I think we're essentially in agreement; you've just defined "know how to use a calculator" a little more specifically than I did.
In my mind, if you don't know the concepts behind what you are doing, you don't know what you are doing. It's like copy and pasting code from the interwebs and then saying you are a python programmer.
But it isn't about balance, it's about using a tool to extend your abilities, not to replace them. If you are doing 36+19 on a calculator, I would posit that you simply aren't every good at math.
This is precisely the example repeatedly cited by the author of the post and the author he quoted: people doing very basic addition using a calculator.
If you focus your vision on these sorts of example, the rise of calculators is reasonably disastrous-looking! My comment meant to destroy the artificial dichotomy that calculators are "good" or "bad". They are clearly capable of generating some appalling lazy mathematical habits, but they're also clearly able to extend your abilities, improve pedagogy, and garner insights impossible to consider unaided.
Science and mathematics have wholeheartedly embraced computers as a tool for analysis and exploration. Education cannot ignore that. Simultaneously, many abstract concepts that people must know to make use of computers are best learned by replicating the exact work the computer can save you later.
The benefits of trading off toward laborious computation are going to be especially pronounced while learning things, of course.
In my mind, if you don't know the concepts behind what you are doing, you don't know what you are doing. It's like copy and pasting code from the interwebs and then saying you are a python programmer.
But it isn't about balance, it's about using a tool to extend your abilities, not to replace them. If you are doing 36+19 on a calculator, I would posit that you simply aren't every good at math.