[bjackman]

Do you think that our society only remembers the skills that we teach children to be able to do with a pen and paper?

More concretely, we already just teach kids that the trigonometric functions are essentially black boxes, you can just look up sin(x) in a table, someone has calculated it already. It doesn't mean we've "forgotten" how to calculate sin.

[Grimblewald]

I think this indicates a bigger problem, we still of math as arithmetic, especially in education. Arithmetic should be viewed as a specialised branch of math, something only learned in depth if you have skills, interest and aptitude. We should focus more on introducing kids to the full breadth of mathematics superficially and then letting them explore and expand their understanding and skills from there.

[7952]

And the modern world is full of those kind of black boxes that only a small proportion will ever understand. And it is a necessity because that is how we build on the work of others.

Personally I think mental arithmetic is worth learning as it gives practice in working with numbers and as a first algorithm. Maybe it should be expanded earlier to other concepts like modulus.