You're making a lot of leaps of logic here, which might be why your colleagues are disagreeing with you. You go from "not everyone can learn algebra or calculus" and "mental disabilities exist" to "therefore intelligence is a scale and controlled by genetics and unalterable," which doesn't really track.
Your previous education, your upbringing, your cultural values, these things all also have huge effects on your aptitudes, and you've just dismissed them out of hand, apparently in favour of pre-determined genetic intelligence. I mean, all I know of you is this comment, so I could easily be missing a lot more context about this argument you've had, but it sounds like you have an axe to grind, not a carefully-considered conclusion.
I think the more people can learn algebra than OP implies, but as a former math educator my experience also indicates some people are genetically limited in mathematics. For reference, my specialty was working with very remedial students and only ever had a few students not make progress (~2%) but I do think that small percent was genuinely hopeless and I don't say that lightly. I have a pet theory as to why those students could not do algebra that that you might find convincing:
To start, I believe that the idea of "working memory" is largely valid. Think of it as the number of distinct ideas you can hold in your head at once, sort of like trying to hold a phone number in your head when you've just heard it for the first time.
The general consensus in psych is that this number for the average person is in the single digits and is relatively static in adulthood till a decline in old age. It's been my observation that people with really incredibly small working memory cannot do algebra. The amount of numbers/ideas held in their head is too large, and multiple students in this group described the experience of attempting an algebra problem as feeling like sand constantly slipping through their fingers.
Many of these students grew up in rich neighborhoods with good parents. They had most advantages you can imagine, seem reasonably intelligent when you talk to them, but Algebra will always be beyond them.
My dad was a math and physics teacher and he had a very similar theory around the working memory. However he also thought that the problem for those students that had difficulties with math was that the working memory was often filled up with other stuff than the math that they were working on. It could be anything from difficulties to concentrate to problems with holding the pen correctly and therefore the working memory was overflowed.
This describes my experience with ADHD except your head is filled with impulsive thoughts (noise), so you struggle to string together a bunch of numbers in a logical forward progression through a formula, which also induces cognitive load when recalling the formula to your working memory when it is overwritten by the impulsive thoughts.
I can get around this by brute forcing the numbers into the formulas on paper and going through each step slowly but surely, even steps that people can do mentally. I just need significantly more time than my peers to finish.
Taking stimulants and increasing my dopamine levels across my synapses alleviates much of the working memory deficits I outlined.
I wonder how many of these students that struggle were just undiagnosed ADHD and not deficient in an low IQ mental handicap sense.
> I wonder how many of these students that struggle were just undiagnosed ADHD and not deficient in an low IQ mental handicap sense.
I've got ADHD that was undiagnosed until a decade after finishing my degree, and maths was my favourite - and best - subject all the way from age 4 through to doing solutions to Einstein's equations involving 10+ A4 pages (both sides) of tensor mechanics for my final year project. My results across that time showed the more maths in a subject the better I did, the more writing it had the worse I did.
Doing maths is like reading is for me - an external cognitive structure that I can follow to make my own brain calm down while in that process. While I don't do much maths nowadays, I literally read whenever I'm not actively doing something else - I read a page or two of my book in-between clicking reply to your comment and starting typing this reply.
Maths involves a lot of "muscle memory" once you get past the initial hump. But it's often poorly taught at an early age to the level of inducing near-phobic levels of discomfort with it which to me seems strange. But I don't think there's any extra issue with having ADHD and maths
ADHD is very comorbid with dyslexia, dyspraxia, dysgraphia and dyscalculia - around 20–60% of people with ADHD also have one or more learning difficulties. Dyscalculia affects as many people as dyslexia, but dyslexia is far more well-known and more likely to get diagnosed and helped with. There's a nice summary box of typical symptoms of dyscalculia in this paper:
> To start, I believe that the idea of "working memory" is largely valid. Think of it as the number of distinct ideas you can hold in your head at once, sort of like trying to hold a phone number in your head when you've just heard it for the first time.
Interestingly, testing myself with the Wechsler reverse-digit-span test, I found very large improvements in working memory from taking 20-minute afternoon naps and from modafinil. I'm not claiming everyone is alike, of course, but working memory is definitely not as fixed as height and eye color.
Specifically with regard to mental math, I find I can do a lot more when I'm lying in bed in a dark room than when I'm in an uncomfortable chair in a noisy cafe with people talking to me. Or, for that matter, classroom.
> Many of these students grew up in rich neighborhoods with good parents. They had most advantages you can imagine, seem reasonably intelligent when you talk to them, but Algebra will always be beyond them.
I tried marijuana once and found the opposite effect: when I was high, by the time I got to the end of saying a sentence, I couldn't remember how it had begun. But people report that I seemed like I was conversing normally; if they didn't know me, they wouldn't have realized anything was off. I wonder if these folks were experiencing something similar all their lives?
> I found very large improvements in working memory from taking 20-minute afternoon naps
Sure. My ability to do anything also drops to near zero if I don't sleep enough. Yet I have not found unlimited increases in capability if sleep more and more...
> modafinil
Yeah, drugs are a quite different beast. Doping happens when individual athlete realizes they have hit the limits what their "natural" biology can do and yet still are not going to win the competition.
Yeah, the drawback of modafinil is that it seems to reduce my ability to recall things from long-term memory. Also, it makes it hard to switch tasks when it's necessary.
I don't think I'm suffering from sleep deprivation. Certainly it is true that if you take enough stimulants your performance will worsen! In fact, if you take enough stimulants you'll die and your performance will be zilch!
> To start, I believe that the idea of "working memory" is largely valid.
Wait, are there mainstream schools of thought where working memory isn't considered valid? I'm a layman but I suffer from ADHD, and very much notice that my working memory fluctuates with my attention span (from lack of sleep/stress/etc).
Google's of no help to me, but I remember a story of some educators, looking at some kids who didnt go to school but worked selling concessions, but in turn, were actually quite good at math. They couldn't answer math questions when written out on a worksheet, but they could do the exact same questions when presented in the form of a complex order. (Double digit multiplication and summation isn't the same as algebra, but being able to do that implies a large working memory, which is claimed is the barrier to learning algebra.)
I do have poor working memory and I did struggle with algebra, especially with copying wrong sign from row to row and things like that.
But I did make paper sort of my working memory and when doing algebra I felt that I was just the very resource limited CPU that executed the instructions from paper-memory.
Algebra always made me feel like I was doing some mindfull exercise where I had to empty my mind, follow the paper script and hope I didn't mess anything while switching from row to row of calculations.
Even today, as a programmer, I struggle to remember class or function names, I just empty my mind and am really good at searching stuff in code.
I read this paragraph in a paper on ADHD and learning disabilities literally after replying to a comment above yours...
> There is also evidence of domain-specific cognitive deficits that contribute to specific learning-related disabilities. For example, phonological processing difficulties have been found in children with poor reading performance, whether or not they also exhibited problems with ADHD symptoms or math, but not in children with deficits in ADHD symptoms or math only. Similarly, both with and without a reading deficit, children with ADHD symptoms exhibit significantly impaired object naming and behavioral inhibition, and math-disabled groups demonstrate visuospatial and numerical processing deficits, while those with only reading problems sometimes do not.
There's significant co-morbidity between learning disorders and ADHD, and despite dyscalculia being as common as dyslexia (~3-7% of the population) it's a lot less well-known, isn't as frequently diagnosed and there are fewer tools to help people with it. It would be very possible to have both ADHA and dyscalculia, given you used symptoms listed for both that are almost word-for-word identical with those in the paper...
I had no problem with reading or abstract thinking or grasping mathematical concepts.
My problem was that oftentimes I would screw up calculations for a math problem and only get 7/10 score on it (the reasoning was mostly right, but the answer was not).
Well, I’m certain cockroaches can’t learn calculus. Neither can apes or monkeys. Some humans can. Therefore I think that brain composition has something to do with learning calculus. There is variation in said brain composition amongst humans. It seems reasonable to think that the set of all people is not a subset of all things that can learn calculus.
I haven’t performed any genetics tests but brain composition is partly determined by genetics so genetics might play role, right?
I always wondered if the teachers understood how much effort people put in. Especially in something like math, where you can't just waffle.
I got the feeling as a kid that a lot of my classmates would just give up. I mean they're sitting there acting like they're concentrating on math, but they aren't. In other classes intermittent attention is enough, you pick up social cues and repeated stories that you've heard, and poof you have a history essay. With math there's a need to have all the steps.
How do you control for that as a teacher observing the kids? How do you know whether a kid has actually tried to learn stuff at home?
I still remember my brother was baffled at how I got top grades in math when he never saw me studying. Of course I tended to do that when he wasn't around.
> How do you control for that as a teacher observing the kids?
The only solution I ever found was not having more than 3 students at a time, not an option for most teachers; I spent most of my career working with 1-3 students as a result. With that few students you can carefully observe the mistakes students are making and ask individual questions about their mental state. Experience will eventually tell you to differentiate students not putting in effort from students who are so lost that they're just flailing and hoping something sticks.
With more students, my experience was that both my attention became too split to give students the kind of careful diagnosis to control for effort.
I didn’t imply anything about the number of people who can’t learn algebra other than that I think the number of such people exceeds the number of intellectually disabled people. I used the word intelligence and put this in quotes because intelligence is not really definable but the word does convey a sense of what I mean. One must have a certain level of cognitive ability to learn something. Where that level is for a given topic I can’t say.
You've offered some evidence as to why you believe some individuals are incapable of learning algebra, but you haven't offered an explanation as to why what you observed is necessarily the result of genetics, there could be dozens of additional factors at play here which are not being considered.
HN crowd doesn't think twice about people who try to run DOOM on a stack of pennies, but are ready to give up before trying to get algebra to run on someone with less working memory. It's weird how different the attitude is.
Have you ever been a teacher? Even a teaching assistant?
I have. Some people are dumb.
You try teaching these people (anecdotally they're less than 1% of the population, with no obvious markers, so you have to actually find one first) and then come back and tell me how it's like "getting algebra to run on someone with less working memory". If I wanted to continue that analogy, I might say that the task is like getting algebra to run on someone whose brain has a power supply that randomly shorts out and spends half its time browned out.
Because some people out there are just not easy to teach.
I'm not sure I understand your comment, this is exactly what I spent hundreds of hours of my life trying to do. Was I unclear that my entire educational career was being the person who got through to students that traditional education was giving up on?
I disagree - we have excellent tooling avaliable to cram and compile code into smallest CPUs, but our teaching methods are still the same as they were in 1800's
I think this reveals a lot of ignorance on the huge amounts of different teaching methodologies and techniques that have risen and fallen over the last 100 years.
How do you know what effect upbringing and cultural values has on math performance? You know because there's research for that.
But you can't base any argument on that when research into alternative (or complementary), genetics-based explanations is being stiffled. Or well you can, but that's just society-scale version of googling for statements that you agree with instead of questions that they're supposed to answer.
When you stiffle research directions for political reasons, you're doing politics, not science, and the arguments based on lack of stiffled research don't hold any more water than arguments based on no research.
> society-scale version of googling for statements that you agree with instead of questions that they're supposed to answer
Unfortunately, in practice science often turns out to be almost as much of a vehicle for confirming answers one already has in mind, rather than open-ended investigation.
There were no leaps of logic made by me. I never indicated or said anything about genetics. I said that it’s clear some people can’t learn algebra and gave an extreme example of such a person by saying that an intellectually disabled person can’t learn algebra. I then said that I’m convinced that there is some level of “intelligence” required to learn algebra.
I said absolutely nothing about what percent of people this is true for and absolutely nothing about why this is true. I brought it up in the context of the article because saying that not everyone can learn algebra is as taboo in education as the thought that genetics plays a role in poverty and success in life in psychology. My reason for thinking this is responses like yours.
There are clearly people who can’t learn algebra: intellectually disable people are such an example. I believe some level of “intelligence” is require to learn algebra.
How can you conclude from what I’ve written that I haven’t thought much about my belief? How can it appear I have an axe to grind from what I’ve written? You have formed an image of me that is wildly incorrect. Do you initially assume that everyone who thinks not everyone can learn algebra has an axe to grind?
Other traits like height, health, beauty vary and are influenced by genetics. Intelligence varies between species, and is therefore, at least in part determined by genetics.
Presuming that there are only mentally disabled and normal people is the weird hypothesis. The baseline idea should be that it varies just like health and height. Affected by both genetics and outside factors such as malnutrition and injuries.
This is very nicely put. I wish I had thought of this phrasing when I posted my original comment. The point of my comment was to mention that there are heretical ideas that people won’t discuss in other areas of intellectual inquiry. That was the relation of my comment to the article.
"Nature vs nurture" in the hairless ape presupposes free will, which is a linguistic universal but a metaphysical unprovable.
Look closely enough and there is no essential difference between genetics and other causative factors. Other than maybe some people jumping to the conclusion that one has an axe to grind with minorities when one attempts to explain certain things with genetics. Which is just as much an arbitrary social taboo as the preceding taboos that constitute what we today call bigotry. (For the record, I'm a staunch opponent of all forms of violence and oppression.)
For me it makes exactly zero difference. Even if free will does exist in some essential sense, I do not believe that people generally choose what opinions to espouse. They simply acquire them through mimesis of their social environment. If that makes me a nihilist and a coward, then so be it.
Thought experiment: English Prime but also excluding any constructs expressing intentionality. I dream of a world where the concept of free will is considered just as poor taste as racial slurs. I think that, perhaps paradoxically, it will be a much more free and just world.
> Thought experiment: English Prime but also excluding any constructs expressing intentionality.
I like this idea of a "deterministic" language. In fact it reminds me of Nonviolent Communication, and is probably a good tactic for discussions that might otherwise devolve into personal attacks.
Saying "there is no essential difference between genetics and other causative factors" is arbitrarily different from saying "all is one, separateness is an illusion". That is, it differs in connotations and not in the essential content of the statement.
Which is exactly what you said, except that you chose to ignore that connotations conduct meaning, when you asked your rhetorical question. This is not e-prime, it is a plain old adverb answering the question "how?" like adverbs normally do.
No, I'm not. Can you be more precise in what you mean by "causative factors"? Without further context, and based on my understanding of the world, virtually anything internal or external to a person could cause them to be more or less skilled at something. It contains everything, and so seems that your statement could be interpreted that genetics and everything else in existence are one in the same.
You asked what was the difference between my statement (that genetics is not more special than other causes of being more or less skilled at something) and the statement that "all is one, separateness is an illusion". I answered that the difference between these two statements is arbitrary, which I still believe to be the case. Apologies if something else happened to you.
My original comment had the purpose of questioning the validity of the "nature vs nurture" distinction. It just seems like an unhelpful distinction, but then again I'm not a biologist, just a lay person who likes their concepts tidy.
Genetics is obviously not the same as everything else in existence; I'm not sure that even makes sense as a statement. You seem to have somehow derived that I am arguing against the concept of distinctions at all. I'm not sure if language would be feasible without distinctions.
I don't disagree with any of what you just said, but I fail to see what point you are trying to make or what you are arguing against. Without the (linguistic) act of making distinctions, everything is indeed one and the same, but that's... kind of pointless?
EDIT: Sibling poster also seems to fail to make the distinction whether (a) we're comparing genetics to other causative factors, or (b) we are comparing my statement about genetics to your "all is one" interpretation of it.
In case it's still unclear, (a) and (b) are two completely separate things and I'm not sure how this conversation got to the point of conflating them. It just serves to reinforce my belief that the ambiguity of our language's syntactic structures makes it inordinately difficult to reason about many things in everyday language. Or maybe I'm just a bad communicator. "Me bad", "you bad" that's supremely easy to express lol
EDIT2: Correction, TheSpiceIsLife does actually get it.
> My original comment had the purpose of questioning the validity of the "nature vs nurture" distinction. It just seems like an unhelpful distinction, but then again I'm not a biologist, just a lay person who likes their concepts tidy.
The confusion is in the difference between proximal and ultimate causes, the rest of the discussion is over the ultimate cause of certain phenotypic features being down to genetics, some other mechanism or not significant at all. You've then said "all these different things are just proximate causes and [because free will doesn't exist] the ultimate cause is the laws of physics" to which people have unsurprisingly gone "what the hell does that have to do with anything?" because, well, it doesn't.
The fact that the ultimate cause of me taking a dump is "the laws of physics" doesn't mean the proximal cause wasn't me 'deciding' to go to the loo, and the fact that you can always say "the laws of physics" (or some higher power) is the cause doesn't make talking about higher level causes any less useful.
I don't believe in free will but its such a good trick that you act as though it were true almost 100% of the time, and talking about my 'decisions' as causes is useful the same as talking about 'genetic' and 'environmental' is useful. We talk about the causes of the Big Bang usefully despite time only coming into existence when the Big Bang happened :)
What sprang to my mind when I read the arbitrarily response is that you have equally little control over the genes you’re born with as you do the place, time, family, society, economy, technology, and culture you’re born in to.
> How is this any different from saying "all is one, separateness is an illusion"?
> It's not arbitrary. "Other causative factors" is boundless.
These are distinctly different lines on inquiry. One is an inquiry to in the illusory nature of separateness, the other is an inquire in to the boundless nature of causative factors.
Fair enough. I still believe that tiptoeing around these issues gives power to those who consciously perpetrate and benefit from institutionalized violence.
Like another commenter said, operating with a comfortably skewed mental model doesn't help resolve the actual socioeconomic issues.
I was a little hyperbolic in my original answer. In all honesty, I think it's probably best to continue research in this area. However, in the current state of the world I don't see how that research is especially beneficial. Every finding would have to be taken with such a massive grain of salt that I have a hard time imagining we would find practical applications for it.
In the current state of the world, most scientific research will be co-opted by some violent apparatus or another. Does that mean we should lose hope and stop doing any research altogether?
By current state of the world, I mean that any research into this topic can't control for all the possible variables. That's why we'd have to take it with such a large grain of salt.
That's why I brought up metaphysics and e-prime actually. We can't resolve societal contradictions in a fundamental way if we do not have the tools to reason about them, and the main tool we have for that, human language, can at times be pitifully inconsistent and ambiguous - even if one does, in fact, control for people's automatic emotional reactions to controversial subjects.
How does this not track? It's clearly obvious that there are intellectual boundaries that exist (E.g. if you're not this smart you're going to struggle).
Previous education, upbringing, cultural values, etc are all separate effects that may influence your overall ability, but intelligence __definitely__ influences your ability.
Low intelligence + good education = poor overall ability
> Your previous education, your upbringing, your cultural values, these things all also have huge effects on your aptitudes, and you've just dismissed them out of hand, apparently in favour of pre-determined genetic intelligence.
They didn't seem to do this at all. It can simultaneously be true that there are some who, due to genetics, simply cannot complete a particular task, no matter how conducive an environment they are put in, while for others genetically do not have these hurdles but whose success is still dependent on their environment.
If anything, you are the one dismissing this possibility out of hand, and making leaps of logic.
The thing which I think gets missed out of these discussions is the notion of community. We're such horrific individualists in the West that we seem to see nature and nurture as distinct, which of course they aren't. The nurture of a child is a product of the combined abilities (from nature and nurture) of the people in their family and community. There is no "I"; our DNA and mores are all part of a greater whole.
That's because we haven't yet cornered good ol' "free will" yet like we have this subject, or if we have, it certainly isn't trotted out as regularly and forcefully by the Right, likely because the virtue of the concept is to support punitive discursive apparatuses.
My feeling with math is that moving on too soon is disastrous. If you move past a subject without having grasped it, you don't have a good base for the next subject. This compounds, and the explanations stop making sense.
At that point people are trying to help you but saying things to you as if you are stupid, but you still don't understand. That really sucks, so people get afraid of math. Avoiding it, and nodding when asked "do you understand" when really they do not.
This is hard to fix because you need to go back to the point they did not understand, but the fear and pain makes even teaching that a lot harder to fix as well.
My feeling is that most people should be able to understand algebra. However, I think that requires a very deliberate and personalized approach for some people. Certainly with collective classes, if you go at the speed of the slowest student there will be slow progress and a lot of people who are bored and mentally check-out.
If any approach is going to work for people who have real difficulties, it needs to be small-scale personal teaching, and it needs to come with trust. Someone needs to feel like they can keep saying "no I do not understand" without disapproval, disappointment, or frustration from the tutor.
This is so true. I'm Black and attended one of the worst performing elementary schools in my city for the first four years of school, which gave me an awful base for my math learning when I was finally transferred to a much higher performing school in a Jewish neighborhood on the other side of the city, not to mention high school and college. Only when I started working in programming did a lot of algebra and trig click (probably helps my first junior role threw me in the deep end working with linear algebra and trigonometry in animation and was lucky to have a senior around who chose to take on a mentor role). Math in public schools is basically magical spell incantation and it appears to most kids that you either have "it" or you don't. Math is a subject I believe requires long-term work that doesn't easily fit into the grade pass/fail structure of school, but then again a lot of aspects of mass education are fundamentally broken.
Your previous education, your upbringing, your cultural values, these things all also have huge effects on your aptitudes, and you've just dismissed them out of hand, apparently in favour of pre-determined genetic intelligence. I mean, all I know of you is this comment, so I could easily be missing a lot more context about this argument you've had, but it sounds like you have an axe to grind, not a carefully-considered conclusion.