Take as an example adding two digit numbers. I don't know anybody who does math as a part of their job who does the old "carry the 1" routine from elementary school. To me, a far better way to add numbers (and is the basis for the algorithm) is realize that 62+26 is 60+20 + 2+6. This is exactly the object of ridicule #7 in the previous link. I've been teaching my son how to add and subtract this way, and now he can pretty easily add and subtract numbers like these in his head (and no, he is not a math genius). From there, it was pretty easy to extend to other numbers and different situations as well, like, say, 640+42 and the such. I see absolutely no point in him even bothering to learn the old algorithms at this point. I think that those of us who developed mathematical skills in the old curriculum probably succeeded more despite the system than because of it.
The results of decades of algorithmic learning are students who have little conceptual understanding, and even worse, are frankly scared to think. I can't tell you how many students come to my office hours who essentially want me to spoon feed them how to solve a particular problem so that they can reproduce it correctly on a test. The result is people whose basic understanding is so weak and algorithmic that they are unable to deal with new situations. Consider this quote from the NYTimes article from a child complaining about the Common Core:
“Sometimes I had to draw 42 or 32 little dots, sometimes more,” she said, adding that being asked to provide multiple solutions to a problem could be confusing. “I wanted to know which way was right and which way was wrong.”Even at this young age, already there is a "right way" and a "wrong way". Very dangerous!
I'm sure this Common Core thing has many faults. Beyond the obvious "Well, if it was good enough for me, grumble grumble harrumph!" reactions, I think there are probably some legitimate issues, and some of it probably stems from the fact that teaching math conceptually is a difficult thing to systematize and formalize. But from what I've seen, I think the Common Core is at least a big step in the right direction.