I think a surprising number of people simply can't math.
This seems incredible if you're one of the people who can math.
But really, I've known otherwise bright people whose brains fall apart at the first hint of abstraction.
Basic arithmetic is fine, but you can forget about trying to teach them anything more complicated.
Simple equations? Trig? Basic stats? They just can't do them, no matter how many times you repeat the explanations, or how many different ways you try to present them.
So I think it's not unlikely that an aptitude for math and symbolic abstraction is unusual, and not something you're going to find in most of the population.
Remember, by the time you get to a university you're in the top 20% of the population anyway. (More like 10% for STEM.)
So it's maybe not so realistic to assume that's how most people are.
TL;DR I am currently taking an adult who "can't math" through Khan Academy from K-2nd on up and she's "mathing" wonderfully now that we're comprehensively filling in the understanding gaps. Too bad she still doesn't like it. :P
I know someone in that class of people that "can't math". Initially I tutored her in algebra and she did alright when we were working together, but as soon as I turned her loose or she went in to take a test she couldn't remember or apply the techniques. She was allowed to go into Pre-calculus (she wants to be a Chem Major). But without extensive help on each section she would fail spectacularly. And after a while it became obvious why. She could think logically and when explained clearly or relating to other concepts she's recently learned it all made sense, but she had so many deficiencies in basic math that nothing past that would really stick. As an example I taught her the formula for computing the area of a square multiple times, but she would swear this was the first time each time because there was no foundation to hang that new knowledge on.
Now I but I have her working through Khan Academy from the ground up (K-2nd) and now that she's up to 5th grade and I've explained how basic concepts relate together, like multiplication and area or fractions and division she's actually starting to "get it".
She just lost the thread of "mathing" around 3rd grade and never found it again. Now that she can go through it at her pace and has someone that can patiently explain it from multiple angles it makes sense and she's doing things on her own that I was afraid she's never "get".
That said without Khan academy and a detailed list of sub-topics in math (45 individual skills for dealing with fractions for example) I'd have never been able to cover all the small things that add up to a detailed understanding of arithmetic. I'd have covered fractions from maybe a handful of angles and called it good knowing that it wasn't enough practice without having an answer for how to practice more without stupid rote repetition of the same kinds of problem.
I think it just that Math requires abstraction and abstraction is genuinely hard. Because it is hard and highly desired skill very few teachers are good at it
This seems incredible if you're one of the people who can math.
But really, I've known otherwise bright people whose brains fall apart at the first hint of abstraction.
Basic arithmetic is fine, but you can forget about trying to teach them anything more complicated.
Simple equations? Trig? Basic stats? They just can't do them, no matter how many times you repeat the explanations, or how many different ways you try to present them.
So I think it's not unlikely that an aptitude for math and symbolic abstraction is unusual, and not something you're going to find in most of the population.
Remember, by the time you get to a university you're in the top 20% of the population anyway. (More like 10% for STEM.)
So it's maybe not so realistic to assume that's how most people are.