Transforming the Difficult Child - The Nurtured Heart Approach. Help the school give him positive feedback on good behavior so he gets attention for following the rules instead of breaking them. Is he externally motivated by screen time or some other activity - turn that thing he values into a reward. For instance, all screen time in our house is earned with points - points are for listenting the first time, keeping hands to yourself, etc.
Does he need a nap? Also, (and I don't know where you are and maybe it is really too cold to go outside) but maybe they should re-evaluate when it's too cold to go outside. Would they consider and/or would they be able to provide space for him to get himself moving without going outside?
Good luck - I have an energetic one too.
