I was first exposed to "common core math" when Blake was in kindergarten. At that time I was perplexed with the new math, but not upset. When he was in first grade I was a bit more apprehensive of the "new way" of thinking. But, we trudged along and I realized that for Blake the traditional way of math did not make the most sense to him.
Fast forward to this year. Blake is in second grade and I'm teaching first grade. I had a light bulb go off one day while teaching.... common core math is mental math on paper. When we as adults do math in our heads we short cut it. Well we are teaching the kids these short cuts, they just do it on paper or with manipulatives instead of in their head.
For example, if I was to ask you to solve 37+53 in your head, would you say 7+3 is ten... carry the one 3+5+1 is 9. ok then put the 9 here and put the zero here? Probably not. You might say 30+50 is 80. 7+3 is 10. 10+80 is 90. Or you may start with the 7+3 is then and then say 30+50+10 is 90. Remember this is all done in your head. We don't always think about doing these steps.
When we make change you start with the smaller number and build up to the bigger one... even though making change is subtracting.
We as adults look for patterns in math... that is why we teach kids to make 10s, learn their double facts, how to see the addition fact in a subtraction problem, and find patterns on 100s boards.
I often hear people talking about not having 100s boards to carry around. Well, you don't carry around base 10 blocks, a number line, cubes or any other strategy that we are teaching now or have taught for the last 20 years to early math learners. These are just ways to see the process while learning.
I can tell you as a teacher I have very few kids who do not comfortably use 2 or more of the strategies we teach. One of the first thing we also talk about is the need to learn the basic facts (addition and subtraction of numbers 0-20). Again this helps with the mental math aspect.
I feel that if more people stop and look at what this math strategy is teaching and stop just saying it's not the way I learned... you may see that it is trying to help children not fear math. There is more than one way to solve it.... what works best for you? How did you solve it? What will you try next time?