[shiro]

I guess it depends on each child. My son is diagnosed ADHD and even when I'm teaching him 1-on-1 he keeps moving some part of his body or change his posture frequently. It bothered me before, but I learned that for him it's actually easier to work on the task. Restricting movement seems to make some part of his brain hyperfocused and in a short period of time his brain "shuts down".

In his school, the classroom is a kind of free style and although he has assigned desk he can choose other places to work on his task, which seems to help him a lot. (It's Montessori, so most of the time each kid works independently according to his/her own study plan.)

[bayesian_horse]

That's exactly what I mean. Children without ADHD are able to sit still and focus at the same time, building that muscle.

Managing ADHD seems to be (from my non-medical non-professional perspective) all about training and using that capacity to focus.

Even for ADHD children, sitting still trains the brain, it's just that they can't stand it for very long, and there seems to be no benefit in forcing them much beyond what they feel comfortable with.

[shiro]

I'm not sure what source you derive from about the particularity of "sitting still". You imply that not being distracted from the given task? Or the physicality of sitting still has the benefit? (The two can be distinguished easily---if the latter is the case, "sitting still without doing anything, and just daydreaming wildly" would also have benefit.) Or you mean meditation? That's a different activity at all.

In the ADHD case, it seems about the way of processing stimuli. They (or at least my kid) need a sort of synchronization stimulus (or, outside distrubance, in the way that disturbance suppresses the divergence of hypersensitive systems) to keep his mind on rail. If no such stream of stimuli is provided, he must create one by his own. I try to make him find and build his own toolset to work with. (One of the activities, for example, is tapping along metronome while doing other tasks.)

[Edit] I see your comment in other thread that you refer to Zen meditation. I've learned meditation and I agree on its benefits, but it can't be applied to the current discussion of school setting---"sitting still listening lectures" and "sitting still meditating" are very different activities. The latter would certainly develop the ability of the former, but I'm dubious about just forcing the former.