I'm unconvinced that calculators have made most people a lot worse in arithmetic. There have always been people who are bad at math. It's likely there are fewer people who can quickly perform long division on paper, but it's also possible the average person is _more_ numerate because they can play around with a calculator and quickly build intuition.
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.
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.
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?
Sure there have always been people bad at math. But basic arithmetic is not really math. We used to drill it into kids but we no longer do so and I can usually see the difference between generations. For example, women in my mother’s generation were not prioritised for education but they often are pretty quick at arithmetic. But kids and young adults I come across pull out their phones for basic additions and divisions. And I find myself pulling out my phone more and more often.
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.
For instance, you can certainly say that 381/7 is a positive number. And if I say "381/7 = 198", you can easily say that it is clearly wrong, e.g. because you immediately see that ~200 is roughly half of ~400, so it cannot be anywhere close to 1/7th.
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?").
I see what you're saying, but I just don't care that much about numbers to draw any conclusions you did about the figure you presented. I just see a string of digits.
Try standing in line at a grocery store and listening to people get upset because the amount is much higher than they thought it would be. You will hear statements like "But how is it $43? I didn't buy anything that costs more than $5"
People that failed to grasp arithmetic cannot reason about numbers to a useful degree.
> 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.
