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?").
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.
> 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?
I can't do arithmetic more than a couple digits, though, that's what the python console is for.
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?").
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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.
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.