D.C. Council member Betty Ann Kane, a former member of the school board whose three years on the council have been marked by strident criticism of Mayor Marion Barry's administration, filed papers yesterday to be a candidate for mayor in next year's elections. Kane said improvement of the city schools will be a focal point of her campaign.

Kane's action makes her the third major candidate to go on record as a challenger to Barry, who has said that announcing his candidacy for reelection is just a matter of when, not if.

Yesterday's filing with the D.C. Board of Elections and Ethics effectively entitles Kane to raise funds openly for an effort that has already taken many informal steps over the past several months.

In an interview with a reporter yesterday, the 40-year-old Democrat said little about her election strategy or the amount of money she expects to raise to implement it.

"My priority in the weeks ahead will be to set a positive tone. I care very deeply about this city, its people and its future," she said. "I intend to focus -- as I have throughout my years as a public official -- on common sense, practical solutions to the serious problems of crime, jobs, housing, education and finance."

"I have a broad base in education and with parents, which is not surprising since I spent four years on the board of education," Kane said. "Education is a continuing priority. I believe that good schools are the key to a good city in terms of jobs, economic development, crime and housing."

Kane said she would not alter her plans and run for reelection to her city council seat or for council chairman -- a decision that could leave her out of public office if her bid for mayor is unsuccessful.

"I think that anyone who has been into a campaign for five or six months and it became clear that the campaign was not going well would look at other offices," Kane said. "But that is not my plan. I am not planning this as some exploratory venture or putting a 'finger in the wind.' This is real. I am serious. I intend to run hard."

"I have no plans to run for anything except mayor, absolutely no plans to do anything but run for mayor -- run, run well and win," she said.

Kane's campaign organization, "Citizens for Kane," will be headed by five persons, including Marilyn Tyler Brown, an assistant superintendent of schools who supported Sterling Tucker for mayor in l978, and one-time D.C. Corporation Counsel John R. Risher Jr., who supported former mayor Walter E. Washington's campaigns in l974 and l978.

The announcement was greeted politely by Kane's principal opponents:

"I would say I find it interesting, but it doesn't impact upon my plans," council member John Ray (D-at large) said. "Her announcement should make it a spirited campaign."

Council member John A. Wilson (D-Ward 2), said he was not impressed.

"I think I'm a more personable candidate," Wilson said. "In any campaign, though, the more people get in who really haven't done that much, the better it is for me. I just hope the campaigning doesn't degenerate to the level it did during the last Virginia election."

Mayor Marion Barry was unavailable for comment.

Although she was not officially a candidate before yesterday, Kane has already assessed her chances in a poll by former Carter administration pollster Patrick Caddell, financed by a group of prominent developers and real estate brokers.

The poll found strong opposition to Barry, indicated that Kane could narrowly defeat him in a two-way race and showed that those surveyed did not believe that the mayor of the city, whose population is 70 percent black, must be black to understand and deal with city problems. Kane is white.

"I have never seen any indication that voters in this town make decisions on anything other than who is qualified," Kane said yesterday. "I have never seen any indication that people want anything other than the best.

Kane began her career in city politics in 1974, when she was elected to fill an at-large vacancy on the school board created when Barry was elected to the city council. She was reelected to the board in 1975.

In the September l978 Democratic primary, she led a field of nine candidates for the party's at-large council nomination. Kane received 34 percent of the vote and won in the four city wards where the white vote is significant -- wards 1, 2, 3 and 6 -- the same wards that Barry won.

She did not win in the heavily black areas of the city -- wards 4, 5, 7 and 8 -- though she lost Ward 4 by fewer than 100 votes.

Later, during the general election, Kane polled 48 percent of the vote and took all eight wards.

Richard A. Jackson, 43, is the fourth candidate who has filed for the election. Other possible Democratic candidates include former Council Chairman Sterling Tucker and Patricia Roberts Harris, who held two Cabinet posts in the Carter administration.