“Our results support the suggestion that it’s best to avoid sitting still for long periods of time,” says Cade, “and even fidgeting may offer enough of a break to make a difference.”

Among women sat for more than seven hours per day and who didn’t fidget much, their risk of mortality was 43% higher than those who sat for less than five hours. 

kids with ADHD performed significantly better on the task when they were free to engage in extraneous activities: tapping their feet, moving their hands, playing with the objects around them. 
... Dr. Rapport

What we've found is that when they're moving the most, the majority of them perform better, Rapport said. They have to move to maintain alertness.

Telling them to sit still, in other words, would only make things worse.

They found that the more intensely that the children with A.D.H.D. wiggled and fidgeted — the more ferociously they bobbled their legs — the more accurate their answers were.

let them squirm and fidget and bounce and jiggle and generally maintain that constant, disconcerting restiveness, if you want them also to be better able to concentrate.

If they move their bodies while they’re working it doesn’t disturb anybody but it fills their own neurological need for motion and activity.
- Ms. Keller, Guidance Counselor

What we found was that when the children with ADHD had intense movement—the kind of movement a teacher or another child would notice in the classroom—they did better on the task,
... Dr. Julie Schweitzer,