Comment by MangoToupe
6 days ago
Arithmetic is also near-useless if you have access to a calculator. It's also a completely different skill thab reasoning about numbers, which is a very useful skill.
6 days ago
Arithmetic is also near-useless if you have access to a calculator. It's also a completely different skill thab reasoning about numbers, which is a very useful skill.
But, logically, you need to spend time thinking about numbers to be good reasoning about them, and the calculator is about reducing that time.
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.
I understand what you're saying, but I legitimately am unconvinced learning long division is necessary to learn by hand to master division. If anything, perhaps we should be asking children to derive arithmetic from use of a calculator.
I think it’s pretty hard to reason about numbers without having mastered arithmetic. Or at least beat your brain against it long enough that you understand the concepts even if you don’t have all the facts memorized.
I disagree; i think the focus on arithmetic actually enables people saying they're "bad at math" when symbolic reasoning is a completely different (and arguably much easier) skill. You an easily learn algebra without knowing long division.
Hell, if I had to do long division today without a computer I'd have to re-derive it.
I don't think it's so much about doing a long division. To me, it's more about having an intuition that 30/100 is roughly "one third", and that you can put three thirds in the full thing.
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.
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I agree you can learn algebra without knowing (or being good at) long division on paper, but you need to have a good conceptual understanding of what division is and I don't think a lot of people get that without the rote process of doing it over and over in elementary school.
I can do plenty of arithmetic much faster than I could type it on a calculator keypad. That's like saying hardware keyboards are near-useless if you have access to a touchscreen.
I just don't really work much with arithmetic to begin with. Almost 100% of the numerical work I do is symbolic.
All well and good, but don't mistake a practice you don't use as being generally useless.
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Would you be able to do your numerical work without understanding what an addition or a subtraction is?
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?
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