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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

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.

palata 1y ago
> I'm unconvinced that calculators have made most people a lot worse in arithmetic. There have always been people who are bad at math. Arithmetic is a subset of maths.
- MangoToupe 1y 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.
  - recursive 1y ago
    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.
    - MangoToupe 1y ago
      I just don't really work much with arithmetic to begin with. Almost 100% of the numerical work I do is symbolic.
      - recursive 1y ago
        All well and good, but don't mistake a practice you don't use as being generally useless.
        MangoToupe 1y ago
        Similarly, don't mistake a practice you do engage in as necessary!
      - palata 1y ago
        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?
        recursive 1y ago
        You can have a solid understanding of "+" without being able to quickly add three digit numbers.
  - SoftTalker 1y ago
    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.
    - MangoToupe 1y ago
      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.
      - palata 1y ago
        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.
        MangoToupe 1y ago
        Fair point, I concede that maybe i'm overly-optimistic at even basic intuition for basic figures and concepts.
      - SoftTalker 1y ago
        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.
  - nitwit005 1y ago
    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.
    - MangoToupe 1y ago
      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.
creakingstairs 1y ago
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.
techpineapple 1y ago
"it's also possible the average person is _more_ numerate because they can play around with a calculator and quickly build intuition." This is not actually possible.
- MangoToupe 1y ago
  Why? I am honestly befuddled with this response. manually computing arithmetic is not necessary to reason about numbers.
  - devmor 1y ago
    > manually computing arithmetic is not necessary to reason about numbers It absolutely is. If you can't add or subtract, what reasoning are you doing that is worthwhile?
    - MangoToupe 1y ago
      You can grasp the concept without executing the mechanics. I don't see how that's difficult to grasp.
      - palata 1y ago
        > I don't see how that's difficult to grasp. 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?
        MangoToupe 1y ago
        I can't do arithmetic more than a couple digits, though, that's what the python console is for.
        palata 1y ago
        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?").

palata 1y ago

> I'm unconvinced that calculators have made most people a lot worse in arithmetic. There have always been people who are bad at math. Arithmetic is a subset of maths.

MangoToupe 1y 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.
- recursive 1y ago
  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.
  - MangoToupe 1y ago
    I just don't really work much with arithmetic to begin with. Almost 100% of the numerical work I do is symbolic.
    - recursive 1y ago
      All well and good, but don't mistake a practice you don't use as being generally useless.
      - MangoToupe 1y ago
        Similarly, don't mistake a practice you do engage in as necessary!
    - palata 1y ago
      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?
      - recursive 1y ago
        You can have a solid understanding of "+" without being able to quickly add three digit numbers.
- SoftTalker 1y ago
  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.
  - MangoToupe 1y ago
    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.
    - palata 1y ago
      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.
      - MangoToupe 1y ago
        Fair point, I concede that maybe i'm overly-optimistic at even basic intuition for basic figures and concepts.
    - SoftTalker 1y ago
      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.
- nitwit005 1y ago
  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.
  - MangoToupe 1y ago
    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.

creakingstairs 1y ago

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.

techpineapple 1y ago

"it's also possible the average person is _more_ numerate because they can play around with a calculator and quickly build intuition." This is not actually possible.

MangoToupe 1y ago
Why? I am honestly befuddled with this response. manually computing arithmetic is not necessary to reason about numbers.
- devmor 1y ago
  > manually computing arithmetic is not necessary to reason about numbers It absolutely is. If you can't add or subtract, what reasoning are you doing that is worthwhile?
  - MangoToupe 1y ago
    You can grasp the concept without executing the mechanics. I don't see how that's difficult to grasp.
    - palata 1y ago
      > I don't see how that's difficult to grasp. 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?
      - MangoToupe 1y ago
        I can't do arithmetic more than a couple digits, though, that's what the python console is for.
        palata 1y ago
        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?").