Disagree. I say: Bad math teachers really filter out people in a way nothing else does.
"Here is a list of rules which can be used in specific circumstances. I am not going to tell you why you would need them and the exam will feature several corner cases. Also, I will not provide any examples or detailed explanations because what would other people think of me, then?"
This is over the top, but boils down my experience starting from highschool. I was in love with math when I was in primary and middle school. I really did.
But Highschool and university killed every last bit of enjoyment I used to have.
Okay, I did really like the first 2 semesters of math. I found an amazing online class which covered the same topics we did. Finally I understood and doing the exercises with such ease felt like cheating.
But even with the best teachers for every field, math or sport will filter out people way more harshly, and sooner, than any other field.
You can smooth things out with quality teaching, but there is a human hardware limit, and you reach it sooner with those two.
Many people don't like to hear it because their ego is bruised or because it goes against the idea that "everybody can do anything".
This is wrong. Birds fly, fishes swim. There is nothing bad about either.
Shmaybe. But I doubt many people ever approach it. What they hit is, instead, a "software lockout" - a limit of the kind that some hardware vendors (such as those making oscilloscopes or farming machines) put in their products, where the hardware is already there, but its capability is restricted in software, and you need to pay to have the restrictions lifted.
If you'd seen me as a kid, you'd say I am one of those people with rather low "hardware limit" when it comes to math. But then, when I was around 13, that limit suddenly shot up so high and so fast, it may as well have disappeared. What happened? I started to learn to code, with an intent to make videgames. Eventually I reached the point when I was trying to figure out how to rotate some sprites, and made a mental connection between what I want (understanding how to implement rotating images) and what I was taught at school (trigonometry). Immediately, math switched from being something I had to learn, and became something I wanted to learn. So, what you'd think was a severe hardware limit, was actually a purely software one - and it went away the moment I found the magic unlock code (which, in my case, was "find something that makes math seem relevant and exciting, instead of a bullshit chore").
And yes, I'll admit that I do have a hardware limit relevant here - most kids do well at math without having to find a motivational "cheat code", but people like me, with impaired executive functions, can't naturally power through bullshit, and need workarounds to keep up. But this is a different kind of limit. It's also one we're getting increasingly good at understanding, recognizing and overcoming, and it teaches us that what you see as hardware skill limit, may just be a software limit induced by another problem.
Or, in short, if someone told the twelve year old me the things you wrote here today, it would have derailed my life. Fortunately, nobody did, and this lazy and dumb-ish kid ended up handling undergrad-level math perfectly fine.
I have a hard time with this mentality. I would have agreed a few years ago perhaps, and do still agree that we all have our own aptitudes, but the level of absolution in a statement like this just isn’t really quite as applicable to humans in my opinion. There are things I never thought I’d be capable of that I’ve recently begun to excel at.
What I thought was a hardware limit turned out to just bug in my psycho-software that needed a patch. Obviously at the extreme end’s of the spectrum, the human hardware limit is very real. But for most (healthy) people, engaging in most activities, I believe that any perceived immutable barriers or obstacles are almost entirely psychological.
Laws of physics are laws of physics. And biology is applied physics.
People in sport have known that for a long time. You can train as much as Usain Bolt, he still has a huge advantage.
Thinking the other human characteristics are not affected by this is weird. You will never be Von Neumann, no matter how much you spend in the class room.
It's not that training has no effect, it does, a lot. Yet this doesn't remove the fact we have a variability between individual.
And there is not a tipping point, it's a spectrum for each characteristic.
It turns out math exhibit some early barrier in that spectrum. There is nothing wrong with that.
I told her to come to office hours and I gave her problem sets to solve, first easy then progressively harder. As she got confidence that she could do this her demeanor in class changed and in the space of a month she went from failing to a B-
After this I started asking anyone who said they had math anxiety or did not like math if they had a bad math teacher they remembered. I have asked close to a hundred people this over the last 30+ years and invariably they not only remembered the name of said bad math teacher but also relived how they were told they were dumb and would never be good at math. They stopped learning at that point.
Nonetheless math is hard because it is not an evolutionary survival skill we developed. I say jokingly that math is an unnatural act. I am not a gifted math student but I like solving problems and I would just solve every problem in the book ploddingly and stubbornly. So I dont hate math and I am not in love with it either. It is a very powerful tool for problem solving and also gives you powerful analytical capability you can use in other places in life.
Maybe that is all it takes to be a "gifted" math student?
Tangental:
I have always hated the term gifted. I will not deny there are some absolute phenoms out there in regards to any domain. Those individuals are few and far between and should be celebrated because of it. Maybe I am being semantical, but being "slightly better" does not make one gifted.
Learning a subject that is being taught to someone quicker than their peers does not make them gifted. Show me what they have created or discovered with their alleged "gift," and then we will see.
Von Neumann is not remembered because of how much quicker he learned math than others or how easy the subjects were for him. He is remembered for what he discovered and what he created -- that is what makes one truly gifted in my opinion.
If not, what makes you confident that your peers were falling behind due to some sort of innate inability, instead of as a result of compounding poor teaching or other environmental factors?
Unless you can mass edit all the factors, then it remains that some people simply cannot do math past a certain level.
But for what it’s worth, it was a very small school in a VERY poor area. (Median income probably at or below $20k / year) The teaching was actually above-average for the area, but probably below average over a national rating.
I do think factors matter in my personal anecdote of my particular high school. However my LIFE has reinforced my observations: most people are profoundly bad at math, from a seemingly fundamental level.
And I also got into teaching between dev gigs.
