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I wouldn’t be a bit surprised if half the adult population of the US has an understanding of fractions that falls apart if you move past what you need to read c

I wouldn’t be a bit surprised if half the adult population of the US has an understanding of fractions that falls apart if you move past what you need to read cooking recipes (which nb. is basically none whatsoever, unless scaling recipes up or down). Maybe a lot more than that. Many with bachelor’s degrees or higher. I think both the level of numeracy in and the degree to which it is perceived to actually matter for the general population is greatly overestimated on sites like HN. [edit] in this particular case the person had likely gotten by pattern-matching 1, a slash, and a 3, as one-third, and simply never cared why one might write 3/1 to mean 3, for example. Why do that, after all? I see a one, I see a slash, and I see a 3. One-third. It’s worked every single time before so why would your thing be a special case?

core-questions 6y ago
It's actually terrifying to think about. I don't want to denigrate people or be mean, but when you realize that your own standard of literacy is something many people truly struggle to obtain, it helps make a lot of things make sense. For example, I saw a thread on Reddit the other day where someone mentioned "taking the 30 seconds to read something"; the discussion went on a tangent where someone called themselves a slow reader because it took them a whole minute, and then others chimed in that it was taking them longer still. So, I timed myself and it took me 14 seconds to read it. What that made abundantly clear to me was that my own experience in the world - seeing _words_ as first class entities everywhere, immediately tagged and understood as whole components, instantly, without ever "reading" them... is not everyone else's experience. Some adults who nominally believe themselves to be literate must actually have to sit there and spend some effort to recognize each letter and sound out a word, the way my children did when they were ~4 (and some children get even younger). What is the world like for these people? I can often speed-read a paragraph and come away with an understanding within seconds, skimming over it for key words and familiar grammatical constructs; my assumption is that most people posting here can do the same. Maybe that's not the case? There's also a lot of talk on the Internet in the last year or two about inner monologue, with the growing realization that it is likely that a large part of the population simply does not experience the ability to talk to themselves within their own head. This makes me wonder if they can read silently without having to mouth the words; perhaps this is the tip of the iceberg for a differentiation in intelligence that hasn't really been extensively studied yet (unsurprisingly, since psychometrics are not in vogue right now).
- Nasrudith 6y ago
  Speaking of lack of internal dialog I noticed a quieting of it as a side effect of a medication I was on - normally volume didn't exactly apply but it was difficult to head myself think - not like it getting drowned out but that the thoughts themselves were harder to hear. Speaking of mouthing the words when reading - subvocalization occurs when reading with most people in their larynx. Most people who don't mouth the words silently say them instead as a "good enough" measure. Obviously not the case in deaf-mutes who never learned to speak of course.
  - core-questions 6y ago
    > harder to hear. Interesting. Would you really qualify that as being like "quieter volume", or was it more like it was harder to "recognize" words out of the dialogue? > Obviously not the case in deaf-mutes who never learned to speak of course. I wonder what reading is actually like for these folks, since letters symbolize sounds; they _must_ recognize word-at-a-time with no sub-vocalizing, right? I hope we get lucky and a random person with experience in the field stops by ;)
    - Nasrudith 6y ago
      Like a quieter volume - even though normally the concept of a volume to thought words didn't even apply.
- throwaway0a5e 6y ago
  >I saw a thread on Reddit the other day where someone mentioned "taking the 30 seconds to read something"; the discussion went on a tangent where someone called themselves a slow reader because it took them a whole minute, and then others chimed in that it was taking them longer still. So, I timed myself and it took me 14 seconds to read it. Not that I don't agree with your overall message but petty one-upsmanship at things one should never strive to one-up someone else on is kind of a staple of Reddit and that's probably what you were reading.
  - 6y ago
yodelshady 6y ago
Being more charitable, you could argue fractions are complicated - you're essentially passing someone a function, rather than the result. You could argue that of any number system, but if you can count to ten and understand "more left of decimal point = bigger, more right = smaller" then most comparisons in numerals are easy. 0.25 vs 0.33, 1/4 vs 1/3. We are, I believe, the only animals able to comprehend either, especially in conjunction with units of measurement. Side note, but one of my favourite gotchas is in optimisation - say for a race car, where we want to minimise time (for a constant distance), rather than maximise speed. Strictly speaking, they're equivalent, but people doing the latter almost always end up focusing on top speed, and overlooking the time lost going slowly.
- pantaloony 6y ago
  Oh, I wasn’t trying to be insulting. I think it’s a sign of 1) how legitimately hard “basic” math stuff is for a lot of people, and yeah, fractions seem to be the earliest point at which a lot of (even actually, truly smart!) people stop really “getting it”, 2) people not getting why they should care, and never being sufficiently motivated to care—frankly a lot of math comes off not just as pointless, but like mathematicians are trolling the mere normals, as commonly presented, and 3) “math people” largely not getting that math beyond basic arithmetic actually doesn’t matter very much for a huge portion of jobs and lives, and that they’re failing as a field to communicate the ways in which it could. You might guess from the above that I’m pretty firmly in the camp that thinks “k-12 math just isn’t mathy enough and that’s why it’s bad” is dangerously wrong. You’d be right about that.

core-questions 6y ago

It's actually terrifying to think about. I don't want to denigrate people or be mean, but when you realize that your own standard of literacy is something many people truly struggle to obtain, it helps make a lot of things make sense. For example, I saw a thread on Reddit the other day where someone mentioned "taking the 30 seconds to read something"; the discussion went on a tangent where someone called themselves a slow reader because it took them a whole minute, and then others chimed in that it was taking them longer still. So, I timed myself and it took me 14 seconds to read it. What that made abundantly clear to me was that my own experience in the world - seeing _words_ as first class entities everywhere, immediately tagged and understood as whole components, instantly, without ever "reading" them... is not everyone else's experience. Some adults who nominally believe themselves to be literate must actually have to sit there and spend some effort to recognize each letter and sound out a word, the way my children did when they were ~4 (and some children get even younger). What is the world like for these people? I can often speed-read a paragraph and come away with an understanding within seconds, skimming over it for key words and familiar grammatical constructs; my assumption is that most people posting here can do the same. Maybe that's not the case? There's also a lot of talk on the Internet in the last year or two about inner monologue, with the growing realization that it is likely that a large part of the population simply does not experience the ability to talk to themselves within their own head. This makes me wonder if they can read silently without having to mouth the words; perhaps this is the tip of the iceberg for a differentiation in intelligence that hasn't really been extensively studied yet (unsurprisingly, since psychometrics are not in vogue right now).

Nasrudith 6y ago
Speaking of lack of internal dialog I noticed a quieting of it as a side effect of a medication I was on - normally volume didn't exactly apply but it was difficult to head myself think - not like it getting drowned out but that the thoughts themselves were harder to hear. Speaking of mouthing the words when reading - subvocalization occurs when reading with most people in their larynx. Most people who don't mouth the words silently say them instead as a "good enough" measure. Obviously not the case in deaf-mutes who never learned to speak of course.
- core-questions 6y ago
  > harder to hear. Interesting. Would you really qualify that as being like "quieter volume", or was it more like it was harder to "recognize" words out of the dialogue? > Obviously not the case in deaf-mutes who never learned to speak of course. I wonder what reading is actually like for these folks, since letters symbolize sounds; they _must_ recognize word-at-a-time with no sub-vocalizing, right? I hope we get lucky and a random person with experience in the field stops by ;)
  - Nasrudith 6y ago
    Like a quieter volume - even though normally the concept of a volume to thought words didn't even apply.
throwaway0a5e 6y ago
>I saw a thread on Reddit the other day where someone mentioned "taking the 30 seconds to read something"; the discussion went on a tangent where someone called themselves a slow reader because it took them a whole minute, and then others chimed in that it was taking them longer still. So, I timed myself and it took me 14 seconds to read it. Not that I don't agree with your overall message but petty one-upsmanship at things one should never strive to one-up someone else on is kind of a staple of Reddit and that's probably what you were reading.
- 6y ago

yodelshady 6y ago

Being more charitable, you could argue fractions are complicated - you're essentially passing someone a function, rather than the result. You could argue that of any number system, but if you can count to ten and understand "more left of decimal point = bigger, more right = smaller" then most comparisons in numerals are easy. 0.25 vs 0.33, 1/4 vs 1/3. We are, I believe, the only animals able to comprehend either, especially in conjunction with units of measurement. Side note, but one of my favourite gotchas is in optimisation - say for a race car, where we want to minimise time (for a constant distance), rather than maximise speed. Strictly speaking, they're equivalent, but people doing the latter almost always end up focusing on top speed, and overlooking the time lost going slowly.

pantaloony 6y ago
Oh, I wasn’t trying to be insulting. I think it’s a sign of 1) how legitimately hard “basic” math stuff is for a lot of people, and yeah, fractions seem to be the earliest point at which a lot of (even actually, truly smart!) people stop really “getting it”, 2) people not getting why they should care, and never being sufficiently motivated to care—frankly a lot of math comes off not just as pointless, but like mathematicians are trolling the mere normals, as commonly presented, and 3) “math people” largely not getting that math beyond basic arithmetic actually doesn’t matter very much for a huge portion of jobs and lives, and that they’re failing as a field to communicate the ways in which it could. You might guess from the above that I’m pretty firmly in the camp that thinks “k-12 math just isn’t mathy enough and that’s why it’s bad” is dangerously wrong. You’d be right about that.