2 ms·

In university, I was notoriously bad at "remembering" things (iow, I was lazy to learn things by heart). I was pretty good at making connections, and I could pr

In university, I was notoriously bad at "remembering" things (iow, I was lazy to learn things by heart). I was pretty good at making connections, and I could prove theorems from only knowing a couple of definitions and simpler theorems in advanced math courses. I generally scored average in tests, but I rarely failed (though I occasionally had "original" solutions that teachers commended on even though I failed to reach maximum scores). But I was never under the illusion that this constitutes working knowledge. I was able to come up with solutions for some problems only because I had some basic knowledge memorized, which allowed me to effectively manipulate ideas and concepts which I did know of. Even then, I used to semi-joke how the hardest thing in theoretical math is all the memorization required. If you've ever explored any scientific field deep enough, you'll know that it's festered with tricks found by accident and roundabout ways to get to a solution that, if you haven't seen it before, you have no hope of applying in practice. Or you might think that consulting a book or two (or Internet) will allow you to prove Fermat's theorem while you are being tested for 2h.

janekm 4y ago
Well... I have deeply explored a scientific field (in computer science, not math) the way you are talking about. By reading other's research papers, implementing what they proposed, trying to improve upon it, coming up with novel solutions etc etc. Very little of what I used on a day-to-day basis came from rote learning, a lot came from the deeper understanding that I got from actually actively engaging with the concepts. I'm not proposing doing away with schooling completely, but the model should change (much in the way more progressive schools are doing anyway, just a shame that not many parents can afford to send their kids there).
- necovek 4y ago
  > Very little of what I used on a day-to-day basis came from rote learning The question is not how much non-rote learning is required to adequately perform any task, but whether rote learning is a necessary component of it. By engaging with research papers (often requiring multiple readings), you "accidentally" also memorize a lot of the material (even if not for ever and ever), which makes it possible for you to "try to improve it" etc. So all I am saying is that rote learning is a necessary component of applying any suitably advanced material. Whether that happens organically by engaging with the material deeply enough or on purpose by simply rote-learning is orthogonal to the need for that knowledge to be there. At issue here in this thread is whether testing for such knowledge is signalling anything of value. I still believe it is because you'll have that knowledge with either approach, even if only one of those approaches will gain you more functional knowledge: basically, such a test is a proxy for you having engaged in the material. Which is why I suggest a mixed approach in a sibling comment: test for knowledge of "factoids" to simplify test development and application of such knowledge where you are required to manipulate "learned" concepts (so only part of the test is hard to create and keep consistently hard/easy).
- P5fRxh5kUvp2th 4y ago
  thinking from first principles, it's needed to be good at math.

janekm 4y ago

Well... I have deeply explored a scientific field (in computer science, not math) the way you are talking about. By reading other's research papers, implementing what they proposed, trying to improve upon it, coming up with novel solutions etc etc. Very little of what I used on a day-to-day basis came from rote learning, a lot came from the deeper understanding that I got from actually actively engaging with the concepts. I'm not proposing doing away with schooling completely, but the model should change (much in the way more progressive schools are doing anyway, just a shame that not many parents can afford to send their kids there).

necovek 4y ago
> Very little of what I used on a day-to-day basis came from rote learning The question is not how much non-rote learning is required to adequately perform any task, but whether rote learning is a necessary component of it. By engaging with research papers (often requiring multiple readings), you "accidentally" also memorize a lot of the material (even if not for ever and ever), which makes it possible for you to "try to improve it" etc. So all I am saying is that rote learning is a necessary component of applying any suitably advanced material. Whether that happens organically by engaging with the material deeply enough or on purpose by simply rote-learning is orthogonal to the need for that knowledge to be there. At issue here in this thread is whether testing for such knowledge is signalling anything of value. I still believe it is because you'll have that knowledge with either approach, even if only one of those approaches will gain you more functional knowledge: basically, such a test is a proxy for you having engaged in the material. Which is why I suggest a mixed approach in a sibling comment: test for knowledge of "factoids" to simplify test development and application of such knowledge where you are required to manipulate "learned" concepts (so only part of the test is hard to create and keep consistently hard/easy).
P5fRxh5kUvp2th 4y ago
thinking from first principles, it's needed to be good at math.