to run for the ward eight school board seat, representing the Anacostia section of Southeast Washington, where incumbent Julius W. Hobson Jr. has decided not to seek re-election.

Among them is R. Calvin Lockridge, who was elected last year to the D.C. Democratic State Committee on the Open Party slate backed by Mayor Walter E. Washington. The other two candidates are Wilbert Williams of Martin Luther King Avenue, SE and Genevieve B. Artis of 9th Street SE.

In ward two, the Adams Morgan and Mt. Pleasant area of the city, incumbent William Treanor has decided not to seek re-election and three candidates filed petitions to run for his seat. They include Alaire Rieffel, 32, an attorney and president of the Ross School Parent-Teacher Association; Gloria Hand Holloway of Vermont Avenue NW; and Alverta Munlyn of 1st Place NW.

Among the three other incumbents besides Simmons running for re-election is Carol Schwartz, representing war three, the area of Washington west of Rock Creek Park.

Opposing Schwartz wil be Gwendoline Graham Reiss, 48, a real estate salesperson who ran unsuccessfully for the same seat in 1975 and worked in Hilda Mason's City Council campaign this summer; and Kenneth T. Lange of Warren Street N.W.

Victoria T. Street, who was ap- pointed to fill the ward four vacancy created by Mason's resignation to serve on the City Council, will be trying to win the spot in her own right Nov. 8. Ward four is in upper Northwest Washington. Her two opponents are Gilbert A. Diggs, 62, A former assistant and regional superintendent in the city school system; and PhilipE. Pannell, a community outreach worker with the Howard University Center for Sickle Cell Disease. Pannell, 26, is president of the D.C. Young Democrats and ran unsuccessfully for the board in 1975.

The ward seven seat was vacated by the resignation of James S. Featherstone Jr. last year and has, since January, been filed by former teacher Minnie S. Woodson, who filed petitions yesterday to run for election to the post.

Rufus (Catfish) Mayfield, a former director of Pride Inc., will be one of her opponents. The third candidate in ward seven, the near Southeast and far Northeast section of the city, is Gloria J. Anderson, 34, a social worker of the Anacostians Concerned for Senior Citizens.