I have been trying to get better at chess lately. I grew up playing it so I'm already fairly proficient, and I've been putting a decent amount of free time into studying openings and playing puzzles. Yesterday, I played my friend who hasn't played in literally years and never really played seriously anyway, and he beat me handily 3/3 games. I know that I do not have the brain to be a chess master, no matter how much time I put in, because I don't have enough working memory to keep the board in my head.
Life circumstance stratification, certainly, and you will get no disagreement from me that some people don't have the time or energy necessary to devote to something as not-immediately-useful as calculus, but from an intellect perspective, no.
Everyone who is not experiencing some kind of mental illness has the intellectual capacity to learn calculus, though I will capitulate it is fortunate for me and this statement that we do classify a low enough IQ as a mental illness!
Are you seriously suggesting trying to raise multiple children while simultaneously learning calculus is approximately as hard as living alone and trying to learn calculus?
Honestly, I think you're trying to find a neat solution where none exists. You haven't stumbled on anything here, you're more likely ignoring the real-life circumstances your students find themselves in, and your colleagues are not.
To suggest it? No. To be taken seriously though?
I could be living in a ditch down by the river, or I could be the leading researcher into how people learn calculus and it wouldn't make a difference with regard to my argument (though, practically speaking if I were the lead researcher on how people learn calculus, I'd be more likely to back my argument up with objective research, and that would strengthen my argument).
> (of an argument or reaction) directed against a person rather than the position they are maintaining.
Nothing about a reputation or using it to discredit them.
For example, I'm not a calculus teacher, therefore I couldn't possibly form a valid argument about how teaching works. That would be an ad hominem, because it focuses on who I am (not a teacher), rather than what I've said (the teacher I was replying to hasn't eliminated any variables at all before drawing their conclusion). (It's also nonsensical, considering how many other things people teach, and how small a percentage of all teachers calculus teaching ends up being, and how unrelated-to-the-science-of-education calculus is).
It's actually funny, because the example you've given isn't an ad hominem, since you have evidence to support the idea that I can't cook (the burnt toast). You're equating an absence of information about me with specific data, which is different.
People have to make judgments with imperfect knowledge. It’s reasonable to discount the unsubstantiated opinions of someone with no experience with the topic at hand.
It should at least be interesting to you that it was obvious from your comments that you don’t have experience teaching mathematics in the classroom. Why was that so obvious to those of us with that experience? The previous question is rhetorical.
What is interesting to me is the fact that you retreated to this ad hominem the moment you were challenged, because it tells me you don't have any real explanation for how you eliminated other possible causes for your students sometimes performing poorly.
You'd prefer to live in a world where your experience has meaning than to live in a world where your experience is not valuable when faced with this question, which is completely human of you, but ultimately not useful in this discussion, due to its anecdotal and un-rigorously collected nature.
I can't stop you from throwing this New Yorker article, and the other works of Dr. Harden, in the face of your colleagues, but I can hopefully dissuade others from making the same logical mistakes you're making. I believe I've succeeded at that, by clearly highlighting the carelessness of what you've said here.
Ultimately, what I find most fascinating is, in real time, you've demonstrated how right Dr. Turkheimer ultimately is and how dangerous this research can be when put in the hands of folks who don't understand its delicacy or even the basic facts surrounding these arguments.
I'm grateful for your engagement with me, it's been helpful to work through this with someone like you, but I'll commit to the thing you tried and failed to do; I'm no longer going to reply to your comments in this thread. You're clearly (and I mean clearly) wrapped up in a need to think of some of your students as too dumb to learn calculus, and there's literally nothing I or anyone else here can say that would convince you otherwise, and at this point I've done my part in preventing others from thinking that your insight is useful or helpful in this conversation.
Have a great rest of your evening!
Here’s an example:
… I must be a calculus teacher in order to challenge your assertion that IQ is the primary source of the problems your students have with learning in your classrooms..
No one has said any of these things and no one has implied any of these things. I never said or implied that IQ is the primary source of anything. No one believes that you must be a teacher of calculus to be right. What people have wondered is if you are a teacher because some of your statements seem to the the type of statements only a non teacher would make.
Given the immense complexity involved with learning, there's essentially no way for you to describe the situation with enough detail for anyone to be able to make an informed judgement. It's extremely common for bad players to describe themselves as 'proficient', spending a 'decent amount of time' can mean anything, studying openings and playing puzzles is likely the wrong way to practice, the skill level of your friend is impossible to ascertain, etc.
The way you actually get better at anything is by:
1. Dedicating enough time to it, consistently (~20h per week or so maybe if you want any sort of quick results). The incredibly common trap here is that people think that spending time on a game equals getting better at it. There's no way to improve without spending a certain amount of time playing, but spending time playing does not make you better on its own.
2. Doing whatever it is you want to get good at (doing anything else does not count - if you want to learn how to play regular chess, play regular chess; puzzles or anything else does not count).
3. Reviewing your games to find mistakes you've made - this part is crucial, if you can't see any mistakes you made, you cannot improve. If that's the case, get someone better than you to review your game(s).
4. Playing while trying to work on addressing one mistake at a time, until you don't make it anymore.
Chess is actually really easy to improve in - fast, trivially repeatable games, chess engines, lots of learning resources, objective rating system.
> I know that I do not have the brain to be a chess master
I'm not sure what exactly you mean by 'chess master', but for example getting into the top 10% of players is pretty easy. You are indeed incredibly unlikely to be one of the best, because for that you will have to dedicate your entire life to playing chess. But unless you literally want to be one of the best (top 1%+ of players), genetics will not limit you. You may take more time to get to any given level than someone gifted with more working memory or whatnot, but it's still doable.
> because I don't have enough working memory to keep the board in my head.
Because of humans' limited memory and processing power, we play games not by exhaustively analyzing but via building simplified models and heuristics so I don't see why you'd need to 'keep the board in your head'.
I don't think the onus is on me to prove you wrong, so much as the onus is on you to prove that your experience is scientifically rigorous and representative of more than just your personal experience.
And to be clear, I don't doubt that many people "can't" learn calculus in the same way I "can't" run a marathon; we don't have the desire, discipline, and free time necessary to do the work required. This does not speak in any way towards our capacities to do so, only our desire.
So I suspect the vast majority of your students didn't have the sufficient desire to learn a lot more than they were incapable, and I think it's a critical distinction, because you can change people's motivations, but you cannot change their capacity.
As stated in my original comment I’m quite liberal. In education we talk a lot about social conditions and their effects on education. It’s why teachers’ unions strongly support universal healthcare, school lunch programs, etc.
After 20 years on the job I’ve come to the conclusion that some can’t learn it. This isn’t controversial in some sense since we know retarded people can’t learn algebra. So what level of capability is necessary to learn it? I don’t know but I suspect it’s well above being mentally retarded.
I could be completely wrong but given your lack of experience in the topic my experience ought to at least make you pause a bit. In another comment you wrote about me:
… you're more likely ignoring the real-life circumstances your students find themselves in, and your colleagues are not.
Talk about making an assertion with no evidence! At least I waited 20 years before stating my absurd assertion.
Also not for nothing, but "retarded" hasn't been a medical term for some time now, with institutions such as the AMA and SSA both replacing the term with "intellectual disability". The only remaining reasons you'd use it are either because you are thus uninformed, or you're signaling something...
I’ll read whatever response you have but won’t comment further. I wish you well. Keep up the good fight!
I think you, and everyone who thinks like you, need to take a very hard look at what you've done to eliminate the environmental factors related to your viewpoint that some people aren't smart enough to learn something, because its extremely easy to trick yourself into thinking someone is incapable when in reality other factors abound.
As the article explains, if society refused to educate/feed/raise/nourish red-headed children, there would be a genetic correlation between red-headedness and intelligence.
How absolutely confident are you that you've accounted for every explanation besides the genetic one in determining why some people can't learn algebra?
My university would conditionally admit students who had a math score below a certain threshold on their ACT, I think it was 19 or something. Anyway, as part of their admittance criteria, they had to attend an after class lab for an additional hour an a half for a total of three hours per week dedicated to learning pre-algrebra. There were four modules where they would do some reading, work through some example problems through interactive software, and then have some homework to work through that was almost identical to the examples. Students would try and try and try and try to learn the material, and they would take days to work through the problems on their own (often with my guidance, giving pointers on how to think about the problems) to finish the module so they could take the quiz and pass the module. Near the end of the semester many students made appreciable progress, but for others the inability to retain and apply what they've spent so much time on results in tears, especially because they don't know if this requirement will keep them from being able to graduate.
Given infinite time, could these guys all have figured out pre-algrebra enough to pass? Maybe. But the amount of time it takes them to learn math concepts that are very easy for us means that it's entirely impractical to expect them to ever achieve proficiency in advanced mathematics.
This just does not look like a universally effective way of teaching to me, irrespective of the topic. It's hardly any wonder that some people fell through the cracks if they were unfamiliar with the subject in the first place. What about leveraging stuff that's actually been tried and tested, like the Khan Academy videos and their automated interactive, school-like environment?
Your VO2max, max heart rate, and other factors appear to be significantly determined by genetics, and will absolutely contribute to your capacity to run a marathon. If it takes you a year of hard training, but it takes me a few practice runs a few weeks before, it's not fair to say we required the same amount of desire, discipline, or free time to succeed. I would instead say we had a very different capacity to run a marathon.
Are you saying that similar things could not possibly be true for learning math? Or really anything else that humans do?
All healthy people can learn calculus and run marathons, with varying degrees of success and effort, due to genetics and environmental factors.
I also don't think "healthy" and (presumably) "not healthy" are useful categorizations. There are many people in that fuzzy in between area between "healthy" and "not healthy", for both physical and mental health.
Is it really worth so vigorously arguing the semantics of "some people are incapable of learning algebra" and "it requires an impractically large amount of effort for some people to learn algebra"?"
You can overcome difficulty, you cannot overcome (by definition) impossibility.
What you keep ignoring in what I'm saying however, is that I do think certain things are impossible for some people. I will never play in the NBA, for example, but that's a far cry from being "very good" at basketball.
Learning calculus and completing a marathon are not the point at which "healthy" (and yes, it's fuzzy, but precision is impossible on this topic) people are sometimes unable to do things. Winning a marathon and getting a Ph.D. in mathematics, I would acquiesce to your argument.
In other words, I think anyone can dabble in anything, but you do need an alignment of genetic and environmental circumstances to be in the top 1% of something. I could be argued into top 10%, but below that, it appears the data supports almost anyone being able to do almost anything, or at least well beyond whatever artificial lines we might draw to discourage people from achieving.
To turn it around: Do you have any evidence that your "anecdotal evidence" doesn't simply reflect your teaching skills?
This is a strawman. They never said 'gifted', they just said that some people have it and some don't.
> deficiencies in one area can be made up for in other areas
Not what we're talking about. GP is probably great at things that aren't chess. That doesn't mean they're good at chess.
> Where genetic gifts are lacking, determination and perseverance can almost always make up the difference
Determination and perseverance aren't (at least partially) genetic gifts?
Honestly I think 'genetics' are a bit of a red herring here anyway because the real underlying assertion being challenged is that all humans have equal potential in all things (which anyone who has ever taught any mildly difficult topic will know is trivially disprovable). The precise mechanism whereby innate human potential differs isn't important if you can't even agree that it differs.
Your belief should probably be considered heretical, even among your conservative colleagues, because your colleagues should recognize how deficiencies in one area can be made up for in other areas, sometimes (but not always) at a higher efficiency cost.
Where genetic gifts are lacking, determination and perseverance can almost always make up the difference, especially at a basic algebra/calculus level.