When confronted with an overly active child, many exasperated teachers and parents respond the same way: “Sit still!” It might be more effective, though, to encourage the child to run. Recent research suggests that even small amounts of exercise enable children to improve their focus and academic performance. By now it’s well known that diagnoses of attention deficit hyperactivity disorder are increasingly widespread among American children: The label has been applied to about 11 percent of those between the ages of 4 and 17, according to the latest federal statistics.

Interestingly, past studies have shown a strong correlation between greater aerobic fitness and attentiveness. But these studies did not answer the question of which comes first, the fitness or the attentional control. Addressing that mystery was a goal of a study published last year in The Journal of Pediatrics. Researchers at the University of Illinois at Urbana-Champaign recruited 40 8-to-10-year-old boys and girls, half of whom had A.D.H.D. They all took a series of computerized academic and attentional tests. Later, on one occasion they sat and read quietly for 20 minutes; on another, they walked briskly or jogged for 20 minutes on treadmills. After each task, the children wore caps containing electrodes that recorded electrical activity in the brain as they repeated the original tests

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