I also just couldn't stop myself so I made this gif that's supposed to show how cool it is to count on your fingers in dozenal.
http://s28.postimg.org/b37crlk59/hand_counting.gif
If we'd been using the dozenal number system, teaching kids quarters
(why is a quarter 0.25?) and thirds
(wtf 0.333 infinitely repeating??) would be so much easier because you can literally just count out a third of twelve on your digits. Oh look that's just 0.4 because you need to have three 4's to get to a dozen! It'd be much more intuitive. For the rest of us, really the biggest challenge is to stop thinking of
"10" as ten, and start thinking of it as
"1 gr0up of the base I'm using", so in base ten, 10 is 1 group of tens, and in dozenal it is 1 group of twelves. That's it, after getting used to it, 6 + 6 = 10 becomes intuitive.