Waving a hand and saying the "old way" is simply an algorithm and a poor method because it glosses over the details is like saying teaching someone how to use a calculator will make them forget how math works.
That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.
That was a point I made elsewhere on this thread. When helping my second-grader with her homework, it sometimes seems that they are just changing what the student is required to memorize (and also increasing the volume), without necessarily imparting additional understanding.
That problem relies on what they call the "Add it Up" method, and it is specifically a technique with which I've helped my daughter. I observed that kids can completely learn the method and ace a test without understanding the concepts behind it.
> That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.
You do not understand what it is trying to teach. It is teaching children that taking one number from another can be done using columns, but it can also be done in your head by breaking big numbers down into small numbers and counting up.
You are not a six year old child learning arithmatic. You have missed the point.
> The problem with that method is that if I ask students to explain why it works, they’d have a really hard time explaining it to me. They might be able to do the computation, but they don’t get the math behind it. For some people, that’s fine. For math teachers, that’s a problem because it means a lot of students won’t be able to grasp other math concepts in the future because they never really developed “number sense.”
Mental methods are taught so that children do understand numbers, which gives them a better grounding for future learning.