It's Grandparents Day at Ruxton Country School, and Clarence and Louise Simms are sitting in the classroom with their 8-year-old granddaughter, watching the teacher lead her bright-eyed pupils through a reading exercise.

This is the second year they've come to Grandparents Day, taking advantage of the leisure granted by retirement to spend more time with Katrina.

"When you're younger you're so busy making a living and making sure things go right, that you don't have a chance to enjoy your children as much as you would like," says Mr. Simms, a retired Bethlehem Steel employee.

As the nation's elderly men and women grow in number and live longer, grandparents are increasingly playing a larger part in the lives of their grandchildren, often taking on new roles with unexpected responsibilities.

The March issue of New Choices cites U.S. Census figures showing that in 1989 almost 3 million children were living in households headed by at least one grandparent -- that's 5 percent of the nation's children.

In reaction to the new roles they've taken on, many of America's 60 million grandparents are forming advocacy and support groups, such as the Grandparents Rights Organization and Creative Grandparenting.

Ruxton Country School has noted these changes and in response instituted Grandparents Day last year. "These days some grandparents are raising the children and even paying the tuition, so they're much more interested in being involved," says Judith Banker-Barrett, headmistress at the school.

Agreement is nearly unanimous on what makes the relationship between grandparents and grandchildren so special: The pressure is off. Attitudes are less rigid. Time is more abundant.

"You have a different perspective," says Mrs. Simms. "You know it's not all that important to have the shirt ironed. You don't get as emotional. You don't yell. The relaxed attitude makes a difference."

Clio Riddick, interviewed at the Waxter Center for Senior Citizens, agrees. "My husband and I just didn't have the time with our own children," she recalls. "Now . . . we can be more patient."

For grandchildren, benefits can be as exciting as a trip to Disneyland or a day at the ballpark. Three years ago the Simmses took Katrina and two grandsons to Disneyland. They have included their grandchildren on excursions to Nag's Head, N.C., for a week at the beach. And coming up soon is a visit to Epcot Center.

As idyllic as these relationships can be, problems often occur. This realization prompted writers Dee and Tom Hardie of Butler to start their weekly syndicated "Grandparenting" column a year ago. Their printed advice, in response to questions sent by readers, now appears in 50 newspapers across the country.

Parents of four grown children and the grandparents of four, the Hardies receive about a hundred queries a week from perplexed readers. Among the most persistent complaints is the lack of a thank-you from grandchildren for a gift or a good time.

Letters also raise such thorny questions as homosexuality in a grandson, promiscuity in a granddaughter, and the adverse effect in-laws can have on the relationship with a grandchild.

The latter is a painful issue brought up by several grandparents interviewed at the Waxter Center.

Marilyn Albert expresses deep hurt because she rarely sees her only grandchild, who lives in the Washington area. She feels differences between her and her daughter-in-law have made the distance far greater than the 40-minute drive.

"My grandson doesn't even know me," laments Mrs. Albert. "I feel by the age of 5 he's established his family [in his mind] and I'm nothing to him. It may be too late."

Dr. Arthur Kornhaber, director of integrative psychiatry for the St. Frances Academy, in Lake Placid, N.Y., and author of "Between Grandparents and Grandchildren," urges families to carefully nurture that relationship, to sit down and work out differences for the spiritual and physical well-being of all concerned.

He views the relationship between the two generations as highly charged spiritually, with an "extra dimension of being. . . . It's the only bond where unconditional love is so pervasive, and two people celebrate each other's existence for its own sake," he explains.

What all that theory means in everyday life is perhaps best described by Mabel Brown, a widow who shares her Baltimore home with three of her seven grandchildren.

"They come up to me and say, 'I love you, Grandma' and kiss me, and sometimes they crawl into bed with me," she says happily.

"They're so nice to have around."

RESOURCES FOR GRANDPARENTS

The groups listed below offer a variety of outlooks on being a grandparent today. When requesting information or sample copies of newsletter, please send stamped, self-addressed envelope.

* Creative Grandparenting. Support group now building a cross-country network. Newsletter. 609 Blackgates Rd., Wilmington, DE 19803.

* Foundation for Grandparenting. Information on a grandparents/grandchildren summer camp. Newsletter. PO Box 31, Lake Placid, NY 12946.

* Grandparents Against Immorality & Neglect. Attn: Betty Parbs, 720 Kensington Place, Shreveport, LA 71108.

* Grandparents' Little Dividends. Information and referral center. Also organizing Young Grandparents' Clubs. Newsletter. PO Box Shawnee Mission, KS 66207.

* Grandparents Raising Grandchildren. Attn: Barbara Kirkland, PO Box 104, Colleyville, TX 76034. Send SASE with 58 cents postage.

* Grandparents Rights Organization. Deals with visitation and custody rights issues of grandparents and is promoting a nationwide "grandparents rights study." Suite 600, 555 S. Woodward Ave., Birmingham, MI 48009.

Grandparents Visitation Rights. Information on visitation rights in all 50 states. 5728 Bayonne Ave., Haslett, MI 48840.

* The Too Faraway Grandparents' Newsletter. Offers tips on how to sustain a relationship with grandchildren over a distance. PO Box 71, Del Mar, CA 92014.

Grandparenting tips

Here are a few suggestions about how you can be a greagrandparent. They are offered by Dr. Arthur Kornhaber, a psychiatrist, educator Sunie Levin and others:

* Take the role seriously.

* Cultivate a good relationship with your son-in-law or daughter-in-law even before the child arrives.

* Develop early bonding with your grandchild.

* Be helpful to your children as well as to the grandchildren.

* Spend quality time with the grandchildren.

* Help with homework and other projects.

* Take vacations with grandchildren and allow the parents to go on a second honeymoon.

* When living away, keep in touch through letters, tapes and phone calls.

* Pass down keepsakes, family customs, rituals.

* Be there when you're needed.