Just where does one go these days in Washington for a good game of marbles?

One answer is: The Kennedy Center.There, shooting marbles is just one of hundreds of so-called "educational" diversions designed to raise the creative thresholds of school children -- and their parents, if they can let their hair down -- in an exhibit that opens today.

Its title is pretty broad: "Reflections: The Child in America." But the five-week show in the Center's North Gallery and the adjoining Musical Theater Lab is pretty broad too. There is a photo exhibit of enlarged works from the book "The Family of Children," and a series of panels in chronological sequence illustrating "the changes in attitude toward the child in America.

Then follows the fun part, called "participatory activity centers." There are four large colorful tents, each full of the diversions. There is one for sounds (you can conduct in front of a mirror to a record of a Sousa march); one for visual arts (from finger painting to needlepoint); one for movement (by this they mean anything from athletics to dance); and another for letters and words (practice your spelling on a transistorized calculator). Each is full of background material (did you know, for instance, that the 1922 marbles shooting champ was Bud McQuade?). And each has a "master artist-teacher" on duty who can furnish expertise and enthusiasm.

Finally, there will be a regular mini-theater at which the Kennedy Center will sponsor at least 15 children's theater groups during the Center's fall "Children's Art Series."

The result is a combination that adds up to a small festival. The Center's director of operations, Thomas R. Kendrick, notes that "this is the first time we have mixed children's performing arts and an exhibition in the same event.

About 300 area school children will be ushered through the show each weekday, and it will be open to the public on Fridays (6 to 8 p.m.), Saturdays (10 a.m. to 5 p.m.) and Sundays (1 to 5 p.m., starting Oct. 7).

After the Kennedy Center, the show will tour the country in six-week intervals at various cities for the next two years.

It was designed by CEMREL, Inc. in St. Louis for the Dept. of Health Education and Welfare at a cost of about $100,000 to celebrate the International Year of the Child.

Further details of the schedule can be obtained from the office of the Center's Education Coordinator.