We call this new math, but it isn’t new at all.
In fact, it has been around for a very long time. It’s called number sense. And it’s the way mathematicians have been thinking about numbers for centuries.
Mathematicians are insanely smart people. I should know, I got my Computer Science degree in a Math department at a University. They also don't think like normal people do. I should know that, too, as I am often accused (rightfully so) of thinking about things differently.
If I believe what this piece is saying, Common Core math is trying to impart the math wisdom of these really smart people onto the masses. Instead, it comes off as really confusing, even to kids who actually know how to do math. One of my kids who is smart with numbers was deploying different tricks to solve these problems and found whatever it was they were teaching in Common Core confusing. My wife had to re-teach our children basic math after being traumatized by Common Core in elementary school.
It seems to be we are going about this the wrong way. They should teach the basic, tried-and-true methods first, then supplement with number sense to show other, more memorable ways to solve the problem. Or maybe encourage students to come up with their own methods to achieve the same answer and allow them to teach it to their peers.
Of course, there are some people who just don’t have any number sense whatsoever and won’t no matter how you teach it or who teaches it.