Yesterday, in the half-sized gymnasium of a Fairfax County elementary school, the melting pot of America shone like gold for a blue-collar Korean immigrant and her three children.

"Education is everything," Hyo Cha Yi once told author Brent Ashabranner; and yesterday before an assembly at Bucknell Elementary, Ashabranner surprised her with a copy of his new book, "The New Americans," which features Yi and her 12-year-old daughter, Myong, on its cover.

Yi, who came to the United States with her family five years ago, works the night shift (3-11 p.m.) at Bucknell as a custodian. The cover of the book shows her in her blue uniform dress and Fairfax County employe patch.

Next to her stands Myong in velour Izod pullover and grosgrain ribbon bow at her neck--a typical American sixth-grader who this week fulfilled a small part of her parents' dream by graduating from Bucknell's gifted-talented program.

"I had to call Kwang Yi's 16-year-old son to plan this," principal Freda Skirvin told the assembly, "and he said, 'This is awesome. We are just ordinary, hard-working people, and now we're going to be in a book!' "

"Koreans have a special feeling for education," says Kwang, a junior at nearby Groveton High School. "But in Korea, a good education is very hard to get, while the U.S. provides such a great one--especially Fairfax County."

And so here, despite the language problems and the culture shock, the Yi children have found a home amid the basketball goals, the Star Wars T-shirts, and the autographs (Joe Theismann, Ronald McDonald) on the cement walls.

Ashabranner featured the Yis in his book because he said they illustrated the emphasis many new immigrants place on educating their children. A former deputy director of the Peace Corps, Ashabranner said the Yis told him they emigrated from Korea in large part to take advantage of American public education.

Ashabranner says his book, designed for teen-age readers, examines "inter-cultural relations," sociological jargon for the crazy-quilt identity the Yi children are forging.

Kwang, for example, says he doesn't feel like an immigrant anymore--or look it, in blue shirt, tan chinos, topsiders and no socks. "But it doesn't matter how long we are here, Korea is our mother country."

His younger sister, Myong, in blue jeans and oversized yellow Izod pullover, has absorbed the look but not the outlook of the preteen preppie. She is still amazed at the offhand attitude American children take toward school and homework.

School in Korea is "much worse--harder, stricter, longer," says Myong. Not only that, "after you graduate from sixth grade, you must pay."

The children's education, while it may be free now, has cost the Yis in other ways. Kwang says his father, Ki Chong, has taken a job as an auto mechanic in Anchorage to set aside money for Kwang's college tuition.

His mother, who used to work a morning job as well, still undertakes extra work as part of the family plan. Yesterday, building supervisor Louise Pierce, who sometimes uses sign language because of Mrs. Yi's limited English, "sent her home to change clothes. She came in her uniform . . . she thought she'd just stay and work through."

For the Yis, education is a means to a very practical end--their children's security. When Myong says that perhaps she would like to pursue a career in art, Kwang frowns, "I don't think our father would approve."

"The war interrupted his education," says Kwang, "and now he wants us to major in the hardest courses." Kwang plans to become a doctor.

Their parents' fervor for study has made its mark already on 10-year-old Son Ho. Molly Cook, Son's reading teacher, says, "He's the most motivated child you'll ever see. You just can't do enough for him. He's always ready: 'Let's read, let's read' . . . and with a smile on his face all the time."