Obviously there are people who couldn't learn a given topic under one type of educational regime but who could under a different regime. But that doesn't eliminate the obvious: Some people can't learn a given topic at all, under any circumstances. OP's example of the mentally retarded (which I learned recently is a valid medical descriptor) is just an extreme example.
It's so funny watching people scramble to avoid admitting that genetics has a huge impact on humans and their potentialities.
Granted, as a species, we are the closest to blank-slate out of any species ("niche-switching is our niche"), but reality doesn't go away just 'cause we don't like it.
A good deal of the folks enmeshed in various delusions related to their belief that reality is socially constructed, I've found, are folks that have little concrete experience with reality. Academic types, those who've exclusively worked in knowledge-production or in offices. Rock climbers and farmers are very much not prone to these delusions, for a couple of examples.
Try to convince a dog breeder that dopey English Mastiffs are just an environmental change away from gaining the intelligence of the German Short-Haired Pointer, which can practically solve Sudokus.
Look, there's a "valid medical descriptor" for grandpa who is in a nursing home with Alzheimer's disease, but this kind of thing is totally immaterial to people who are in school today. There's no way that they'd have that level of cognitive impairment. Saying that "some people just can't learn" so-called "advanced" math such as college algebra and calculus, or programming for that matter, is just pointless speculation with zero evidence to back it. Most likely they can, we just can't be assed to teach them effectively.
> Saying that "some people just can't learn" so-called "advanced" math such as college algebra and calculus, or programming for that matter, is just pointless speculation with zero evidence to back it.
What about the anecdotes of millions of people who self-profess that despite very much effort, they just can't wrap their head around some advanced math concepts? That doesn't count as evidence?
There are also plenty of anecdotes of people who self-profess that for years or decades they couldn't wrap their head around some math concepts, and then one day they met a teacher who explained it in a different way than any teacher before had done, and it "clicked" for them as adults.
I don't know how to weigh these anecdotes, but I think that's suggestive that the methods of teaching might be relevant even to people who struggle with math for decades.
Honestly no. Most people say i can't do X when really they mean, i've decided that its not worth the effort/i dont want to.
If you were arguing that math comes easier for some people than others, sure that's strong evidence. If you're arguing that they are literally incapable, and no set of curcumstances would allow them to learn - that is a very different claim and needs very different evidence.
I'm a farmer, not a teacher, so I can't answer this question as asked.
But I would speculate that of the set of people who bombed the class, they could fall into a number of buckets. E.g., one bucket is people who were mentally capable of learning the concepts, but were to lazy to put in the effort (then we can quibble about whether inherent laziness puts people into the "not capable" bucket). Another bucket is people for whom alternative learning environments might have brought them to understanding and a passing grade. Another bucket is people who just lacked the preliminary background and with a couple years of effort could be made to pass the class as it exists. And finally, another bucket is people who are genuinely incapable, regardless of environment, of understanding the concepts.
This shouldn't be surprising. I have tried to deeply understand quantum mechanics, and while I can parrot some of the most well-known and more simple concepts, I truly believe that I lack the capability of grasping the very core, deep insights in an intuitive way. I might pass undergraduate level classes in the topic, but I am fairly certain I couldn't achieve a PhD. I'm not the dumbest bulb in the shed, but I can see that there are people much, much brighter than I, and it is obvious that their ability to understand more advanced and deep concepts is greater than mine; This leads to the observation that of the set of understandable knowledge in the universe, some of it is available to some people but not available to me, no matter how hard I try. (I take solace in Feynman's quote, "If you think you understand quantum mechanics, you don't understand quantum mechanics.")
Then look at every human capability and its distribution across the universe of humans, and it's pretty clear that we all can't do everything, every one person has some cutoff beyond which they aren't capable of understanding in any given topic. For some people (and hey, maybe it's a really small slice of the population), that cutoff is somewhere before Calc II.
I think we're getting closer to the actual situation with this description. There are a lot of buckets of people who don't do well in a particular class.
And we both admittedly don't know the size of the bucket of people who cannot, given a lifetime of 80 years continuous study and tutoring, understand a topic.
But in my teaching experience, it's dwarfed by the group of people who doesn't care about the topic and bombs because they don't put in the effort.
It's so funny watching people scramble to avoid admitting that genetics has a huge impact on humans and their potentialities.
Granted, as a species, we are the closest to blank-slate out of any species ("niche-switching is our niche"), but reality doesn't go away just 'cause we don't like it.
A good deal of the folks enmeshed in various delusions related to their belief that reality is socially constructed, I've found, are folks that have little concrete experience with reality. Academic types, those who've exclusively worked in knowledge-production or in offices. Rock climbers and farmers are very much not prone to these delusions, for a couple of examples.
Try to convince a dog breeder that dopey English Mastiffs are just an environmental change away from gaining the intelligence of the German Short-Haired Pointer, which can practically solve Sudokus.