When Amy Hagstrom was 9 years old, she wrote and illustrated a story. Many youngsters do that. Last month, however, Amy's tale of a young boy, and old Native American and a threatened herd of Appaloosas -- titled Strong and Free, and quite colorfully done -- was published. Now that's unusual.

Amy, now 11, lives with her parents in Portola, Calif. She was the 6-9 age category winner of the 1986 National Written & Illustrated By contest. The prize for her and the winners in the 10-13 and 14-19 groups was publication by the competition's sponsor, Landmark Editions in Kansas City.

"It's a good experiencem" says Amy, who adds that she's "not too sure" where she got the idea for her story: "I think it was just that I liked horses and liked adventure stories, and just sort of made it up as I went along."

Landmark is the brainchild of author David Melton. "Kids know that books are extraordinary things, and that if you have written and illustrated a book, it raises you above 95 percent of all other people," he says. "The self-esteem that is developed out of writing is marvelous, whether the book is printed or not."

There is no fee for entering the contest, although each entry must be submitted by a teacher or librarian. This not only acts as a screen -- although Landmark still got 1,600 entries for the '86 competition -- but makes sure adults are aware of what's going on. The three winners get trips to Kansas City to prepare their books for publication, and a 5 percent royalty on each $12.95 copy sold.

Sound like a great deal? Amy's mother was initially suspicious, and thought the youngster might be "used" in some way. But after her experience with Landmark, she has nothing but praise for Melton and company. "I've been really pleased," Julie Hagstrom says. "They are the greatest people."

Landmark is aiming to market its winners through libraries and schools. Students who find out about the contest in the back of the winning volumes will be encouraged to enter themselves, which will increase the popularity and the prominence of the winning books -- a procedure that should benefit both the young authors and Landmark.

Says Amy Hagstrom: "When my friends saw my book, they thought it was pretty neat, and they really wanted to write one too. My little sister is going to enter the contest for next year."

Winners of the 1987 contest will be announced soon; the 1988 contest is open until May 1. For more information: Landmark Editions, 1420 Kansas Ave., Kansas City, Mo. 64127. Chris Van Allsburg

CHRIS VAN ALLSBURG didn't set out to be a writer and illustrator of children's books. "I did The Garden of Abdul Gasazi as a kind of lark," says the teacher of art and two-time winner of the Caldecott Medal for illustration. "It was a breather from making sculpture -- it got me away from sawdust. I did it with the expectation that it was something I could buy on the remainder tables at a very big discount, so I'd have Christmas presents for years to come."

Even now -- after eight successful and acclaimed picture books, including the newly published The Z Was Zapped (Houghton Mifflin) -- Van Allsburg isn't positive he's a children's writer. "I still feel like a beginner. I look up and wonder how I got here. Most of the time," he says, "I'm just trying to please myself."

Of course, he's pleasing children, too: dozens of letters and stories pour in each month. The Mysteries of Harris Burdick, a provocative series of drawings that were purportedly done by the elusive title character, prompts the greatest amount of communication. "The thing that really surprises me is how many people really believe there is such a person as Burdick," Van Allsburg says. "Both children and adults. I don't really want to disabuse them. I think of them as the lucky ones."

Some of his correspondents, however, are not so fortunate. "You can tell when their imagination begins to be corrupted by television," he says. "By the time they get to the 6th grade, their imagination has been at least temporarily buried. It's video-narcosis."

When it comes to sales, Van Allsburg's most popular book is The Polar Express, a modern classic that skirts the edge of the sentimental. "Not believing in Santa Claus is a thing parents hate to see happening," the author notes. "It tells them their children are getting older. But the ending of the book says it's not a necessity."

Van Allsburg, 38, lives with his wife Lisa in Providence, R.I., where he teaches courses at the Rhode Island School of Design. At the moment, his classes are straightforward: poster design and drawing with pen and ink. An earlier course, however, was called "Design Your Own Country": students had to create, from postage stamps to posters, artifacts that would describe and illuminate their mythical territory.

When it comes to the artist's own landscapes, the action is often portrayed from an unusual perspective. Last year's The Stranger, a reinterpretation of the Jack Frost tale, unobtrusively used different angles to present the scene. "One of the first things I think of is where I am when the action takes place," Van Allsburg says. "I don't limit myself physicially -- I could be up in the air, as tiny as a fly, or get into places where a human couldn't." Boy and Tiger

BILL WATTERSON is becoming the J.D. Salinger of comic strips. Creator of Calvin and Hobbes, the most popular new strip since Bloom County, Watterson has increasingly shied away from the attention that goes with success.

When a collection of the adventures of 6-year-old Calvin and his sometime-stuffed tiger Hobbes was published early this year, the cartoonist declined to go on tour to promote it; now that it's a major bestseller, he declines even to give phone interviews. And after persistent fans began tracking him down at his home in Hudson, Ohio, he decamped; his last known whereabouts were "out west."

"He's very sensitive about protecting the source of Calvin and Hobbes," says a spokeswoman for his syndicate, Universal Press. "If he allows himself to be interrogated too thoroughly about where these ideas come from, he's afraid he could harm it . . . I don't anticipate him doing another interview in his career."