I mean it’s not the end of the world and as you’ve said the raw number of people of numerate people are rising thanks to technology. But technology also seem to rob people of motivation to learn somewhat useful skills and even more so with LLMs.
Arithmetic is a subset of maths.
This is not actually possible.
Hell, if I had to do long division today without a computer I'd have to re-derive it.
It absolutely is. If you can't add or subtract, what reasoning are you doing that is worthwhile?
I feel there's a bit of a paradox, with many subjects, where we all know the basics are the absolute most important thing, but when we see the basics taught in the real world, it seems insultingly trivial.
And I don't mean specifically those numbers, obviously. Same goes with 20/100, or understanding orders of magnitudes, etc.
Many people will solve a "maths problem" with their calculator, end up with a result that says that "the frog is moving at 21km/s" and not realise that it doesn't make any sense. "Well I applied the recipe, the calculator gave me this number, I assume this number is correct".
It's not only arithmetic of course, but it's part of it. Some kind of basic intuition about maths. Just look at what people were saying during Covid. I have heard so many people say completely wrong stuff because they just don't have a clue when they see a graph. And then they vote.
Maybe that's because you actually can do arithmetic, to the point where it's difficult for you to see how it would be if you couldn't?
People that failed to grasp arithmetic cannot reason about numbers to a useful degree.
I think you're extrapolating far too much from such a simple interaction, which doesn't imply anything about ability to reason about numbers, just their ability to compute addition. If you say "if a is larger than b, and b is larger than c, is a larger than c?", you're testing numerical reasoning ability.
I feel like arithmetic is part of the basics to build abstraction. If I say "y = 3x + a", somewhere I have to understand what "3 times x" means and what the "+" means, right?
Or are you saying that you can teach someone to do advanced maths without having a clue about arithmetic?
About 30% of US adults do not have the basic ability to conceptualize the relationship between whole numbers.
I believe that this is an acquired skill that requires basic arithmetic. But if you need a calculator to realise that 381 is roughly twice as big as 198, then you can't do any of the reasoning above.
One may say "yeah but the point of the calculator is to not have to do the reasoning above", but I disagree. In life, we don't go around with a calculator trying to find links between stuff, like "there are 17 trees in this street, 30 cars, what happens if I do 17+30? Or 30-17? Or 30*17?". But if you have some intuition about numbers, you can often make more informed decisions ("I need to wait in one of those lines for the airport security check. This line is twice as long but is divided between three officers at the end, whereas this short line goes to only one officer. Which one is likely to be faster?").
And you go to the shorter line, even if it's slower? :-)