Marian L. Greenblatt, a controversial member of the Montgomery County school board, announced formally yesterday that she will run for the 8th District congressional seat held by incumbent Democratic Rep. Michael D. Barnes.

Greenblatt, who switched from the Democratic to Republican party less than a year ago, said she decided to run because she is "fed up" by a lack of common sense in the House of Representatives. She is the only Republican actively challenging Barnes.

"I view myself as a problem solver," Greenblatt said in opening remarks at a press conference at her Silver Spring campaign headquarters. "All my life I've been dedicated to learning, to investigating problems, and to solving them. I've found that most problems, after a little thought, can be solved by simple common sense."

Greenblatt, 40, who lives in Silver Spring, has held no elected offices besides her membership on the nonpartisan school board, which expires in 1984.

The race between Barnes and Greenblatt will contrast two strikingly different public styles: Barnes is quiet and professorial; Greenblatt is combative and aggressive.

During nearly six years on the school board, she developed a reputation for outspokeness on racial issues and school closings that alienated her from many minority groups and liberals in the county, who have maintained that her actions were racist--a charge she denies.

Yesterday she portrayed herself as a "moderate, mainstream" alternative to Barnes, whom she has described as an extremist with political views that are "on the fringe."

In most respects, her message reflected the prevailing Reagan administration philosophy that federal spending is too high and the government out of control. Greenblatt said she favors less government regulation, a balanced federal budget and a reduction of government personnel, which she says could be achieved largely through attrition of civil servants. She also wants a revision of the parole system which, she says, has turned the criminal justice sytem into "a revolving door" for criminals.

Greenblatt says her campaign does not have an ideological base. While she supports Reagan on most foreign policy matters, she says she differs with him on certain "social and moral issues," such as abortion, prayer in schools, and the Equal Rights Amendment. She also said that while she favors strengthening defense, she does not endorse the level of Pentagon spending Reagan seeks.

Greenblatt seeks to separate herself from her rival, Barnes, on foreign affairs and defense issues.

Although Jewish leaders nationally and locally have praised Barnes for his positions on Israel and for his successful efforts to help Jews emigrate from Soviet-bloc countries, Greenblatt has described him as a supporter of the Palestinian Liberation Organization and "a spokeman for the terrorists in Latin America."

"He supports the revolutionary groups," she said when asked to substantiate her claim that Barnes supports the PLO, "and they the PLO are part of that." She said it is clear that left-wing revolutionary groups in Central and South America are interconnected and are trained by the Soviet Union, Cuba, and the PLO.

Greenblatt said she would provide "a whole sheet" of evidence soon that will document Barnes' support of terrorists in Latin America.

Barnes has called Greenblatt's charges unbelievable.

If she were in Congress, Greenblatt said, she would endorse further economic assistance and military training for troops led by the government now in power in El Salvador, but would oppose sending U.S. troops to fight against left-wing insurgents there.

"If we don't stop them in El Salvador, are we going to wait until the guerrillas get to El Paso?" she said, repeating one of her favorite campaign lines.