Caltech's engineering program had tests that were open book open note. Memorization would not work. You had to actually understand it.
Posts like yours make me appreciate Caltech.
P.S. My first job was designing the 757 stabilizer jackscrew assembly. I was flying on a 757 just the other day, 40 years later. How marvelous! It's a great airplane.
P.P.S. We had a few "formula memorizers" and "formula pluggers" at Boeing. I was often assigned to go over their work and fix it. Nobody trusted them.
Because I started there as a newbie along with the formula pluggers. I could see what I could do vs what they could do. For example, one task required coming up with the spinning moment of inertia of the jackscrew assembly. A plugger sat a couple rows away, and looked at it, and asked "what book did you get that formula out of?" I said it wasn't in a book, so I used calculus. He just stared at me. He was a nice enough fellow, but didn't seem real interested in engineering, and would try to get by doing as little as possible.
I discovered that an undergraduate degree at Caltech conferred math skills that other universities put off until masters. Because I'd fix the math work of some of them, too. Over time, I was trusted more and more with more advanced work. The pluggers weren't.
I was an average student at Caltech.
I have little idea how Caltech compares today. But I've run into the formula pluggers in diverse engineering areas ever since. They would have all flunked out of Caltech.
I'm not sure why you question the notion that being able to understand where formulas come from is far more valuable than just memorizing them.
I'm sure there are other great universities that educate engineers that actually understand what they're doing rather than plugging in a formula. But I have no personal experience with them.
Wasn't your point that Caltech would have taught them not to be formula-pluggers?
It was just a school, man, relax, you're not actually better than other people.
My point in posting this here is not to brag, but to point out that a college education doesn't have to consist of memorizing formulas. If a particular college program requires that, there are better choices.
Being able to derive the formulas means one knows their limitations. It also means that one can derive a needed formula when it is not in the book. This means that one can solve a significantly larger set of engineering problems.
In aircraft design, this leads to lighter and less expensive parts without sacrificing strength or utility. It's an objectively better design.
Making one who can do this objectively a better engineer.
What is relevant is if one's engineering class consists of memorizing formulas, find a better class that emphasizes the how and the why. Math is a big part of that.
When I hear people like you I always wonder how the human race is supposed to be doomed by a lack of intelligent people, yet somehow throughout history no such constraints are observable.
In the past people had lots of preconceptions of what black people couldn't do, you're doing the same and believing it is socially acceptable. The human brain is amazing, just because someone's brain scores worse than another in some motivation and culture test doesn't mean they are incapable of absurdly broad and vague things like "advanced concepts".
...with current educational methods, that basically expect all students to "teach themselves on their own". Modern-day educators aren't even trying to meaningfully engage students who respond well to more direct forms of instruction, because that would involve actual, verifiable effort and "demean" their role.
For a metaphor of education, I'd say people are like Turing machines. (A) If there is one person who can learn a concept, then any of them can; (B) some are faster than others; and, (C) the "optimal in practice" state is usually limited by need and not capability (i.e., using modern laptops too just check emails and browse the web).
>but saying this in higher education circles is akin to burning a Koran in Mecca.
I'm not a fan of preemptive impersonations of Copernicus. I'd rather read what people said and judge that.
Anyone can learn anything. But to what depth and degree within the time they have on Earth? What can they accomplish with their present knowhow or lack there of? These questions have measurable outputs. It's not enough to rely on potential. At some point, one should know his bearings and limitations.
> But it's a continuous scale, not a yes/no thing. And interest in the subject plays a big role.
Ability itself may follow a continuum, however sufficiency is digital.
In reality, even the best universities have more than a few horrible professors, and a student that’s struggling in class may actually just be going through a rough patch.