20 ms·

An astonishing regularity in student learning rate

115 points by pineaux 4y ago

onikolas7 4y ago
Is it a surprise that an education system targeting the mean produces results close to the mean? It's like training for the marathon by only doing 2 mile runs and then saying people's ability to run long distances shows little variation.
pineaux 4y ago
Differences are mostly attributable to prior knowledge.
- Psyladine 4y ago
  That should likewise account for variations in rate of learning, since you can't predict what prior knowledge they possess of the subject matter. If the rate is consistent, there must be more than existing knowledge bases, or there would be clear staggered tiers or leapfrogging reflecting different accumulative advantage.
  - apwheele 4y ago
    Agree with this, the data is consistent with small, additive, effects of learning over time. (And those additive effects don't show much variance between students, at least for these short courses.) I have a pet theory in general for noisy social science data -- the best we can do is often find additive effects (there is a boutique subset of social science showing "simple models" do almost just as well as more complicated machine learning models). Here there is variance in each of the test stages, maybe I am guessing standard deviation of 5 percent points within person (e.g. if you could have a person retake the entry exam, one time 65, another time 70, another 60, etc. would not surprise me). The variance likely swamps any ability to identify different rates of growth over the shorter course period. (Also for course instruments, truncation of 100% makes it more difficult as well.) Just a pet theory anyway!
- seaners 4y ago
  "Prior knowledge" is a strange way to write IQ.
  - scotty79 4y ago
    IQ has barely anything to do with learning.
    - ryan93 4y ago
      ???? Smarter people require less exposure to the same concept to "get it". You might actually just be lying and there is no reason for me to engage.
      - scotty79 4y ago
        They can understand faster. But not learn (remember) faster. I think higher IQ people might in some cases learn faster because if they understand the thing they are trying to remember, they can "replay it" in their heads bumping up the number of exposures which might help remembering. But not everyone with high IQ does that.
        naasking 4y ago
        Learning isn't just remembering, it's also reflective of skills. Someone with considerably higher IQ can arguably understand how to program computers faster, and thus start writing programs on their own sooner. Would we not say they learned programming faster?
        barking_biscuit 4y ago
        The real difference appears to be they simply cover more ground in aggregate over the long run on their own steam because their physiology makes it calorically cheaper for them to do so compared to their peers. IQ seems to correlate most strongly with working memory, though ones capacity for working memory doesn't seem to have much bearing on the mechanism behind the formation of new memories themselves. Building semantic memory requires repeated exposure. What really matters is the rate at which the individual exposes themselves to learning opportunities. This appears to be a function of how rewarding it is to you, how expensive it is for you, and how much (or in some cases little) executive control you have.
syzarian 4y ago
From the abstract: These findings pose a challenge for theories of learning to explain the odd combination of large variation in student initial performance and striking regularity in student learning rate. My anecdotal experience from teaching math in higher ed for 20 years is that the variation in initial performance might be due to passing students who don’t deserve to pass. Especially in recent years our (teachers’) performance is measure by passing rate and I have very little incentive to fail a student even if they don’t know the material. I have no expertise on this topic but it seems to me that some people are truly smarter than others. As an extreme example consider the difference in intellectual talent between Einstein and a mentally disabled person. I suggest the possibility that maybe some people start off school in kindergarten behind their peers and never catch up. If the rate of learning is largely the same for people then starting off in kindergarten in the upper half in terms of knowledge would likely lead to one ending up in the upper half of knowledge at the end of college.
- korroziya 4y ago
  >I have no expertise on this topic but it seems to me that some people are truly smarter than others Ironic that if you say this almost anywhere (academia, Reddit, your local bar) people immediately assume you're talking about Eugenics, accuse you of racism and try to get you fired.
  - SamoyedFurFluff 4y ago
    I’m kind of confused because I’ve never heard of “some people are smarter than others” to be a eugenicist position. That’s more for stuff like “we should have IQ minimums to become parents” or something.
    - korroziya 4y ago
      Slightly related: https://www.bbc.com/news/world-us-canada-46856779 https://www.bbc.com/news/world-us-canada-46856779
      - 4y ago
082349872349872 4y ago
Does anyone know how a "learning opportunity" is defined? (I failed to find it with a cursory in-document search) If only software-mediated interactions are measured I could imagine that for math, a significant component of initial performance would be "student did (resp. did not) take advantage of the exercises in the textbook".
- zhdc1 4y ago
  There are two tables in the appendix (S1 & S2) where they break down each of the datasets and provide an overview of the associated course and grade level.
gwd 4y ago
From the "Significance Statement": > Prior research, often using self-report data, hypothesizes that the path to expertise requires extensive practice and that different learners acquire competence at different rates. Fitting cognitive and statistical growth models to 27 datasets involving observations of learning and performance in academic settings, we find evidence for the first hypothesis and against the second. Students do need extensive practice, about 7 opportunities per component of knowledge. Students do not show substantial differences in their rate of learning.
- AnonCoward42 4y ago
  It fits a common narrative in that all humans are absolutely equal in mostly everything and can be sculptured like clay.
  - jules 4y ago
    These are college students taking the same course, so the effects you hint at are reduced compared to getting a sample from the general population.
  - gwd 4y ago
    Not necessarily. One of the theories I read had it that practice was the single most important factor for mastery; and that the apparent difference in aptitude between people was actually a difference in interest: If you enjoy something, you're much more likely to drive yourself to practice more, and thus achieve a higher mastery; whereas if you actively dislike something, you're more likely to do the minimum amount you can get away with. So it certainly may be the case that if someone says they dislike math, that they simply haven't been exposed to the right kinds of math, or the right kinds of problems; and that trying different kinds of presentations will allow them to overcome a dislike of it, and practice more than they were. But maybe there are people who will dislike math no matter what form it takes; for those people, doing math will always be a motivational struggle. And in any case, even if you can move someone from "I hate math" to "math can be cool", will that person ever have the drive, the thirst for math which would be required to be a top performer? Seems very unlikely. IOW, even if in theory everyone could reach the same level of expertise by practicing the same amount, it's still not possible in practice for everyone to practice the same amount. (Just as, in theory, everyone can lose weight by simple diet and exercise; but in practice, actually maintaining the "simple diet and exercise" routine to lose weight and keep it off isn't something most people have shown themselves capable of.)
trabant00 4y ago
I guess it depends on what you understand by similar/dissimilar rates of learning. All students are humans and even further they are humans who managed to access that school. So you will not find the difference between a potato and an ascendant god. Meaning the college students are more similar than they are different and findings will reflect that. On the other hand somebody learning even 5% faster all their life will gather a massive difference over the years. And in particular I don't think this conclusion is warranted: > Our evidence suggests that given favorable learning conditions for deliberate practice and given the learner invests effort in sufficient learning opportunities, indeed, anyone can learn anything they want. There's a lot of "given" in there. And you can not expect to invest infinite energy in providing motivation and personalized conditions for everybody. At the end of the day even if intellect, talent and learning speed would be equal, which they are not, somebody who can self motivate and learn in less than optimal conditions will go further.
logicchains 4y ago
This matches my experience in college: some people were miles ahead in CS, but they were all people with an interest in it who put more time into it than the bare minimum. Not necessarily a result of great practical relevance though, as people's interests aren't easy to change.
- kibwen 4y ago
  The dirty secret of perceived intelligence is that, in practice, mental acuity (or however you want to characterize IQ) matters less than passion for the subject matter. It doesn't matter how smart you are if you aren't motivated to immerse yourself in the subject matter. Of course, there's no reason a single person can't have both, but on balance I'll take a passionate person with moderate intelligence over an intelligent person with moderate motivation.
  - vharuck 4y ago
    Yes. I've always seen IQ as a predictor for how fast you can learn material and make connections. So it saves time. Which makes people with high IQ look superhuman during school: new topics are introduced every month, and the smart kids breeze through. After school, when 99% of jobs (even the ones for those smart kids) don't require constantly learning progressively harder concepts, IQ matters less. The time it saves for a disinterested person can no longer compete with the time an interested person can spend.
    - ivanhoe 4y ago
      > I've always seen IQ as a predictor for how fast you can learn material and make connections. This is what we call being talented for something, it's not necessarily related to the one's IQ.
      - csa 4y ago
        > This is what we call being talented for something, it's not necessarily related to the one's IQ. I think you’re just playing word games here. My slightly different short definition of IQ is that it is an indicator of the capacity to learn, extend, and expand on new ideas (with exceptions for mental blocks, which exist even in higher IQ people). That is, it is not just speed and/or quantity. When you take two people with a large IQ difference and have them learning, extending, and expanding in a wide range of unfamiliar domains, the high IQ person will consistently do more and better. This is not merely talent.
twawaaay 4y ago
Nothing surprising here. Real results of studying like for many other activities is not about amount of time spent or effort put in. I met a lot of people who would spend a lot of time learning things and then immediately forgetting it. Why? Because they were not interested in it. Being interested in stuff is what causes you to suck out the information about the topic from the environment. We even have whole structures in our brains like reticular activation system that evolved to help with it. Have you ever noticed that when you got interested in, say, bicycles, you suddenly start noticing what kind of bicycles people are riding, where are bicycle shops around you and that some people in your family have bicycles and some not? Even when this information was previously available to you but you just ignored it because you were not at all interested? You don't have to be actively searching for the information, the information just magically becomes available to you. Our brains are built to ignore everything that is not immediately interesting to you, you have to be interested in something to allow information to pass. When you are interested in something, you will develop complex, long lasting connections between parts of the material. If you are not interested you are at best just forcing yourself to store the material for retrieval. When you are interested in something, whenever you read new information it will cause retrieval of information you learned previously, it will cause you to think about both and will put the new information IN CONTEXT (connected with) the old information. It will also reinforce the older memory. It will also make the new memory much more discoverable, more likely to come up when you think about something else related. This is why students who put in a lot of work but are only interested in good grades can give you answers to the questions but will be unable to connect different things in a way that was not presented in the book. This is why topics like math (which is what I studied) are mercilessly punishing to people who think they can just memorise it. It is also why current way that math is being taught to kids is so misguided -- because it tries to turn the topic to something that can be memorised by only ever testing with tasks that were previously listed in a book so that the student can just memorise all types of tasks and the only thing they have to do is recognise which type of task they are faced with. This does not lead to any ability in math. As an interviewer I am very wary of hiring people who are not interested in what they are doing. Regardless of whether they are able to put in hours they are unlikely to ever improve in any significant way and are almost always only doing minimum to get by. Which in software development tends to result in a lot of technical debt because getting something to run is just about 20% of effort. Employees who are not interested are unlikely to form deeper connections about things they are doing. They stay forever amateurs in their field where mastery requires deep understanding. They will not react to complex problems other than in a shallow way.
gandalfian 4y ago
I read of a study on piano learning. Kids from a wide variety of backgrounds take the same piano lessons so its a good leveller. The result was there was a direct correlation between hours practiced and progress. Nobody really lagged behind or shot ahead. The conclusion was that while not every child would end up a Mozart, none of them became Mozart without practicing. It raised interesting questions about streaming by ability, what are we really sorting children by? Are we really separating and helping the more intelligent or just cutting loose those children with poor study skills or a lack of motivation to do their homework.
- SpeedilyDamage 4y ago
  Also, doesn’t it raise questions about what Mozart was doing at a crazy young age? Was he practicing piano before he could read? Walk? How many things does your toddler practice?
- naasking 4y ago
  > Are we really separating and helping the more intelligent or just cutting loose those children with poor study skills or a lack of motivation to do their homework. Does it then follow that we should keep those students all together, or perhaps should those students with low motivation and/or poor study skills get specialized programs/attention that can improve those qualities that lead to success?
aj7 4y ago
Of extremely more interest than learning rate is learning ceiling. They are not uncorrelated. But the integral of the derivative is vastly more important than the derivative itself.
- barking_biscuit 4y ago
  I'm very curious about this. Can you expand more?
  - aj7 4y ago
    Most of us can learn to play chess in 10 hours. Few can become grandmasters. Most Hacker News readers have gotten through calculus. Few have gotten through the mathemamatics needed to study elementary particle physics, let alone abstract mathematics. Raising the ceiling in yourself or your students is far more important than the time it takes. By the way, speed of learning is very important in not becoming discouraged and in motivation so it strongly correlates to ceiling. I taught my wife fractions in her late 40’s. My Mom taught it to me much faster when I was 8. My wife, a ballerina and professional dancer, tried to teach me to dance. Not only was I abysmally slow at uptake, but my ceiling was very low.
usgroup 4y ago
I roughly read the abstract as asserting that you could write down learning state of an individual as: x_i(1+r)^n_i Where the rate r is common but n_i (time spent) and x_i (starting position) are individual. Sure that’s believable but I frankly can’t be bothered to read enough of this article to see how they argue that a model like that is physically relevant and not just yet another way of writing things down.
qup 4y ago
AI assistants are about to enter the game and level the playing field. Maybe.
WarOnPrivacy 4y ago
Parenting taught me that labeling kids as smart can be crippling for them. Firstly, the label only applies to certain test-reflective metrics and may not align with an ability to achieve the given goals. Secondly, smart kids didn't create their intelligence and won't know much about it. And problematically, the label can create unrealistic expectations - for both kids and adults. By the time kid #3 was in school, I was advising teachers to just ignore whatever aptitude they thought they saw and just focus on how well my child's effort was resulting in the desired outcome.
Izkata 4y ago
Most comments here are basically saying these results don't make sense, but I think they make perfect sense. I was in school during No Child Left Behind, and they only achieved that goal by teaching to the lowest common denominator. Those of us who could learn faster weren't allowed to, or learned in subjects not covered by standardized testing. From the outside, the end result did indeed look like everyone learned at the same rate.

115 points by pineaux 4y ago

Is it a surprise that an education system targeting the mean produces results close to the mean? It's like training for the marathon by only doing 2 mile runs and then saying people's ability to run long distances shows little variation.

pineaux 4y ago

Differences are mostly attributable to prior knowledge.

Psyladine 4y ago
That should likewise account for variations in rate of learning, since you can't predict what prior knowledge they possess of the subject matter. If the rate is consistent, there must be more than existing knowledge bases, or there would be clear staggered tiers or leapfrogging reflecting different accumulative advantage.
- apwheele 4y ago
  Agree with this, the data is consistent with small, additive, effects of learning over time. (And those additive effects don't show much variance between students, at least for these short courses.) I have a pet theory in general for noisy social science data -- the best we can do is often find additive effects (there is a boutique subset of social science showing "simple models" do almost just as well as more complicated machine learning models). Here there is variance in each of the test stages, maybe I am guessing standard deviation of 5 percent points within person (e.g. if you could have a person retake the entry exam, one time 65, another time 70, another 60, etc. would not surprise me). The variance likely swamps any ability to identify different rates of growth over the shorter course period. (Also for course instruments, truncation of 100% makes it more difficult as well.) Just a pet theory anyway!
seaners 4y ago
"Prior knowledge" is a strange way to write IQ.
- scotty79 4y ago
  IQ has barely anything to do with learning.
  - ryan93 4y ago
    ???? Smarter people require less exposure to the same concept to "get it". You might actually just be lying and there is no reason for me to engage.
    - scotty79 4y ago
      They can understand faster. But not learn (remember) faster. I think higher IQ people might in some cases learn faster because if they understand the thing they are trying to remember, they can "replay it" in their heads bumping up the number of exposures which might help remembering. But not everyone with high IQ does that.
      - naasking 4y ago
        Learning isn't just remembering, it's also reflective of skills. Someone with considerably higher IQ can arguably understand how to program computers faster, and thus start writing programs on their own sooner. Would we not say they learned programming faster?
      - barking_biscuit 4y ago
        The real difference appears to be they simply cover more ground in aggregate over the long run on their own steam because their physiology makes it calorically cheaper for them to do so compared to their peers. IQ seems to correlate most strongly with working memory, though ones capacity for working memory doesn't seem to have much bearing on the mechanism behind the formation of new memories themselves. Building semantic memory requires repeated exposure. What really matters is the rate at which the individual exposes themselves to learning opportunities. This appears to be a function of how rewarding it is to you, how expensive it is for you, and how much (or in some cases little) executive control you have.

syzarian 4y ago

From the abstract: These findings pose a challenge for theories of learning to explain the odd combination of large variation in student initial performance and striking regularity in student learning rate. My anecdotal experience from teaching math in higher ed for 20 years is that the variation in initial performance might be due to passing students who don’t deserve to pass. Especially in recent years our (teachers’) performance is measure by passing rate and I have very little incentive to fail a student even if they don’t know the material. I have no expertise on this topic but it seems to me that some people are truly smarter than others. As an extreme example consider the difference in intellectual talent between Einstein and a mentally disabled person. I suggest the possibility that maybe some people start off school in kindergarten behind their peers and never catch up. If the rate of learning is largely the same for people then starting off in kindergarten in the upper half in terms of knowledge would likely lead to one ending up in the upper half of knowledge at the end of college.

korroziya 4y ago
>I have no expertise on this topic but it seems to me that some people are truly smarter than others Ironic that if you say this almost anywhere (academia, Reddit, your local bar) people immediately assume you're talking about Eugenics, accuse you of racism and try to get you fired.
- SamoyedFurFluff 4y ago
  I’m kind of confused because I’ve never heard of “some people are smarter than others” to be a eugenicist position. That’s more for stuff like “we should have IQ minimums to become parents” or something.
  - korroziya 4y ago
    Slightly related: https://www.bbc.com/news/world-us-canada-46856779 https://www.bbc.com/news/world-us-canada-46856779
    - 4y ago

082349872349872 4y ago

Does anyone know how a "learning opportunity" is defined? (I failed to find it with a cursory in-document search) If only software-mediated interactions are measured I could imagine that for math, a significant component of initial performance would be "student did (resp. did not) take advantage of the exercises in the textbook".

zhdc1 4y ago
There are two tables in the appendix (S1 & S2) where they break down each of the datasets and provide an overview of the associated course and grade level.

gwd 4y ago

From the "Significance Statement": > Prior research, often using self-report data, hypothesizes that the path to expertise requires extensive practice and that different learners acquire competence at different rates. Fitting cognitive and statistical growth models to 27 datasets involving observations of learning and performance in academic settings, we find evidence for the first hypothesis and against the second. Students do need extensive practice, about 7 opportunities per component of knowledge. Students do not show substantial differences in their rate of learning.

AnonCoward42 4y ago
It fits a common narrative in that all humans are absolutely equal in mostly everything and can be sculptured like clay.
- jules 4y ago
  These are college students taking the same course, so the effects you hint at are reduced compared to getting a sample from the general population.
- gwd 4y ago
  Not necessarily. One of the theories I read had it that practice was the single most important factor for mastery; and that the apparent difference in aptitude between people was actually a difference in interest: If you enjoy something, you're much more likely to drive yourself to practice more, and thus achieve a higher mastery; whereas if you actively dislike something, you're more likely to do the minimum amount you can get away with. So it certainly may be the case that if someone says they dislike math, that they simply haven't been exposed to the right kinds of math, or the right kinds of problems; and that trying different kinds of presentations will allow them to overcome a dislike of it, and practice more than they were. But maybe there are people who will dislike math no matter what form it takes; for those people, doing math will always be a motivational struggle. And in any case, even if you can move someone from "I hate math" to "math can be cool", will that person ever have the drive, the thirst for math which would be required to be a top performer? Seems very unlikely. IOW, even if in theory everyone could reach the same level of expertise by practicing the same amount, it's still not possible in practice for everyone to practice the same amount. (Just as, in theory, everyone can lose weight by simple diet and exercise; but in practice, actually maintaining the "simple diet and exercise" routine to lose weight and keep it off isn't something most people have shown themselves capable of.)

trabant00 4y ago

I guess it depends on what you understand by similar/dissimilar rates of learning. All students are humans and even further they are humans who managed to access that school. So you will not find the difference between a potato and an ascendant god. Meaning the college students are more similar than they are different and findings will reflect that. On the other hand somebody learning even 5% faster all their life will gather a massive difference over the years. And in particular I don't think this conclusion is warranted: > Our evidence suggests that given favorable learning conditions for deliberate practice and given the learner invests effort in sufficient learning opportunities, indeed, anyone can learn anything they want. There's a lot of "given" in there. And you can not expect to invest infinite energy in providing motivation and personalized conditions for everybody. At the end of the day even if intellect, talent and learning speed would be equal, which they are not, somebody who can self motivate and learn in less than optimal conditions will go further.

logicchains 4y ago

This matches my experience in college: some people were miles ahead in CS, but they were all people with an interest in it who put more time into it than the bare minimum. Not necessarily a result of great practical relevance though, as people's interests aren't easy to change.

kibwen 4y ago
The dirty secret of perceived intelligence is that, in practice, mental acuity (or however you want to characterize IQ) matters less than passion for the subject matter. It doesn't matter how smart you are if you aren't motivated to immerse yourself in the subject matter. Of course, there's no reason a single person can't have both, but on balance I'll take a passionate person with moderate intelligence over an intelligent person with moderate motivation.
- vharuck 4y ago
  Yes. I've always seen IQ as a predictor for how fast you can learn material and make connections. So it saves time. Which makes people with high IQ look superhuman during school: new topics are introduced every month, and the smart kids breeze through. After school, when 99% of jobs (even the ones for those smart kids) don't require constantly learning progressively harder concepts, IQ matters less. The time it saves for a disinterested person can no longer compete with the time an interested person can spend.
  - ivanhoe 4y ago
    > I've always seen IQ as a predictor for how fast you can learn material and make connections. This is what we call being talented for something, it's not necessarily related to the one's IQ.
    - csa 4y ago
      > This is what we call being talented for something, it's not necessarily related to the one's IQ. I think you’re just playing word games here. My slightly different short definition of IQ is that it is an indicator of the capacity to learn, extend, and expand on new ideas (with exceptions for mental blocks, which exist even in higher IQ people). That is, it is not just speed and/or quantity. When you take two people with a large IQ difference and have them learning, extending, and expanding in a wide range of unfamiliar domains, the high IQ person will consistently do more and better. This is not merely talent.

twawaaay 4y ago

Nothing surprising here. Real results of studying like for many other activities is not about amount of time spent or effort put in. I met a lot of people who would spend a lot of time learning things and then immediately forgetting it. Why? Because they were not interested in it. Being interested in stuff is what causes you to suck out the information about the topic from the environment. We even have whole structures in our brains like reticular activation system that evolved to help with it. Have you ever noticed that when you got interested in, say, bicycles, you suddenly start noticing what kind of bicycles people are riding, where are bicycle shops around you and that some people in your family have bicycles and some not? Even when this information was previously available to you but you just ignored it because you were not at all interested? You don't have to be actively searching for the information, the information just magically becomes available to you. Our brains are built to ignore everything that is not immediately interesting to you, you have to be interested in something to allow information to pass. When you are interested in something, you will develop complex, long lasting connections between parts of the material. If you are not interested you are at best just forcing yourself to store the material for retrieval. When you are interested in something, whenever you read new information it will cause retrieval of information you learned previously, it will cause you to think about both and will put the new information IN CONTEXT (connected with) the old information. It will also reinforce the older memory. It will also make the new memory much more discoverable, more likely to come up when you think about something else related. This is why students who put in a lot of work but are only interested in good grades can give you answers to the questions but will be unable to connect different things in a way that was not presented in the book. This is why topics like math (which is what I studied) are mercilessly punishing to people who think they can just memorise it. It is also why current way that math is being taught to kids is so misguided -- because it tries to turn the topic to something that can be memorised by only ever testing with tasks that were previously listed in a book so that the student can just memorise all types of tasks and the only thing they have to do is recognise which type of task they are faced with. This does not lead to any ability in math. As an interviewer I am very wary of hiring people who are not interested in what they are doing. Regardless of whether they are able to put in hours they are unlikely to ever improve in any significant way and are almost always only doing minimum to get by. Which in software development tends to result in a lot of technical debt because getting something to run is just about 20% of effort. Employees who are not interested are unlikely to form deeper connections about things they are doing. They stay forever amateurs in their field where mastery requires deep understanding. They will not react to complex problems other than in a shallow way.

gandalfian 4y ago

I read of a study on piano learning. Kids from a wide variety of backgrounds take the same piano lessons so its a good leveller. The result was there was a direct correlation between hours practiced and progress. Nobody really lagged behind or shot ahead. The conclusion was that while not every child would end up a Mozart, none of them became Mozart without practicing. It raised interesting questions about streaming by ability, what are we really sorting children by? Are we really separating and helping the more intelligent or just cutting loose those children with poor study skills or a lack of motivation to do their homework.

SpeedilyDamage 4y ago
Also, doesn’t it raise questions about what Mozart was doing at a crazy young age? Was he practicing piano before he could read? Walk? How many things does your toddler practice?
naasking 4y ago
> Are we really separating and helping the more intelligent or just cutting loose those children with poor study skills or a lack of motivation to do their homework. Does it then follow that we should keep those students all together, or perhaps should those students with low motivation and/or poor study skills get specialized programs/attention that can improve those qualities that lead to success?

aj7 4y ago

Of extremely more interest than learning rate is learning ceiling. They are not uncorrelated. But the integral of the derivative is vastly more important than the derivative itself.

barking_biscuit 4y ago
I'm very curious about this. Can you expand more?
- aj7 4y ago
  Most of us can learn to play chess in 10 hours. Few can become grandmasters. Most Hacker News readers have gotten through calculus. Few have gotten through the mathemamatics needed to study elementary particle physics, let alone abstract mathematics. Raising the ceiling in yourself or your students is far more important than the time it takes. By the way, speed of learning is very important in not becoming discouraged and in motivation so it strongly correlates to ceiling. I taught my wife fractions in her late 40’s. My Mom taught it to me much faster when I was 8. My wife, a ballerina and professional dancer, tried to teach me to dance. Not only was I abysmally slow at uptake, but my ceiling was very low.

usgroup 4y ago

I roughly read the abstract as asserting that you could write down learning state of an individual as: x_i(1+r)^n_i Where the rate r is common but n_i (time spent) and x_i (starting position) are individual. Sure that’s believable but I frankly can’t be bothered to read enough of this article to see how they argue that a model like that is physically relevant and not just yet another way of writing things down.

qup 4y ago

AI assistants are about to enter the game and level the playing field. Maybe.

WarOnPrivacy 4y ago

Parenting taught me that labeling kids as smart can be crippling for them. Firstly, the label only applies to certain test-reflective metrics and may not align with an ability to achieve the given goals. Secondly, smart kids didn't create their intelligence and won't know much about it. And problematically, the label can create unrealistic expectations - for both kids and adults. By the time kid #3 was in school, I was advising teachers to just ignore whatever aptitude they thought they saw and just focus on how well my child's effort was resulting in the desired outcome.

Izkata 4y ago

Most comments here are basically saying these results don't make sense, but I think they make perfect sense. I was in school during No Child Left Behind, and they only achieved that goal by teaching to the lowest common denominator. Those of us who could learn faster weren't allowed to, or learned in subjects not covered by standardized testing. From the outside, the end result did indeed look like everyone learned at the same rate.