Fred Tate is a pale, sensitive boy with no friends at school and a teacher who doesn't understand him. What's more, his mother, Dede, is more of a kid than he is.

But Fred's not just a troubled youngster. He is a child prodigy. At age 2 he read the label on the bottom of a plate, instead of simply learning the word, "plate."

And now, at the ripe old age of 7, he is drawing intricate chalk Madonnas on the schoolyard blacktop, multiplying reams of numbers in his head, playing classical piano at competition level and reading one college-level book after another. He also has an ulcer because he worries so intensely about the world's troubles and sometimes wakes up after dreaming he's inside Van Gogh paintings.

Meanwhile, Dede is content to spit cherry pits out the window, dance with Fred around her unkempt apartment and listen to old standards on the record player.

So begins "Little Man Tate," which marks Jodie Foster's directing debut and in which she co-stars as Dede. The film is a remarkable first-time-behind-the-camera effort, guided with a sensitive hand by someone who's been in the movie business a long time. Foster literally grew up before our eyes as one of those rare child actors who managed a smooth transition to become an accomplished adult actor, winning an Oscar two years ago (for "The Accused") to prove it. And since she was something of a child prodigy herself, she brings a special understanding to the material.

Playing young Fred is newcomer Adam Hann-Byrd, perfectly cast as the quiet, sincere little boy who isn't just numbers smart. He also has a surprisingly mature level of understanding. His perceptive insights, calmly expressed with perfect innocence, often cut like a knife, which is, of course, the mark of truth.

Still, he's a child, and Dede, though she may be an uneducated, uncouth barroom waitress, knows her son. At one point Fred laments, "I just want someone to have lunch with." Dede understands and is trying to make up for it with love, despite the knowledge that her son still thirsts for something more.

How long can Fred sit in a schoolroom thinking about calculus when basic division is a struggle for the rest of the class?

It isn't long before the third major player in this drama comes along, cold-fish Jane Grierson (Dianne Wiest), a former prodigy herself who now runs a school for child geniuses, writes books about them and each year holds a conference called "Odyssey of the Mind." Yet, she has never learned the social skills necessary to build or maintain friendships.