So what's the methodology here? Or did I miss that part of the thread where this was answered?
First of all, I'm guessing TheSix saw this on facebook or some such shit followed by "Thanks Obama". I doubt sincerely that this is an actual homework problem.
Also, the first example:
32
-12
___
20
That's not showing any methodology at all. That's just showing the problem and the answer. It's not showing that you start from the right and subtract 2-2 first and get zero, and since that's not a negative number, you don't have to cross out the three and put a little 2 above it, you can just subtract the 3-1, and get a 2. It's not showing how you arrived at 20, it's just assuming you memorized 32-12 is 20 just because it is. Contrarily, the "new math" example is going through and listing out all of the steps to get to the answer.
I don't have a strong opinion one way or another about it, but I get what they're demonstrating here.
Since math is a 10-based system, 5s and 10s are easier to count by. So they're saying to start from the number you're subtracting by (12), then get to the nearest 5 (15). If you're still not at the number you're subtracting from (32), then add another 5. Now you're at 20. An even 10 number. Still not to 32, so add another 10. Now you're at 30. Now if you add another 10 or 5, you've gone over the target number of 32, so just add the two. Then it's saying you can add all of the things you added and get the answer.
I'm not saying it's not convoluted or that there's anything wrong with the "old" system of math, but I get what they're doing.
And like Townhall already explained, it has nothing to do with Common Core.