HAS THE recession of the past three years broken the back of the big industrial unions? You might think so, to look at their membership rolls. The United Auto Workers, which had 1.5 million members in the halcyon days of the 1970s, is down to 1.1 million now. The United Rubber Workers has declined from 180,000 in 1978 to 125,000 five years later. The United Steelworkers, which had 1.4 million members in 1972, has some 750,000 dues- paying members today. Membership in the International Association of Machinists is down from 986,000 in 1969 to below 600,000 today.

These figures reflect the decline in heavy manufacturing industries--autos, tires, steel--which has devastated much of the industrial heartland of the nation. These industries and these regions were unionized in a rush, in the great (and sometimes violent) wave of CIO organizing drives in the late 1930s. Ironically, the organization that provided much of the inspiration and financial support for those drives, the United Mine Workers, contracted in size long ago, beginning in 1950, when its leader, John L. Lewis, negotiated for higher wages and fringe benefits for his members and in return allowed the companies freely to mechanize and trim their work forces. The UMW had nearly 600,000 members in the 1940s and has some 230,000 today.

That decline in membership caused pain in many communities, but it also reflected the liberation of many men from difficult, dangerous work; real incomes and working standards are much higher in the coal-mining country today than they were in 1950. The UMW has also remained, despite bitter leadership battles, a union of considerable power and importance. The leaders of the big industrial unions that have had sharp drops in membership are not just talking through their hats when they say that their unions may end up leaner and more effective. As union members feel more outnumbered and beleaguered, they also may develop the kind of solidarity that is forgotten in prosperous times.

That can mean trouble--the kind of bitter conflict you get when unions and management believe they are fighting over shares of a pie that's not getting any bigger and may even be getting smaller. But these unions won most of their gains through increased productivity--by getting a share of a bigger pie. And if we want increased productivity in the future, surely it makes more sense for unions and management to work together than always to act as adversaries. Beyond that, the big industrial unions, and the AFL-CIO as a whole, have been a positive social force, interested in a broad range of issues, most notably in civil rights. Their leaders now face a new but not insuperable challenge: to make sure that the decline in their membership is not accompanied by a decline in the quality of their contribution to public life.