9 ms·

> Well, if everyone uses a calculator, how do we learn math? Calculators have made most people a lot worse in arithmetic. Many people, for instance, don't even

by palata 1y ago

> Well, if everyone uses a calculator, how do we learn math? Calculators have made most people a lot worse in arithmetic. Many people, for instance, don't even grasp what a "30%" discount is. I mean other than "it's a discount" and "it's a bigger discount than 20% and lower than 40%". I have seen examples where people don't grasp that 30% is roughly one third. It's just a discount, they trust it. GPS navigation has made most people a lot worse at reading maps or generally knowing where they are. I have multiple examples where I would say something like "well we need to go west, it's late in the day so the sun will show us west" and people would just not believe me. Or where someone would follow their GPS on their smartphone around a building to come back 10m behind where they started, without even realising that the GPS was making them walk the long way around the building. Not sure the calculator is a good example to say "tools don't make people worse with the core knowledge".

istjohn 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. 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.
- 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?").
ethbr1 1y ago
At the end of the day, it's the average productivity across a population that matters. So GPS makes people worse at orienteering -- on average, does it get everyone where they need to go, better / faster / easier? Sometimes, the answer is admittedly no. Google + Facebook + TikTok certainly made us less informed when they cannibalized reporting (news media origination) without creating a replacement. But on average, I'd say calculators did make the population more mathematically productive. After all, lots of people sucked at math before them too.
- palata 1y ago
  > After all, lots of people sucked at math before them too. A calculator doesn't do maths, it does arithmetic. People sucked at maths, but I'm pretty sure they were better with arithmetic. > At the end of the day, it's the average productivity across a population that matters. You're pushing my example. My point is that AI may actually make the average developer worse. Sure, also more productive. So it will reinforce this trend that has been in the software industry for more than a decade: produce more but worse software. Productivity explains why we do it. It doesn't mean it is desirable.
  - ethbr1 1y ago
    You're looking at this from a human-centric perspective. I'm suggesting you consider it from an objective perspective. It's easily possible for an organization to be more productive with worse developers because of the tools they have access to. And no, that's not some slight of verbal hand in measuring "productive" -- they are able to ship more value, faster.
    - fzeroracer 1y ago
      > And no, that's not some slight of verbal hand in measuring "productive" -- they are able to ship more value, faster. Ship more value faster is exactly a verbal slight of hand. That's the statement used by every bad product manager and finance asshole to advocate for shipping out broken code faster. It's more value because more code is more content, but without some form of quality guard rails you run into situations where everything breaks. I've been on teams just like that where suddenly everything collapses and people get mad.
jen729w 1y ago
GPS has also ruined our city-level spatial awareness. Before, you had the map. So you were aware that Fitzroy was to the west of Collingwood and both were south of Clifton Hill and so on. I had dozens of these suburbs roughly mapped out in my mind. Driving down an unfamiliar road, one could use signs to these suburbs as a guide. I might not know exactly where I was, but I had enough of an idea to point me in the right direction. That skill has disappeared.
- squirrel55583 1y ago
  >Before, you had the map. So you were aware that Fitzroy was to the west of Collingwood and both were south of Clifton Hill and so on. I had dozens of these suburbs roughly mapped out in my mind. >Driving down an unfamiliar road, one could use signs to these suburbs as a guide. I might not know exactly where I was, but I had enough of an idea to point me in the right direction. Reading those sentences feels like I am dreaming. The exploration... The possibilities... Serendipitously finding you way through and getting temporarily lost at night in a big friendly suburban area with trees and in summer...
rainsford 1y ago
But how important is the core knowledge if it isn't necessary to achieve the outcomes people actually value? People only cared about map reading skills to the extent that it got them where they want to go. Once GPS became a thing, especially GPS on mobile phones, getting them where they want to go via map reading became irrelevant. Yes, there are corner cases where map reading or general direction finding skills are useful, but GPS does a vastly better and quicker job in the large majority of cases so our general way-finding experience has improved. This is especially true because the general past alternative to using GPS to find some new unfamiliar place wasn't "read a map" it was "don't go there in favor of going some place you already knew" in a lot of cases. I remember the pre-GPS era, and my experience in finding new stuff is significantly better today than it was back then.
- j_w 1y ago
  Using map reading skills as a proxy for this is a bit of a strawman. People who use GPS habitually have worse navigational and spatial awareness skills. https://www.nature.com/articles/s41598-020-62877-0 https://www.nature.com/articles/s41598-020-62877-0 If you habitually use a calculator for all arithmetic, could the result not be similar? What if you reach to an LLM for all your coding, general research, etc.? These tools may vastly speed up some workflows, but your brain is a muscle.
- palata 1y ago
  I think you're missing the point, which is to say "those tools make us more productive, but less knowledgeable". And you answer by saying "it's okay to be less knowledgeable (and hence depend on the tool), as long as you are more productive". Which is a different question. But to me it's obviously not desirable: if AI allows people to completely lose all sense of critical thinking, I think it's extremely dangerous. Because whoever controls the AI controls those people. And right now, look at the techbros who control the AIs. So the original question is: is it the case that AI reduces the skills of the people who use them? The calculator and the GPS are examples given to suggest that it doesn't sound unlikely.
quantified 1y ago
Apparently 1/3 lb hamburgers didn't help A&W against McDonald's because too many people thought 1/3 is smaller than 1/4. So the Quarter Pounder remains supreme. Snopes: [https://www.snopes.com/news/2022/06/17/third-pound-burger-fractions/ https://www.snopes.com/news/2022/06/17/third-pound-burger-fr...]
fizx 1y ago
Writing has made people worse at memorization. This argument has been around since Plato.
- monkeyelite 1y ago
  That’s also true though. In oral societies they memorize a lot more.
nsonha 1y ago
You're confusing maths with accounting. 30% is an intuition/familiarity, not knowledge.
- palata 1y ago
  I'm not confused. A calculator does arithmetic, not maths. The question was: > Well, if everyone uses a calculator, how do we learn math? Which doesn't make much sense, because a calculator doesn't do maths. So I answered the question that does make sense: if everyone uses a calculator, do we still learn arithmetic? And I believe we don't. And then, if we suck at basic arithmetic, it makes it harder to be good at maths.
presentation 1y ago
But somehow I was born in the age of GPS and yet I ended up with a strong mental map and navigation skills. I suspect there will be plenty of people who grow up in the age of LLMs and maybe by reading so much generated code, or just coding things themselves for practice, will not have a hard time learning solid coding skills. It may be easy to generate slop, but it’s also easy to access high quality guidance.

by palata 1y ago

istjohn 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. 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.
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?").

ethbr1 1y ago

At the end of the day, it's the average productivity across a population that matters. So GPS makes people worse at orienteering -- on average, does it get everyone where they need to go, better / faster / easier? Sometimes, the answer is admittedly no. Google + Facebook + TikTok certainly made us less informed when they cannibalized reporting (news media origination) without creating a replacement. But on average, I'd say calculators did make the population more mathematically productive. After all, lots of people sucked at math before them too.

palata 1y ago
> After all, lots of people sucked at math before them too. A calculator doesn't do maths, it does arithmetic. People sucked at maths, but I'm pretty sure they were better with arithmetic. > At the end of the day, it's the average productivity across a population that matters. You're pushing my example. My point is that AI may actually make the average developer worse. Sure, also more productive. So it will reinforce this trend that has been in the software industry for more than a decade: produce more but worse software. Productivity explains why we do it. It doesn't mean it is desirable.
- ethbr1 1y ago
  You're looking at this from a human-centric perspective. I'm suggesting you consider it from an objective perspective. It's easily possible for an organization to be more productive with worse developers because of the tools they have access to. And no, that's not some slight of verbal hand in measuring "productive" -- they are able to ship more value, faster.
  - fzeroracer 1y ago
    > And no, that's not some slight of verbal hand in measuring "productive" -- they are able to ship more value, faster. Ship more value faster is exactly a verbal slight of hand. That's the statement used by every bad product manager and finance asshole to advocate for shipping out broken code faster. It's more value because more code is more content, but without some form of quality guard rails you run into situations where everything breaks. I've been on teams just like that where suddenly everything collapses and people get mad.

jen729w 1y ago

GPS has also ruined our city-level spatial awareness. Before, you had the map. So you were aware that Fitzroy was to the west of Collingwood and both were south of Clifton Hill and so on. I had dozens of these suburbs roughly mapped out in my mind. Driving down an unfamiliar road, one could use signs to these suburbs as a guide. I might not know exactly where I was, but I had enough of an idea to point me in the right direction. That skill has disappeared.

squirrel55583 1y ago
>Before, you had the map. So you were aware that Fitzroy was to the west of Collingwood and both were south of Clifton Hill and so on. I had dozens of these suburbs roughly mapped out in my mind. >Driving down an unfamiliar road, one could use signs to these suburbs as a guide. I might not know exactly where I was, but I had enough of an idea to point me in the right direction. Reading those sentences feels like I am dreaming. The exploration... The possibilities... Serendipitously finding you way through and getting temporarily lost at night in a big friendly suburban area with trees and in summer...

rainsford 1y ago

But how important is the core knowledge if it isn't necessary to achieve the outcomes people actually value? People only cared about map reading skills to the extent that it got them where they want to go. Once GPS became a thing, especially GPS on mobile phones, getting them where they want to go via map reading became irrelevant. Yes, there are corner cases where map reading or general direction finding skills are useful, but GPS does a vastly better and quicker job in the large majority of cases so our general way-finding experience has improved. This is especially true because the general past alternative to using GPS to find some new unfamiliar place wasn't "read a map" it was "don't go there in favor of going some place you already knew" in a lot of cases. I remember the pre-GPS era, and my experience in finding new stuff is significantly better today than it was back then.

j_w 1y ago
Using map reading skills as a proxy for this is a bit of a strawman. People who use GPS habitually have worse navigational and spatial awareness skills. https://www.nature.com/articles/s41598-020-62877-0 https://www.nature.com/articles/s41598-020-62877-0 If you habitually use a calculator for all arithmetic, could the result not be similar? What if you reach to an LLM for all your coding, general research, etc.? These tools may vastly speed up some workflows, but your brain is a muscle.
palata 1y ago
I think you're missing the point, which is to say "those tools make us more productive, but less knowledgeable". And you answer by saying "it's okay to be less knowledgeable (and hence depend on the tool), as long as you are more productive". Which is a different question. But to me it's obviously not desirable: if AI allows people to completely lose all sense of critical thinking, I think it's extremely dangerous. Because whoever controls the AI controls those people. And right now, look at the techbros who control the AIs. So the original question is: is it the case that AI reduces the skills of the people who use them? The calculator and the GPS are examples given to suggest that it doesn't sound unlikely.

quantified 1y ago

Apparently 1/3 lb hamburgers didn't help A&W against McDonald's because too many people thought 1/3 is smaller than 1/4. So the Quarter Pounder remains supreme. Snopes: [https://www.snopes.com/news/2022/06/17/third-pound-burger-fractions/ https://www.snopes.com/news/2022/06/17/third-pound-burger-fr...]

fizx 1y ago

Writing has made people worse at memorization. This argument has been around since Plato.

monkeyelite 1y ago
That’s also true though. In oral societies they memorize a lot more.

nsonha 1y ago

You're confusing maths with accounting. 30% is an intuition/familiarity, not knowledge.

palata 1y ago
I'm not confused. A calculator does arithmetic, not maths. The question was: > Well, if everyone uses a calculator, how do we learn math? Which doesn't make much sense, because a calculator doesn't do maths. So I answered the question that does make sense: if everyone uses a calculator, do we still learn arithmetic? And I believe we don't. And then, if we suck at basic arithmetic, it makes it harder to be good at maths.

presentation 1y ago

But somehow I was born in the age of GPS and yet I ended up with a strong mental map and navigation skills. I suspect there will be plenty of people who grow up in the age of LLMs and maybe by reading so much generated code, or just coding things themselves for practice, will not have a hard time learning solid coding skills. It may be easy to generate slop, but it’s also easy to access high quality guidance.