Actually the "new" method in the cheat sheet is a much older method than what I expect most of us used to learn addition. It's the math of the abacus familiar to the Chinese, Greeks and Romans. It was still being used by the Russians when they beat the US to space. It's the math used in mechanical calculators, and leads to faster math performance with practice. It especially leads to improved skill at estimation which becomes more important as we have access to electronic calculators to do more precise operations.
I'm not sure about you, but the "new" method is the way I learned math. We just didn't write out the whole 62 = 60 + 2 when we were doing problems, we just had the teacher explain to us and had the understanding that that was what we were doing.
