REPORTERS asked President Reagan questions for half an hour at his White House press conference this week. They raised their hands, got recognized, and put the queries; then the replies went out as news round the the world. It symbolized one of the most cherished democratic institutions.
Walter F. Mondale, former senator from Minnesota and currently an active candidate for the Democratic presidential nomination, wants to extend the system. In a book published nine years ago, ''The Accountability of Power: Toward a Responsible Presidency,'' Mr. Mondale asked why the United States did not expand the press conference. Why leave the questions just to reporters? Why shouldn't a ''question and report'' period be incorporated more closely in government; why shouldn't members of the President's Cabinet, for example, come in person before Congress itself to explain matters?
''By subjecting Cabinet officers to questioning before the entire Senate,'' Mr. Mondale proposed, ''and making this available to radio and television - a question-and-report period might force presidents to nominate stronger Cabinet officers.''
In the present lively preconvention election contest I have been surprised that Mr. Mondale's firm views on this subject have not yet been explored. If he became president, would he use them? They are a conspicuous feature of Parliament in Westminster and Ottawa. Here is what Mr. Mondale wrote in 1975:
''. . . I believe we need a question-and-report period along the lines of parliamentary practice. At present key executive branch officials do come to the Congress, but their testimony is given before committees, not before an entire body. I have sponsored legislation that would help us explore these interests by establishing a question-and-report period, available to all media, including live radio and television, during which appropriate Cabinet and other executive department officials would present themselves for questions before the full Senate and answer all questions posed by senators.''
Mr. Mondale's short book, written right after the Watergate crisis, is in a simple, direct style. ''I recently watched a question period during a session of the Canadian Parliament,'' he reports, ''and came away even more impressed by the vitality of the process.'' Points that impressed him?
''The Canadian Cabinet officers were dealt with not as superior public officials deserving special deference but simply as co-equals who deserved only such respect as they earned. . . .
''I was told by very high officials in the Canadian Parliament that the question period was of great assistance to members of the government, because they could quickly see which of their Cabinet officers were unable to answer questions put to them on an intelligent and effective basis, and they could then make changes before that Cabinet official got them into trouble.''
Yes, and the system of floor discussion, officials told him, helped winnow out impractical policy proposals. As Mr. Mondale brought back word, ''One Canadian official told me that it was always his opinion that if we had had a question-and-report period in Congress, the war in Vietnam - because of its indefensibility - might have ended much earlier.''
The study is also interesting about Walter Mondale. He has been senator, vice-president, and author of a book, and now seeks higher office. Would he change things if he came to the White House? He wrote in 1975:
''I do not want a weak president. The President of the United States, living within the constitutional law, well may be the strongest public officer in the world.'' He wasn't comfortable about the way presidential candidates were selected: ''I am convinced,'' he wrote, ''that the system itself is becoming increasingly irrational, self-defeating, and destructive of the ultimate goal.''
Does he still doubt? He was emphatic then. ''The legitimate strengths of the president make it terribly important that he be accountable to the American people and not be limited by his personal appraisal of his own stewardship. . . . That is why I wrote this book.''