The political arm of the National Education Association, one of the nation's largest unions, yesterday voted overwhelmingly to throw its support to Democratic presidential candidate Walter F. Mondale, according to NEA sources.

It was the former vice president's first step toward a potential sweep of three critical political events this week. The others are the AFL-CIO general board endorsement in Hollywood, Fla., and the Maine straw poll, both on Saturday.

NEA's 65-member Political Action Committee council met behind closed doors yesterday to make its recommendation. The teachers' union's full 124-member board will vote on it this morning, with a 58 percent majority required for approval.

The move is the culmination of a summer in which the candidates did considerable apple-polishing at the teachers' invitation, in the form of written and video-taped appeals and interviews, interrogations conducted by NEA President Mary Hatwood Futrell and personal appearances.

All of the contenders, the teachers say, are considered friends of education. Mondale's ties to the NEA leadership are the strongest, but some sources said that Sen. John Glenn's (D-Ohio) stated emphasis on education has been well received.

Also, in an issues questionnaire reported in the union newspaper, Mondale hedged on support for a federal statute guaranteeing collective bargaining rights for employes, something for which NEA is a dedicated advocate. Mondale said he preferred this to be left to the states. Glenn and all the others, except for former Florida governor Reubin Askew, said they supported it.

The 1.7 million-member NEA, representing school teachers in virtually every congressional district, has emerged as a potent force in the Democratic Party. In 1980, it had the largest block of delegates at the party convention, about 10 percent of the total. This time around, the percentage of delegates likely will be smaller because of party rules changes, NEA officials say.

The board's approval would mean NEA's political machinery could go to work for Mondale. But each state affiliate must concur before the operation can gear up on its turf.

Also, the AFL-CIO's political operation will be competing in the delegate-selection game for the first time. Officials of both these mammoth labor organizations have said they will work together across the country.

Both organizations have substantial Republican constituencies and have indicated they would prefer to work with both political parties, but they are adamantly opposed to a range of Reagan administration policies.

The NEA was involved in a bitter feud with the administration this summer on the issue of merit pay for teachers.