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> 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 w

by 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?").
      - MangoToupe 1y ago
        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.
        palata 1y ago
        > I just see a string of digits. And you go to the shorter line, even if it's slower? :-)
- devmor 1y ago
  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.
  - MangoToupe 1y ago
    > 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.
    - devmor 1y ago
      Not compute addition - understand that addition is a function of numbers conceptually. About 30% of US adults do not have the basic ability to conceptualize the relationship between whole numbers.

by 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?").
    - MangoToupe 1y ago
      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.
      - palata 1y ago
        > I just see a string of digits. And you go to the shorter line, even if it's slower? :-)
devmor 1y ago
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.
- MangoToupe 1y ago
  > 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.
  - devmor 1y ago
    Not compute addition - understand that addition is a function of numbers conceptually. About 30% of US adults do not have the basic ability to conceptualize the relationship between whole numbers.