WASHINGTON (CNN) -- Educators have long considered breakfast "brain food," as essential to learning as books and blackboards. Now there's some science to back them up.

A new study in the Archives of Pediatric and Adolescent Medicine finds that children who eat breakfast not only do better academically than those who don't, but they also behave better.

After four months, researchers found those who ate breakfast generally had higher math grades, were less depressed, anxious and hyperactive, and were more likely to attend class and be on time.

In fact, the breakfast-eaters often averaged almost a whole grade higher than those who didn't eat breakfast.

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A group pushing to get more schools to serve breakfast says the study backs up what teachers and nurses have been saying for years -- that when children come to school hungry, they and others suffer.

"Oftentimes you see it evidenced not just in morning illnesses and headaches, but in temper tantrums, in disrupting the class," says Michele Tingling-Clemmons of the Food Research and Action Center. "It's not just the kids who are falling asleep at the desk, but it's kids who are really stopping the learning process from going on."

The study -- which was funded by those with a stake in breakfast: Kellogg's and a milk marketing group -- also found that children are more likely to eat school breakfast when the program is free for all and not just targeted at lower income youngsters.

The bottom line of the study, say researchers, is that breakfast may indeed be the most important meal of the day.