This Christmas, I finally caved in: I gave my 3-year-old daughter, Sophie, her very own cassette of "The Little Mermaid." Now, she, too, can sit transfixed by Ariel, the perky teen-ager with the curvy tail who trades her voice for a pair of shapely legs and a shot at marriage to a prince. ("On land it's much preferred for ladies not to say a word," sings the cynical sea witch, "and she who holds her tongue will get her man." Since she's the villain, we're not meant to notice that events prove her correct.)

Usually when parents give a child some item they find repellent, they plead helplessness before a juvenile filibuster. But "The Little Mermaid" was my idea. Ariel may look a lot like Barbie, and her adventure may be limited to romance and over with the wedding bells, but unlike, say, Cinderella or Sleeping Beauty, she's active, brave and determined, the heroine of her own life. She even rescues the prince. And that makes her a rare fish, indeed, in the world of preschool culture.

Take a look at the kids' section of your local video store. You'll find that features starring boys, and usually aimed at them, account for 9 out of 10 offerings. Clicking the television dial one recent week -- admittedly not an encyclopedic study -- I came across not a single network cartoon or puppet show starring a female. (Nickelodeon, the children's cable channel, has one of each.) Except for the crudity of the animation and the general air of witlessness and hype, I might as well have been back in my own 1950's childhood, nibbling Frosted Flakes in front of Daffy Duck, Bugs Bunny, Porky Pig and the rest of the all-male Warner Brothers lineup.

Contemporary shows are either essentially all-male, like "Garfield," or are organized on what I call the Smurfette principle: a group of male buddies will be accented by a lone female, stereotypically defined. In the worst cartoons -- the ones that blend seamlessly into the animated cereal commercials -- the female is usually a little-sister type, a bunny in a pink dress and hair ribbons who tags along with the adventurous bears and badgers. But the Smurfette principle rules the more carefully made shows, too. Thus, Kanga, the only female in "Winnie-the-Pooh," is a mother. Piggy, of "Muppet Babies," is a pint-size version of Miss Piggy, the camp glamour queen of the Muppet movies. April, of the wildly popular "Teen-Age Mutant Ninja Turtles," functions as a girl Friday to a quartet of male superheroes. The message is clear. Boys are the norm, girls the variation; boys are central, girls peripheral; boys are individuals, girls types. Boys define the group, its story and its code of values. Girls exist only in relation to boys.

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Well, commercial television -- what did I expect? The surprise is that public television, for all its superior intelligence, charm and commitment to worthy values, shortchanges preschool girls, too. Mister Rogers lives in a neighborhood populated mostly by middle-aged men like himself. "Shining Time Station" features a cartoon in which the male characters are train engines and the female characters are passenger cars. And then there's "Sesame Street." True, the human characters are neatly divided between the genders (and among the races, too, which is another rarity). The film clips, moreover, are just about the only place on television in which you regularly see girls having fun together: practicing double Dutch, having a sleep-over. But the Muppets are the real stars of "Sesame Street," and the important ones -- the ones with real personalities, who sing on the musical videos, whom kids identify with and cherish in dozens of licensed products -- are all male. I know one little girl who was so outraged and heartbroken when she realized that even Big Bird -- her last hope -- was a boy that she hasn't watched the show since.