An astonishing regularity in student learning rate
psyarxiv.com
psyarxiv.com
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.
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.
I mean, that's pretty clearly racism.
I would never say to colleagues at my university that I hold the belief that some people have more intellectual talent than others. Amongst certain vocal subgroups of academia an unassailable core belief they hold is that all people are equal in intellectual abilities and that only external factors contribute to any divergence in perceived intellectual talent or in knowledge.
Einstein's report cards https://www.openculture.com/2020/04/albert-einsteins-grades-...
In that light, this particular achievement of Einstein’s doesn’t seem very impressive.
Edit: to clarify, mine was in the mid-2000s, don't know if there have been changes with things like Common Core, but from what I've seen/heard that seems focused on much earlier years so I don't think it would have affected this part of math education.
If not, it sounds like resume padding by someone who wanted to make Einstein seem even more impressive than he is.
But it may have changed since then.
He is a prime example of how traditional schooling methods are typically stacked against extremely intelligent students who don't conform to those learning methods.
https://theeconomyofmeaning.com/2013/07/27/science-myths-did...
It's a sign of the times that a person with two decades of experience as an educator needs to heavily qualify an obvious fact.
And the problem of grade inflation is more about universities competing for prestige (and keeping wealthy donor/legacy families happy) than about creating outcome equity.
I'd say that one degree program being less difficult than another doesn't make it fake or unserious though. It's just natural that some topics are harder than others. There's a qualitative difference between "unserious" and "easier" I would say.
https://www.npr.org/2021/06/12/1005833496/critics-concerned-...
Latin may not be a requirement for whatever Grievance Studies, but it certainly is necessary if you want to study Virgil.
I could see loosening the requirement, but if the loosening isn't simply to permit French and German (also hugely important in academics, some fields more than others, very influential on English, and also often untranslated in otherwise English texts, so, justifiable for similar reasons) as substitutes, yeah, I'd regard it as likely a step backwards.
In Classics, where Ancient Greek and Latin are principal topics of study
I understand why we might relent on not teaching them as a part of general studies, but in Classics, Theology and Ancient History at the graduate level there's no way to escape the need to read the original, and anyone who must rely on translation will remain crippled in the field as long as they do so.
> JOHN MCWHORTER: Thanks for having me.
> SIMON: Josh Billings - I don't have to tell you, a classics professor who's the department's head of undergraduate studies - says, quote, "having new perspectives in the field will make the field better." What would be wrong with that?
> MCWHORTER: Nothing at all, but I don't want to hear it until I know that it's not a way of saying through the back door that we want to have more Black students, and it's racist to expect them to learn Latin and Greek.
It makes complete sense. If you are already a talented undergrad research that isn't going to focus on european classics in grad school (or in your Junior Papers or Senior Thesis), why make students finish an entire curriculum on ancient rome or greece?
source: this was discussed during princeton reunions at a panel, or I may have heard this from a another alumnus that was a classics major, heard after the change.
edit: cant reply for some reason (?) but ancient china was a mismemory. it didnt go beyond the near east and africa. still makes perfect sense if you specialize in neighbors to mediterranean.
Is that true? It sounds more like classical Greek literature was just removed from the core curriculum.
Heck all students in american education ( K-12 ) should be taught latin at the very least. Why we stopped...
> One course must deal substantially with classical reception or comparative approaches to the ancient world; this requirement may also be fulfilled by study of another language relevant to the student’s interests (Akkadian, Modern Greek, etc., at any course level).
You make such sweeping claims based on a sample size of one. You neglect to account for survivorship bias -- you cannot see all the bullshit papers that were rejected from journals. This all feels obvious to me as issues with your analysis. Where is your intellectual rigor?
The U.S news law school rankings hold a lot of weight. They include statistics for how many of their students place at top law firms. If they grade inflate and lose credibility with these top law firms as to the grades being indicative of the quality of their students, top law firms will stop hiring from those schools, and their rankings will collapse. Of course, if you got a C in law school, that's a bad grade. In fact, you can flunk out if your grades go below a B-. Also, classes are graded on a strict curve. The teacher can only give out a certain number of A+s.
https://www.forbes.com/sites/frederickhess/2021/12/06/gifted...
I have now attempted a few times to finish my higher education, always bounced HARD as I lack the mental facilities needed to deal with the frustration/commitment of actually having to learn.
Most of the ivy league schools are now doing this simply because they are dropping the most, and hoping that other universities will follow them in dropping out (they typically do).
Case in point: I struggled in my algebra class and developed no useful intuition for groups until years later, but by most conventional standards I am a moderately intelligent person.
Can a mentally disabled person learn college algebra?
The answer is yes or no, or some can but others can't. Within the context of college algebra and considering no other areas is it safe to say that some people are smarter than others? I think clearly the answer is yes. Of course a person not smart in college algebra might have genius level talent in programming, writing, art, or some other area.
I'm smarter than the vast majority of people in the world when it comes to mathematics but am completely useless when it comes to engineering, art, writing, physics, and other areas. Saying one is bad at college algebra is not a denigration, it is an assertion of fact and not in any way a determinant on one's worthiness.
I teach mathematics at a university. A large majority of my colleagues think that everyone is equally capable of learning college algebra. I think they are wrong. I think it is obvious they are wrong. They think any assertion that some people college algebra must be rooted in racism or other terrible biases that one has.
Academicians ought not dogmatically cling to notions that are easily disprovable. Namely, it is clear that some people - mentally disabled for instance - can't learn college algebra. We should not shy away from confronting uncomfortable truths.
I agree, natural aptitude absolutely is a thing. I'm somewhat smart, but maths does not come readily to me no matter what I try. And don't even get me started on music - which I have brute-forced myself into being barely able to play.
They have to hold that view, though, else their reason for existence disappears. How can students justify the high cost of hiring a professor, accepted on the premise of being able to make it up with higher future earnings, if they realize that the reason there is a spectrum of incomes is because some people can't rise into higher paying work?
You and I know that the mentally disabled person will never rise into a $500,000 per year job, no matter how hard they try, because of their disability. But your colleagues have to suggest that the mentally disabled person won't only because that person hasn't attended their classes. Their entire marketing strategy of getting students into their seats rests on it. Failure to communicate that to students means they soon find themselves out of job.
It's like everyone here is taking some extreme edge case as the baseline for mental disability where it is immediately obvious that they can throw them into the "too dumb" bucket.
The problem is that the answer isn't yes or no. Performance isn't discrete. Someone who fails college algebra and repeats a semester might do better than their peers next time around. Your oversimplification would mean that no improvement is possible which is at odds with the paper this HN submission is about which is about the fact that the learning rate is the same.
That implies that it isn't a yes or no question. The question is how long will it take. You might bucketize a person that needs 10 semesters to finish his bachelor's (assuming European 6 Semesters) as incapable of learning college algebra.
The problem with this reasoning is that finishing the bachelors could still result in a quite significant improvement in quality of life even for a handicapped person, so acting as an authority telling them they can't do anything is counterproductive.
>. Saying one is bad at college algebra is not a denigration, it is an assertion of fact and not in any way a determinant on one's worthiness.
Now you are moving the topic. Being bad at something is different from being unable to learn something.
People who are capable of learning something can still be bad at it. College freshmen are bad at the things they are about to learn, that is the point of college, to learn new things and get better at them.
What's clear to me is that people have different learning rates and different need for personalized attention. I also would never argue with the assertion that some people have greater natural aptitude for specific things, meaning their ability to pick up the material at a standard pace without a lot of extra personalized help.
There's plenty of research showing that IQ exists and can be consistently measured, but I would hesitate to ascribe the learning outcomes in a higher-level math class directly to IQ. If assessing general intelligence were easy, we wouldn't need decades of psychology research on the topic. So I personally don't think we should be in the business of trying to assess how smart people are in general. Assessing attitude at specific tasks can of course be practical and useful.
That said, have you asked your colleagues for clarification on what they mean by "everyone can learn"? Are they talking about learning it on a hand-wavy pop science level (eg Numberphile), or learning it well enough to derive results and apply it in new problems? Do they have a timeline in mind for learning, or a specific context? Are you sure your colleagues are being dogmatic for fear of confronting uncomfortable truths, or are they just optimistic? Or have they forgotten that algebra is pretty esoteric and far away from what people normally deal with in their day-to-day lives, and might actually be a specialized topic that does require a bit of specialized natural aptitude?
We don't have enough information to say. But what's almost certainly true is that one of you is smarter than the other.
I think a useful analogy is smart = compute, wisdom/knowledge=data.
Your example is not great because "woodworking" is primarily a knowledge game. Nothing is complex to the point you can't understand it.
University-level mathematics is less obvious--there's certainly a knowledge aspect--but I would stay largely a compute game.
Almost all people can become top-tier at knowledge games, not nearly as many at compute games.
I think his example is very good if he requires much more effort to understand straightforward woodworking concepts. It might not be that he can't be an average woodworker but that it takes him 5x more effort - and after just 3x more effort he's kind of done.
Source: I learned college algebra, and I have my woodshop 20 yards from me.
If he was 50 years younger he probably would just be a very mediocre programmer and not have "wasted" his time with this other intellectual activity.
Einstein would be a data entry clerk trying to get a job writing javascript.
I suspect with so many more educated people we have so many more true genius level minds than a 100 years ago but we have narrowed economically useful intellectual life to such a degree that 99% of them are doing well paid sub-optimal bullshit with their genius unexpressed.
Can a paraplegic play college football? I don't get your insistence on catechising the obvious.
We are then left we needing to modify the statement. What is true is the following: Some people, but not everyone, can learn college algebra.
This is an uncomfortable statement for a lot of people because the inevitable follow up is: Who can and who can’t learn college algebra?. Relatedly, one must confront the idea that not everyone is college material. Maybe too many people are going to college and this is why so many in college are struggling in basic courses. I could go on.
Your post appears naive in that you don’t seem to have thought through the implications of the idea that not everyone can learn college algebra.
I think that's a stretch, unless you expand the meaning of "intellectual disability". I would agree that considerably more people can succeed than currently do because effort can make up for a lot, but that's a different claim.
People have different working memory capacity, different abilities to reason deductively and considerably more differences on various other metrics of cognitive performance. There are as many dimensions to cognitive performance as there are ways to measure athletic performance, and people fall on very different parts of this spectrum.
With significant effort over time, I can make up for athletic deficiencies and become a pretty good basketball player, but being 5'9" I almost certainly would never be able to make a college basketball team let alone the NBA. I'm not sure why this same logic applied to cognitive abilities is so controversial.
Not at all. In my experience, many people of mediocre intelligence but a background that has sufficient education think they're geniuses. The variability in intelligence achievable by tutoring vastly exceeds the difference in their intelligence vs. that of the average inner-city high school dropout without a disability.
> People have different working memory capacity
Multiple studies have shown how this is easy to train.
> different abilities to reason deductively
This is also very easy to train by example.
> I almost certainly would never be able to make a college basketball team let alone the NBA
Being able to do college algebra isn't equivalent to making the NBA, which means being in the top fraction of a percent in basketball ability. Being able to do college algebra is equivalent to being able to dribble.
Running ability is also easy to train, that doesn't mean everyone can run a marathon. Some people have flat feet or poorly proportioned limbs unsuited to long-term running. These aren't disabilities preventing them partaking in such activities, but nevertheless limits their potential.
> Being able to do college algebra is equivalent to being able to dribble.
No, it's being able to at least dunk. Again, a common skill but not one everyone can achieve.
Everybody without a disability can run a 5k. High schools used to require students to do a mile run to pass physical education.
> Some people have flat feet or poorly proportioned limbs unsuited to long-term running.
And some people have microencephaly. We're not talking about outliers. We're talking about the vast majority of people.
> No, it's being able to at least dunk.
Look, you're not special for being able to learn college algebra. 95% of Koreans and Singaporeans can do it today, but this wasn't the case 60 years ago. It just requires a basic level of education.
No, you specifically said "people without a disability". Unless you're going to expand the meaning of "disability", various permutations within the range of "normal" physical characteristics will impose different limits on athletic abilities, and analogously, the range of cognitive qualities (memory, focus, spatial reasoning, etc.) will do the same for cognitive tasks.
The fact that these qualities can be improved via training doesn't change the basic fact that those limits will be quite different for different people, even within the normal range. We can quibble all day about whether college algebra falls under that category, but this basic fact won't change.
And that range is smaller than the difference between your ability to perform cognitive tasks and the average high school dropout's ability to perform those tasks. Education makes a much larger difference.
Your study is about the effect of an extra year of badly done education on people who drop out of school, which is worth 1 IQ point. That same study shows that the effect of mediocre education on people who don't drop out of school is an increase of 5 IQ points.
What is funny and ironic is that you falsely accuse me of making a baseless assumption and then in the next sentence explicitly say you are assuming I’m learning English. I think it’s clear that I’m not learning English.
His argument seemed like a pretty straightforward logical deduction to me. If his argument doesn't refute the claim that everyone can learn college algebra, then you must have some unusual definition for one or more of "everyone", "learn" and "college algebra".
It is naive in the sense in that it actively tries to discourage people from trying and learning including the ones who can because they will have this brain virus implanted into their minds that they can't do something because of some unchangeable factor and then turn the mind virus into reality where they are unable to perform which then further tells them that they can't perform because they aren't smart enough. It is basically the equivalent of pulling up the ladder under the pretense of avoiding injury in case someone falls. You can tell anyone that they aren't smart enough and tell them to not do something but only people who try and succeed can disprove them.
So you have this constant cheap troll attack about people talking how you can't do things and then you must put in the expensive effort to disprove them which they can only do in a few disciplines.
No one's discouraging anything. Differences in cognitive abilities should be no more surprising than differences in ability to jump and run, thus resulting in differences in one's ability to be a professional basketball player.
It is simply a fact that most people cannot play in the college level basketball, let alone the NBA. This should not be surprising, nor does this fact discourage people from playing basketball causally for fun or fitness. I'm not sure why this exact same argument would suddenly be discouraging when applied to cognitive activities.
My non-professional experience is that most people are capable of learning most things with enough time and dedication, up to a certain level of sophistication. There's a huge range of variation in how quickly different people can learn different topics, how capable they are from learning by reading versus listening, how much they struggle with various emotion management problems that might inhibit their otherwise-highly-capable cognitive abilities, et multa alia.
Moreover, very very very few students are ever taught how to study and how to learn. Even fewer still are taught how to understand their own minds, and how to find the balance between training their minds to learn in certain ways and finding learning styles and subject areas that work well with their minds. Some students instinctively realize that writing, drills, and practice form the seeds of intuition, which is the basis for understanding, while others never really figure this out on their own. Some students understand how to take notes that work for them, while others have bad handwriting and find it difficult to take notes at all.
I think that what we tend to perceive as "intelligence" is some combination of "ability to learn a limited set of desirable subjects relatively quickly from conventional instruction techniques and resources" and "well-spoken".
If that is true, then if we want more equitable learning outcomes, we should be focusing on helping students to explore how their own minds work, to learn self-awareness and emotion management skills, to improve communication skills, and to learn their own innate mental strengths and weaknesses, so they can more easily self-select into and self-direct within their own learning environments. And society in general should offer and hold high esteem for a greater variety of learning environments and types of intelligence.
Of course, some people will indeed struggle with emotion management, or communication, just like some people will struggle with learning mathematical proofs or understanding complicated historical events. But I think that's better than our current status quo of just hoping that students figure all this stuff out for themselves. I would even hypothesize that parental involvement in these areas specifically might be causal for some % of differences in student education outcomes.
Edit: All of the above is of course possibly contradicted by the article under discussion here. I'll have to read it in more detail, and maybe I'll update my beliefs as a result.
As a less offensive example, there are people who literally cannot comprehend a=b, b=c, a=c. They just can't do it.
There are people who can't do abstraction.
There are people who can't do accounting, because they get stuck on debit/credit.
There are people who can't hold huge multidimensional models in their heads.
There may be various measures of intelligence, but no matter what the measure there will always be someone at the bottom of it.
The point of my post was not to deny this, but to assert that what we perceive as intelligence in our day-to-day lives might not be something as deep as that.
- Some people are taller than others, Basketball Coach
- Some people can run faster than others, Track Coach
- Some people have more musical talent than others, Piano Instructor
- Some people are sicker than others, Emergency Room Nurse
Tends to be a lot of "convert at the point of a sword" from the authoritarians, as usual for them.
“Some people are taller than others” is dogma?
Sure. That doesn’t make the underlying variation non-empirical, i.e. dogmatic.
But your straw man does not stand up under his own power. The concern is and always will be what differentiates peoples' abilities, and which abilities in which people are incentivized / selected for in our society. These are of course still matters of intense debate. We are reasonably sure by now that it is both nurture and nature -- indeed, a synthesis of the two perspectives -- that is vital to understand all the forces at play.
On the "nature" side, genetic damage resulting from multi-generational trauma has been identified as a reasonable explanation over that of some notion of "inherent" genetic differences by race. So, while the contributing aspects of "nurture" happened in the past, it is the "nature" of the specific individual, born already with those disadvantages, that largely determines the outcomes of their lives. There is of course still the "nurture" of that individual, whose environment can influence the balance of advantage or disadvantage for that person after they are born as regards positive outcomes. This is not limited to family life but extends to all forces incident on that individual.
Then it seems inevitable that, as a result of any focused campaign of coercion or discrimination, persistent statistical patterns will arise within oppressed sub-populations which impact outcomes for future generations. In other words, we are all still living among the echoes of the past.
Proponents of everyone can go to college and be successful ought to be precise in their statements. What they really mean is that more people are capable of succeeding in college than our currently attending college. If they would argue thusly and say it as such then a real discussion can be had. Instead we have people saying everyone can go to college. This shuts down any notion that perhaps too many people are going to college. No reasonable discussion can be had when one starts with the clearly false statement that anyone can go to college.
Why some people aren’t capable of succeeding in college and the causes of such is a different discussion.
Can you cite some examples that reflect this exists on a meaningful scale?
I never ran into this at college nor have I known anyone to say they witnessed it. It seems like we should have, if this is a routine thing.
A majority of incoming college students place into pre-college level courses. A recent trend is to ban pre-college level courses and instead do supplemental instruction in college algebra. Too many students are underprepared so we ban the courses to get them prepared. It is now a trend to no longer require college algebra level knowledge to get a college degree. The only reason for this trend is because a lot of people fail college algebra.
The only discussion I’ve seen regarding limits to learning algebra is at this link:
https://matheducators.stackexchange.com/questions/11396/what...
If you acknowledge you have such a limited viewpoint, why make such strong assertions of facts? You cannot possibly know the things you are pretending to be an authority on.
It is common for people to make conclusions on topics based on their experience and what they’ve read. We all do this since none of us can possibly fully research all topics. In my first post I specifically declared that I have no expertise on these matters. I think this topic is an emotional one for you and this is clouding your interpretation of what I have written.
I’ve encountered people like you at the various colleges I’ve taught at. You make it hard to have discussions regarding uncomfortable ideas. Such is not befitting of a person with your apparent intellectual capabilities.
The only strong assertion that I’ve made is that some people can’t learn college algebra. If you can find a severely mentally disabled person who has learned college algebra then please present your evidence. I suggest you are part of the problem in education. If we can’t acknowledge even the obvious (namely that not everyone can learn every topic) then we will continue the trend of dumbing down standards and curriculum and just passing people through the system in a misguided approach to educational equity.
Normative, not substantive. "Other people speak without knowing the limits of their knowledge" is not a good reason to emulate them.
Research is not about filling your bucket of known knowns: that's merely literature review. It is about converting unknown unknowns to known unknowns related to some question or goal, and then chipping away about the unknown-ness of whatever enables you to reach your conclusion. With this exploration of the limits of knowledge I hope comes some humility about what people are willing to state in such strong and unwavering terms.
> If you can find a severely mentally disabled person who has learned college algebra then please present your evidence.
Straw man. Who has claimed this? The question of who is given advantage in the educational system is not related to this strange fixation of yours. I can acknowledge that someone defined as "disabled" is "dis-abled" from performing certain acts. This is uncontroversial.
I suspect you are hiding behind this innocuous claim to avoid having the more uncomfortable conversation about what you think actually holds people back in the educational system. So far you have said "some people are smarter than others". I proposed a way this could be explained. You seem to have rejected it, but have not replaced it with another theory of your own.
> I think this topic is an emotional one for you and this is clouding your interpretation of what I have written.
Yeesh. Good luck out there.
I scanned the paper, but I don't recall if this was just K-12, or also higher ed, but I wonder if this result would fall apart in more complex subjects.
Also, no matter what the learning rate really is, if a student isn't interested in the subject, good luck getting them to learn much at all!
As an autistic person I agree with this, but it comes at a huge cost of much worse understanding of facial expressions of people and much less adaptability to change.
Also one more big disadvantage is that most people can't distinguish between a smart person and an a$$hole (Dr House is a good example of a person focused on saving lifes, but still people think he's an a@@hole... Elon Musk is an even more controversial example)
Let's suppose that there are no such examples. What then? If a person is an asshole what does it matter why they are an asshole?
I don't believe that intellectual ability necessarily requires you to miss out on facial expressions or adaptability. It occurs in some people, but even, e.g., John von Neumann was famously gregarious and friendly. Furthermore, it is worth noting that autism (even high-functioning autism) does not consistently present with exceptional ability in formal reasoning — that is also a "sometimes".
>Dr House is a good example of a person focused on saving lifes, but still people think he's an a@@hole
Dr. House is a fictional character. I don't think there has ever been a real life doctor who diagnoses his patients consistently from intuition and then sends his residents on a scavenger hunt for kicks.
Neurotypical high-intelligence gets less media attention. I have an aunt that's an incredibly intelligent aerospace engineering professor who the military regularly brings in to teach fighter pilots the math behind flight. (This is a non-trivial achievement.) She's just a regular person.
This still does not explain why some performed less than others (the ones that should and ones who should not pass).
> I have no expertise on this topic but it seems to me that some people are truly smarter than others.
This is a fact indeed, but the real question is how much variability in performance/learning this explains, and if there are other factors that explain part (and how much) of this variability. For this we need data.
At one time, students were routinely "held back" if they didn't understand something well enough to pass. That gave them a chance to catch up, so that when they got back into the class, they would be more likely to succeed.
It always seemed to me that this was an act of kindness, for the alternative is for them to sit in classes of more and more demanding material, feeling less and less adequate.
Back in those days, it was not really considered a terrible thing to spend some extra time catching up. Folks would ask me around report time whether I had passed my exams. It was not meant as an insult, and was not taken to be one, either.
I see postsecondary students all the time who clearly have missed some steps at around grade 9 or so. Being smart and ambitious, these students would definitely have caught on, if someone had assessed them honestly. Instead, they live in an imposter-syndrome world, always waiting to be "found out".
Folded in with the false kindness of passing everyone is, as others have pointed out, the deeply corrosive influence of measuring teaching performance by passing rates.
It doesn't really take a lot more than honesty and sometimes a helping hand, to let students realize their potential, whatever it might be.
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.
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.
You can also test normal but be very high functioning. So there is no necessary or causative connection between IQ and effective capacity.
Robots like ChatGPT May test substantially in some IQ tests and have no intelligence or agency at all.
I think many people put the onus of predicting success on measures of IQ, and most/all good IQ tests don’t claim to do this. There would be a face validity issue, and there are much better tests that can predict success (however success is measured) than IQ tests. I think that this is grossly unfair to IQ tests.
Will AI be able to do well in IQ tests? Maybe, but I don’t think that it will be relevant.
My stance has been and is that IQ tests measure the capacity to learn, extend, and expand on new topics (in humans). Nothing more, nothing less.
Some other points:
- IQ tests are not a measure of effectiveness. Many, many more variables go into that.
- IQ tests are biased, and pretty much have to be. That said, good IQ test designers try to minimize the bias for their target audience. I think that this has been more or less effectively done in the US for folks in the middle class or higher.
- Related, any give score on an IQ test should be seen as an IQ floor rather than an IQ ceiling. There are many reasons why someone may not score their maximum score (or even close to it) when taking an IQ test. Anxiety and fatigue are simple examples.
- IQ is correlated to income, but is this is a very broad correlation. Specifically, average income goes up with IQ up to about 135 or so (can’t remember the exact number) and then starts decreasing (possibly due to being in lower paid fields like academics, possibly due to social dysfunction). But these are all aggregated numbers. The individual results vary wildly within any narrow IQ band.
- As you alluded to, effectiveness and/or success is predicted by many other things other than IQ, and in many cases IQ may only be a weak predictor. IQ tests don’t claim to predict success. Things like social skills, socio-economic status, access to resources, physical health, and mental health can be much better predictors of effectiveness/success depending on the task.
- IQ tests are quite good at finding people at the extremes (very low and very high), but actually does a fairly poor job of differentiating folks at those ranges. On a personal level, I think the main use of IQ scores would be to identify these folks early and get them the resources they need.
To close, here is a decent article that discusses one view on how IQ and “success” are only loosely related:
https://www.verywellmind.com/are-people-with-high-iqs-more-s...
You absolutely must be joking.
This tells me that you have never learned a foreign language to a high level of proficiency, and that you know very little about art.
Regarding the rest of your post, talent certainly exists, and things like motivation and talent are better predictors of success than IQ, but IQ tests don’t claim to predict success (even though IQ scores and success might be mildly correlated).
As I mentioned in another reply (please read it), folks seem to think that IQ tests claim to predict success. They don’t. It’s an unfair onus to put on IQ tests.
Well, I've obviously learned English well enough to fool you :P
Anyways, I might have misunderstood you, dunno... my impression was that you're saying exactly that - that IQ is the main predictor of academical success - which is something that I both strongly disagree, and have a plenty of anecdotal examples around me that prove it wrong.
Cheers. I walked straight into that. That said, I imagine that there is more to that story.
Fwiw, IQ is mildly correlated to a lot of things, including academic success. But as I said and strongly believe, success in academics has much stronger predictors than IQ.
I have personally trained many groups of “low performers” and “less smart people” to run circles around high IQ people. I have a mountain of (unfortunately proprietary) data that shows how much certain types of training can accelerate learning.
All that said, the toughest and most abstract ideas/areas are pretty much limited to the high IQ people. I will add that this comes with baggage — they are often frustrated that their peers don’t see or understand what they see and understand.
And maybe "great" leaders have figured out how to make a boring topic interesting for their ICs.
One thing I've learned over my time in tech is that it's a lot easier to tap into someone's ego than it is to tap into their inherent interest in their job. People might be interested in preserving their ego more than they like the actual work involved in building/maintaining a random service.
Sounds like it fits perfectly both with what I've said and what the submission is about, and again has nothing to do with "crazy smarts". Just practice.
I'm talking about, all else equal, good learners and good leaders can "tap into" passion at will, either in themselves or in others, to gain an advantage in practice consistency, which leads to improved fluency in the task. A learner's IQ ends up being a wash; if they have this skill, they can learn better than someone with their same IQ (or higher) without this skill (and I do suspect it to be a skill, as people modulate over their ability at learning over their lifetimes).
The rest of what you say is too poorly defined to be a well reasoned model of how reality works at a fundamental level.
And if you can't be specific about what I'm saying that's wrong, I might start to suspect you don't know what you're trying to say.
It's more like a music degree program, in that regard, except I think those usually reject people who try to apply without substantial prior experience and facility with music. Or like attempting an art major when you don't already have above-average-for-your-age art skills. Like, I'm pretty sure the 100-level biology classes don't assume you've already spent hundreds to thousands of hours dissecting frogs for fun, but rather, have maybe done a very little of it in high school.
> 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.
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.)
If practice is the single most important factor, then e.g. exam scores should be a function of time spent studying, and not of the test taker.
I know people from college that worked a lot harder than me and spent a lot more time studying than me, and they got worse grades. I never "practiced" and aced all my exams.
Practice shooting basketballs leads to better results at shooting basketballs.
Practice playing piano leads to better results at playing piano.
Practice studying leads to better results at studying.
Practice scoring well on exams leads to better results at scoring well on exams.
That's how the parallels work. And it's clear true: however one defines studying, it gets easier as one practices it. It might or might not be effective in improve exam scores, for many reasons, but it definitely improves studying itself.
> you're proposing that practice studying should result in improved exam scores
I'm not sure that he is. Me and my kids tended to ace tests without studying, often with the barest understanding of the material (that vanished soon after).
I'd guess his solution might be to have a complex representative problem to solve as proof of knowledge. Have it ready at the beginning of the course and as soon as kids can solve it, they're done.
Unfortunately, this doesn't line up with predetermined schedules which tend to dominate every mm of schooling.
But lets not get bogged down in the weeds. OP's theory is that "practice", or time invested, is the single most important factor in mastery. However, it is clear that some people can reach a significantly higher level of mastery in less time than others. Some people walk out of lecture understanding the concepts clearly, whereas some need to spend hours struggling with it to get that same level of understanding.
So suppose there were three people who received the same lecture:
A's mind naturally and enthusiastically is drawn to considering the concepts discussed in class; without any conscious prompting or effort, for the pure joy of it, their brain spends a few hours in the day after the lecture chewing over the content and assimilating it.
B's mind has no such natural draw; their brain only goes over the material of consciously prompted -- but at least when this conscious review is being done, their brain dutifully considers and chews over the material.
C's mind actively dislikes the material. They have to expend willpower every moment that they're studying; and their brain is always looking for excuses and other things to do.
Now, it will appear that A has spent very little looking at the material, because they have spent no conscious study time looking at it; but in fact, if you could measure actual brain engagement time, A has spent hours and hours engaging with the material.
Similarly, it will appear that C has spent hours and hours looking at the material, because they have spent hours trying to study it. But because they're working against their brain's inclination, their brain has actually only spent a fraction of that time actually engaging with the material.
Thus it appears that A achieves mastery without practice, B achieves mastery with practice, and C fails to achieve mastery even with practice. But in fact, A has practiced the most -- driven to because of their natural interest in the subject; while C has practiced the least -- impeded by their natural aversion to the subject.
ETA: I should note this is no moral judgement on either A or C: far from it. In high school almost all subjects were interesting, and thus easy for me; when I got to university, I began to find certain subjects less interesting, the result was that I avoided taking classes in those subjects if I could.
I've got similar anecdotes. In high school, the way I studied for history exams was to come in to class early and listen to two of my classmates quiz each other with flashcards. In my head: "Yup, knew that one. Yup, knew that one. Oh, didn't remember that one. Hmm, didn't know that one either." My classmates got 100% on the flashcards, then got C's on the exam; I got an A.
My sophomore year of university, at the beginning of the year, there were three of us -- myself, K, and C, who got along well and sat together in lectures. C eventually got bored and stopped coming to class. The morning of the final exam, K was basically giving C a crash-course for the entire semester -- patiently explaining all the concepts and techniques that C had completely missed by not coming to class. Then they took the exam, and K got a 'C', and C got an 'A'. (So did I.)
The thing about both of these anecdotes is that in both cases, as far as I can tell, the people who got C's actually knew the material. I didn't grade any of their exams, so I don't know exactly what went wrong; but whatever's happening is more complicated than simply, "They weren't smart enough to master the material."
How many things does your toddler practice?
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?
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.
> 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.
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.
This might explain why open source volunteer projects rarely ever have non-technical management.
As a person with high IQ I was always frustrated how slowly I learn things regardless of how rapidly I can understand new things.
The problem with "speed of learning" is that the result is not defined here. What is the result of learning? Is it being able to recite the material back? Is it being able to use it in real world?
I would expect that high IQ will help with learning complex material and may potentially be a detriment when learning stuff that requires a lot of rote memorisation. I know it is a detriment for me... my mind is just unable to stick to a monotonous task of remembering things and will naturally get distracted with anything more rewarding intellectually.
Which is to say that learning by rote memorisation isn't very interesting to me and this makes me inefficient at doing it. I am much more likely to learn facts when in context of solving problems that are interesting to me.
I assume it's about retaining something in memory.
So basically we might have CPUs of different speeds but the chemistry of our RAM works at the roughly same speed for everyone.
I guess education has traditionally been about exposure to topics, a "learned" person was someone who knew "lots of things". But in the age of wikipedia on your mobile, creative and insightful intelligence is even more valuable than rote memorization.
The implication is that this study is novel in its ability to measure rote memorization performance, and if that's true that the overall field of study struggles in core metrics of even that "rote" ability, hoo boy they'll never make progress in actual novel/powerful intelligence.
With that said, we all know high-IQ people (which presumably aren't measured necessarily on rote knowledge) that are imbeciles in real life, and even if most hacker news people are "smart", we each know how we are imbeciles in some aspect or manner.
In the end this will probably feed the "memorize and test" educational lobby, which is not a good thing.
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.
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.
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!
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.
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.
I think the point of this research is that this requirement is pretty consistent in humans regardless of their other capacities or prior knowledge.
Reading through all the comments I can see a lot of people struggling to reconcile this result with their existing mental models of intelligence and learning.
Or not.
I'm been labeled gifted my whole life and typically require much more exposure to concepts, in order to catch up to most folks. The gifted part comes in with what I can do once I reach their level.
Think of a skill where 'a' is an entry-level understanding, 'c' is average and 'e' is exceptional.
Most people transition easily, hitting a then b then c. Past that is harder and most don't go there.
For me to get to b, I have to learn a.1-a.100. To get to c it's b.1-b.100 (hopefully faster).
By the time I get to c, I'm far, far behind everyone else. However, my much broader understanding of a, b & c might make the hop to d & e trivial for me.
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.
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".