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SaidAchmiz comments on Rationality Quotes April 2014 - Less Wrong
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Speaking as a student: I sympathize with Benito, have myself had his sort of frustration, and far prefer understanding to memorization... yet I must speak up for the side of the students in your experience. Why?
Because the incentives in the education system encourage memorization, and discourage understanding.
Say I'm in a class, learning some difficult topic. I know there will be a test, and the test will make up a big chunk of my grade (maybe all the tests together are most of my grade). I know the test will be such that passing it is easiest if I memorize — because that's how tests are. What do I do?
True understanding in complex topics requires contemplation, experimentation, exploration; "playing around" with the material, trying things out for myself, taking time to think about it, going out and reading other things about the topic, discussing the topic with knowledgeable people. I'd love to do all of that...
... but I have three other classes, and they all expect me to read absurd amounts of material in time for next week's lecture, and work on a major project apiece, and I have no time for any of those wonderful things I listed, and I have had four hours of sleep (and god forbid I have a job in addition to all of that) and I am in no state to deeply understand anything. Memorizing is faster and doesn't require such expenditures of cognitive effort.
So what do I do? Do I try to understand, and not be able to understand enough, in time for the test on Monday, and thus fail the class? Or do I just memorize, and pass? And what good do your understanding-based teaching techniques do me, if you're still going to give me tests and base my grade on them, and if the educational system is not going to allow me the conditions to make my own way to true understanding of the material?
None. No good at all.
Ah. I think this is why I'm finding physics and maths so difficult, even though my teachers said I'd find it easy. It's not just that the teachers have no incentive to make me understand, it's that because teachers aren't trained to teach understanding, when I keep asking for it, they don't know how to give it... This explains a lot of their behaviour.
Even when I've sat down one-on-one with a teacher and asked for the explanation of a piece of physics I totally haven't understood, they guy just spoke at me for five/ten minutes, without stopping to ask me if I followed that step, or even just to repeat what he'd said, and then considered the matter settled at the end without questions about how I'd followed it. The problem with my understanding was at the beginning as well, and when he stopped, he finished as if delivering the end of a speech, as though it were final. It would've been a little awkward for me to ask him to re-explain the first bit... I thought he was a bad teacher, but he's just never been incentivised to continually stop and check for understanding, after deriving the requisite equations.
And that's why my maths teacher can never answer questions that go under the surface of what he teaches... I think he'd be perfectly able to understand it on the level to give me an explanation, as when I push him he does, but otherwise...
His catchphrase in our classroom is "In twenty years of questioning, nobody's ever asked me that before." He then re-assures us that it's okay for us to have asked it, as he assumes we think that having asked a new question is a bad thing...
Edit: Originally said something arrogant.
Why do you think that?
Oops, I didn't mean to sound quite so arrogant, and I merely meant in the top bit of the class. If you do want to know my actual reasons for thinking so, off the top of my head I'd mention teachers saying so generally, teachers saying so specifically, performance in maths competitions, a small year group such that I know everyone in the class fairly well and can see their abilities, observation of marks (grades) over the past six years, and I get paid to tutor maths to students in lower years.
Still, edited.
Word of advice: don't put too much attention into your "potential". That's an unfalsifiable hypothesis that you can use to inflate your ego without actually, you know, being good. Look at your actual results, and only those.
If you're really curious, have you considered a private maths tutor? I wouldn't go anywhere near the sort of people who help people cram for exams, but if there's a local university you might find a maths student (even an undergrad would be fine) who'd actually enjoy talking about this sort of thing and might be really grateful for a few pounds an hour.
Hell, if you find someone who really likes the subject and can talk about it you may only have to buy them a coffee and you'll have trouble getting them to shut up!
Thanks for the tip, and no, I hadn't considered going out and looking for maths students. I mainly spend my time reading good textbooks (i.e. Art of Problem Solving). I had a maths tutor once, although I didn't get out of it what I wanted.
I schlepped through physics degree without understanding much of anything, and then turned to philosophy to solve the problem...the rest is ancient history.
From what I hear, philosophy is mostly ancient history.
It's mostly mental masturbation where ancient history plays the role of porn...
Kinda like this site. :-)
This site has different preferences in pr0n :-P
writes down in list of things people have actually said to me
I had this experience in a context of high school, with no homework and no additional study at home.
None of the students' classes assigned any homework?!
Some of them probably did, but most didn't. The "no homework and no additional study at home" part was meant only for computer science, which I taught.
This is not usually true in the context of physics. I recently taught a physics course, the final was 3 questions, the time limit was 3 hours. Getting full credit on a single question was enough for an A. Memorization fails if you've never seen a question type before.
Not all tests are like that. I had plenty of tests in math that did require understanding to get a top mark. Memorization can get you enough points to pass the test but not all points.
It's more useful than that, even.
There are also times where the problem isn't necessarily memorization, but just lapse of insight that makes it hard to realize that a problem as presented matches one of your pre-canned equations, even though it can be solved with one of them. Panic sets in, etc.
In situations like that, particularly in those years when you have calculus and various transforms in your toolkit (even if they aren't strictly /expected/), you can solve the problem with those power tools instead, and having understood and being able to derive solutions to closely related problems from basic principles ought to be fairly predictive of you being able to generate a correct answer in those situations.