The most 'fair' math classes (specifically, I'm thinking of algebra and calculus type courses) I have been in, allowed a good in-between. Basically, you were totally allowed to use a Calculator, even one with a built-in CAS, but you -had- to show the in-between steps if you did so on a test.

This was pretty useful in it's own right, as you at least had a way to check your work, and frankly it was extremely useful for helping me solidify knowledge in those fields. [0]

Of course, AI muddles this, since it can explain the steps for you.

That may be the strawman, but that's not the real reason why people ban calculators when you learn arithmetic. The reason is because learning to manipulate numbers in your head abstracts to other things, like learning to estimate and learning to manipulate equations.

Higher-level math classes usually encourage calculators, and graduate-level math classes will often allow Matlab or Mathematica, as long as you can write a short sentence explaining what the computer algebra system is doing. Where I went to school, this was colloquially called "proof by Steven (Wolfram)."

It is a strawman. But I wonder how much better we'd be able to do those other things if we'd been taught to do them with calculators as a tool instead of being forced to do the basic arithmetic in our heads.

If you look at the natural experiment on that in society right now, much worse.

Many people today do math only with a calculator and correspondingly lack any sort of numerical reasoning skills whatsoever, despite having learned both mental math and numerical reasoning in school. That growth of innumeracy coincides with the rise of calculators and computers who do it for you.

Also, students are taught in more advanced classes to use calculators (and later computer algebra systems) as a tool. This comes after they have learned the basics, not as a replacement for the basics.

Writing (hello ChatGPT) and math are like muscles: use it or lose it. If you can't do the basic versions, you can't do the harder stuff either.

See also the ability to read a map...

I'm fascinated by linguistics, and once attempted a degree in Deaf Studies, so yes on the sign language (it's not a language, by the way: it's a class of languages, alongside spoken language, which is another class of languages), but the idea that basic arithmetic is worthless is completely alien to me.

Not worthless, obviously, I was maybe being a tad overblown ;)

But I do think that as we move forward with technological tools for this kind of mental task, that we should embrace them in our education system. If we have to teach every generation from first principles then we won't get them comfortable with the actual tech they'll be using in their lives.

thanks for the clarification on sign language :) One of those things on my bucket list that I keep meaning to learn but never get started on.