It's worth chastisting a little bit, because "smart" is at best an oversimplification. I wrote at length about this in another post, but the tldr is that, in expectation, most people are good at some things and bad at others. If I'm good at university-level mathematics but terrible at woodworking, am I smarter than someone who is good at woodworking but has a hard time wrapping their head around group theory?
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.
Of course smart is a vague term and it's not one that can be precisely defined or measured. However, let's consider the question,
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.
>The answer is yes or no, or some can but others can't.
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.
Leave mental disability out of it, because it's not relevant to the discussion.
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?
> A large majority of my colleagues think that everyone is equally capable of learning college algebra.
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.
How is this supposed to be good faith advice? The mentally disabled person may earn $15/h as a janitor or $25/h in some high productivity job that would usually pay $60/h and requires a college education but also has some accomodations for their disability. Mental disability isn't linear and it isn't a discrete yes or no either.
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.
We also calibrate our definition of smartness to expectations. I say my cat is smart because he opens the front door to let in his deer friends. That doesn’t mean I think he can learn algebra. (Meanwhile, the beagle never figured out how to walk on the same side of a tree as me while on leash.)
I think that is a very dangerous hole those academicians have dug themselves into. And not even healthy for themselves as they're surely always on the look out for the bogeyman?
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.
Jim Simons is a great example. Has made 28 billion from algorithmic trading, has Chern–Simons form named after him in math but has said he sucks at computer programming because he can't remember syntax well enough.
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.
> If I'm good at university-level mathematics but terrible at woodworking, am I smarter than someone who is good at woodworking but has a hard time wrapping their head around group theory
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.
> Your example is not great because "woodworking" is primarily a knowledge game.
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.
Sure, if that were true. But it's not. Anyone who can understand college algebra can understand woodworking concepts, because woodworking concepts have virtually no cognitive complexity.
Source: I learned college algebra, and I have my woodshop 20 yards from me.
A better example would be my ability in strategy games such as checkers, chess, bridge, et alia. I'm generally worse at such games than most of my friends, none of whom have any special training or aptitude for strategy games.
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.