The way I explained it to my boss, is to give him a list of numbers to add up in his head and come up with a total. He looked at the list for a couple minutes, then gave me the answer (I framed the whole thing as a riddle). I then looked at him and said it looked like he wasn't working on the problem for the last couple minutes. He replied that he was thinking during that time. My reply back is "That is what I have to do the majority of the time on my projects, is think about it then spend a relatively short amount of time spitting out the answer. The problem is I also have to look busy while I'm doing it". He then saw the light.
As long as they are willing to learn, I think that's fine.
I like to make parallels with sports: when I am on the court, I am so much dumber about what's going on. Suddenly, when I am on the sidelines, I can see patterns, strengths and weaknesses for each team and so forth. It's not that I was dumb while on the court, it's just that your brain is in a different mode of operation (focusing on your own performance in this particular case).
This is great! Wish our senior director would understand this. The man loves the idea of butts in seats for long hours and can’t wait to have us back in the distraction riddled office.