If kids don't learn how to do these problems quickly, they'll never be able to do higher order problems in a timely fashion.
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.
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.
It's like asking why ever read a book, with a level of english past the level of a memo asking if you have completed a task. This article also seems to suggest that people don't understand how to preform basic mental arithmetic.
In the states there also seems to be this insane way of thinking that you should learn an algorithm to do things in a particular way, if you can do it one way you should understand it and all the other methods should just fall into place.
This is a pretty good explanation of the problem. https://www.youtube.com/watch?v=5ZED4gITL28
(hey I took double maths for A-level and enjoyed every minute of it)