I couldn't hold back and replied with a long comment because a previous commenter said they had opted their child out of common core testing. Here's what I said:
The example on the right is a terrible example of a common core method and hard to decipher. They are saying decompose 37 into 5+2+10... Without plus signs. Then counting up. Inefficient.
We want kids to know you don't always have to add from right to left. For example 53 plus 37 is the same as 50 + 3 and 30 +7. 7 and 3 makes 10 which represents that little 1 being carried in the standard algorithm. Then add 10 to 50 and 30 and you get 90.
One reason we will not teach the standard algorithm for example for subtraction first is for example doing 100 - 3. It makes no sense to cross out numbers and regroup. Why not break up 100 into 95+5 then minus 3. Now I got 95 + 5 - 3 which is 95 + 2 or 97.
Final point. When kids are taught a procedure they regurgitate it then forget it. If you learn it conceptually, struggle, learn strategies cooperatively with your peers, the odds go way up for retaining the information.
I read a book this summer. Common core math for parents for dummies. It's great and talks k-12. Hope this helps or gives you a different point of view. I obviously support common core."
And the person thereafter replied with:
Everyone should read the book. Teachers, parents, administrators. I already did.