Two critical tests took place before the nation's largest gathering of teachers this week The National Education Association was tested on politics. It earned high marks. The Carter administration was tested on education. It scored high on style, low on substance.

The setting was the annual convention of the NEA, the nation's largest teachers' organization, held in this city of the lakes and liberal politics.It was the first time the body had met since the NEA broke its long tradition of political neutrally last year and threw its support and manpower behind Jimmy Carter.

Vice President Mondale came to let the teachers know that "President Carter and I will never forget the role you played in last year's election." His papearance was a natural. The convention was in his home state, and he has long and close ties with the NEA.

But Sen. Hubert H. Humphrey (D-Misn.) noticed something different. Looking at Mondale's somber dark suit and ciff links, Humphrey, who wore a bright plaid sport coat, said, "He's more conservatively attired in this liberal administration than he used to be. But I haven't changed suits since Nixon and Ford."

Mondale's rhetoric was also more conservative. He praised teachers, he cajoled them. He told them. "Today you have a partner in the White House," which has "turned around the education budget."

The crowd loved it.Mondale left the 7,785 delegates at the Minneapolis Convention Center with a broad smile on his face.

But the NEA leadership was clearly disappointed. Mondale had completely ignored the issues they care most about - creation of a Cabinet level department of education and passage of a collective bargaining law for federal employees - and left the impression with their membership that the Carter administration had gone to the barricades to press for hikes in educational spending - some of which it had opposed.

"I thought it was a terrific performance," said NEA executive director Terry Hendon. "But I didn't think there was any sign of substantive administration commitment to education."

"I was very disappointed that he didn't say anything about the department of eduction," said NEA President John Ryor. "I don't know what that means. There's apparently something going on in the administration. Mondale supported the idea for years and C arter was for it in the primary, but now Mondale isn't saying anything about it. I guess he's wearing different shots now."

When a critical story appeared in The Washington Post the morning after Mondale's presentation, he made a frantic rearguard effort to refurbish his image as a friend of educaiton. He and his staff made a series of calls to editors and the NEA brass. The Vice President solicited a letter from NEA President Ryor in a long conversation with him.

This put the NEA on the spot. Privately, the organization's leadership was upset that Mondale, acting on behalf of the Carter administration, had attempted to claim more than what they regarded as due credit for increases the House and Senate had made in Labor-HEW appropriations bill.

The letter they drafted was a very noncommital one. The only words of defense it offered Mondale and Carter was to say that NEA did not consider the two men "recent converts to the desirability of increased federal funds for public education."

The message the organization wanted to send the White House, numerous high-ranking NEA sources said, was that Carter should not take them for granted.

This leads to the other major test this week here: that of the NEA's ednorsement of Carter and continued movement into the political arena. The movement has been a gradual but controversial one among the organizations membership. This week was the first time that movement had been put to a test before the membership since last fall. Little opposition to the politicalization of the organization surfaced, however.

With its 1.8 million members, NEA has the potential to become the most powerful political force in organized labor. Unlike other unions, its members are scattered in every precinct in the country, with an average of 6,000 members in every congressional district.

Last year, it spent more than $2.5 million on national, state and local elections. Of 26 candidates it endorsed for the Senate, 19 won. Of the House candidates it endorsed, 272 won.

And in a speech that opened the convention last Sunday. Ryor warned, "NEA is not going to be lulled into complacency by presidential promises and fireside chats. We're much more interested in collecting chits than chats."