PRESIDENT REAGAN has promised that the Education Department will soon be only trivia-quiz fare having to do with short-lived Cabinet-level departments. But what will happen to the department's programs once the institution is dismantled? No one is suggesting that all federal education programs be abandoned. Some government group will have to keep an eye on the over $12 billion invested yearly in the 160 federal education programs, such as Title I and student loans.Terrel H. Bell, the secretary of education, is said to be considering three possible ways to handle the Education Department's duties in the future.

First, there is the foundation approach. The Education Department would become a government-subsidized foundation with little or no policy-making power. That would ensure, Mr. Bell's aides say, that the department would not meddle in local or state decisions on how to educate children.

Second is making the department into an independent -- but not Cabinet-level -- agency. Under that arrangement the department would fit into the government in much the same way NASA does. It would report to the president as the need arose, but it would be off the front line of Cabinet-level agencies and without the Cabinet status that leads to larger budgets, larger staffs and larger federal clout in the school districts.

The third course being considered by Secretary Bell is to make the department into a quasi-public corporation, like the Corporation for Public Broadcasting. In this approach, the department would lose much of its controversial official policy-making character and, using business standards, its growth would be limited.

Notice that the options mentioned do not include returning the Education Department to its former living arrangement with what is now the Department of Health and Human Services. You remember that combination: Health, Education and Welfare -- HEW to its intimates. Secretary Bell is aparently convinced that the old setup in HEW stifled the importance of education under layers of bureaucracy. One of the arguments for creating the separate department was that education had become a stepchild in HEW, getting the least attention and the least money and unable to get fast approval for decisions.

We didn't buy that justification for setting up a new Cabinet-level Department of Education two years ago. We don't buy it now as a good reason for not putting the E back in HEW. Reestablishing HEW sounds even better after analyzing Secretary Bell's list of options. As a foundation, the current Education Department would be lobbying at one moment and proposing legislation at the next. The same would be true if it were to become an agency or semi-private corporation.

The foundation and the quasi-public corporation sound like devices to ensure a steady flow of federal money with neither a clear line of political responsibility upward nor much control over the ways in which the money is spent. If the administration's goal is to cut down federal meddling in local schools, that's best done directly. As for the concept of the independent agency -- a reversion to the original Office of Education, presumably -- that's hardly more hopeful. An agency with the sole function of disbursing money is quickly captured by the client lobbies, operating through congressional committees. As the administration thinks more carefully about the choices, it will see the virtue in folding education back into a broader Cabinet-level department. Let's hear it for HEW.