I've seen the intuition in my 10 year old nephew.* Perhaps I've
  just tainted his mind through exposure to me :P but he has a
  natural mathematical mind; does the math his own way.* I had to
  explain to him last year in 4th grade, when he was pissed off
  about SHOW YOUR WORK - [because he "knew" the answers - what's
  there to show?] - how to fake "show your work* and why the
  teacher wants you to show it. I said, "Just do it the way you
  want in your head, and show the teacher what THEY want so they
  can show their boss (the principal that they're a good teacher,
  and the Principal can show the school district that they're a
  Good school so that the Government will pat the school on the
  head, say, "Good job, little School! Here's your Money!" Had him
  rolling on the floor laughing 'cause I use funny voices, but it
  worked.* His math grades shot up again.

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