And motivation was often impeded by either trauma or not finding a way to make it relevant to the student. Those are prereqs for learning anything. The common denominator for people that are good at something is that they liked it, so they did it more.
I know plenty of people that went through an engineering degree with me that do not like math, but they are competent at all the way up to what an electrical engineer needs to know, which is not research level math, but what most people would call advanced. I would never say I "like" math for example but I've always thought about it as something important to learn and get decent at to succeed in life.
I have way more interest in history and philosophy but the way I figured is I can learn all of that on my own because all you need is to read. Math is actually hard so I better get "trained by someone" at it.
I’m similar to you, except to upgrade my practical math skills at college I did cultivate a “liking” for math comparable to other technical areas I pursue. Namely, I started reading popular math books and articles, watching math youtubers, solving recreational puzzles from math periodicals… It was like, half actual interest and half contrived interest, seeing if I could develop in that direction. One summer when I had a lot of free time, with the help of a mathematician friend, I worked through a few advanced textbooks and video lecture series beyond anything I strictly needed. Progress was real but agonizing, and then I promptly forgot everything. It turns out that just maintaining a mid-to-late-undergraduate-level understanding of applied math is all I can be responsible for. It’s a responsibility I attend to, but my brain is only so mathy. At some point it becomes a question of both motivation and ability.
You also don't know the people who didn't make it through, because for whatever reason they aren't able to learn something they weren't able to like. Glad you were able to make it work.
I don't know the people that didn't make it through? You're under the impression I didn't meet anyone outside of those 25? And that I didn't have classmates all the way from first grade to university? Wat
I always find these types of explanations doubtful, because you can always dismiss someone of subpar ability as not trying hard enough or you could define trying hard enough in a way that is not defacto practical.
My experience teaching is limited (but I have taught some, to be clear) but I have found learned helplessness to be the biggest barrier. People have varying aptitudes for different tasks, and varying aptitude and a finite lifespan does imply some people have a lower ceiling than others in a given subject, but humans are powerful general learners. They don't generally reach their ceiling in most subjects. The limit for someone "bad at math" is almost certainly self-fulfilling prophesies they internalized.
Speaking for myself I have in the last five years or so been learning I have much more of a capacity for making art than I had thought. My art is nothing special, but I am improving every time I practice. But when I was younger I thought that I was just good at STEM-yy things and bad at other things. Relatively speaking I am better at STEM-yy than art-yy things, and I'm probably worse at art-yy things than most other people. But I have huge room for growth and I think I will eventually produce some beautiful watercolors.
As an aside, I've also found that almost everyone thinks they're bad at math? My friends with PhDs don't think they're good at math but they've forgotten more than I know about it. I think I'm bad at math but I can prove a thing or two. My spouse thinks they're bad at math, and they can't do the things I can do. But a few months ago they needed to do some simple algebra at work, and a coworker said, "dang, I wish I was good at math."
Somewhere out there Terence Tao is saying he's alright at math but he has nothing on that Euler fellow.
Could not agree more. I also taught for some time and generally had good results, almost everybody "got it".
There was one person, though, that I just could not get anywhere with. Even after several private lessons. Turned out that somehow she convinced herself that she will never get it and never be able to progress. Even if she did get it right one week, the next week was as if that never happened. I found no way across that barrier :(
I also agree. Doing university sudies in stem fiels is just.. doing the work, grinding until you get it. I was not very good at maths but i managed to pass the courses that I had. Most of my fellow students didnt.
It is what differentiates stem fields fron liberal arts, in my biased view. You are either talented at maths, physics, chemistry or you just grind, study with thr books snd exercises, until you know enough to pass the exams.
Coming from gymnasium/high schoolit is very different. There the teachers tell you what to do, at uni you have to figure out yourself how you need to study to get the results.
US universities have been known in Europe for being a childs play, if you were any good at all in stem fields