it never took you longer than a day to solve it incrementally?
Well, not until college, certainly, except that I used to do the USAMTS which really did give you weeks to play around. But I got a different idea from what you've previously said: I got the impression that it took you a week to do the problems because you hadn't been taught the material you needed to solve the problem.
This is not what I'm talking about. I mean, yes, I've had plenty of problems like that too, especially in college, and, sure, they took me the entire week to solve, but that's not interesting or useful to me pedagogically because the solutions are either "beg the TA to teach us what we need to know to solve the problem" (which I have done) or "learn this thing by myself or with the help of B, College Partner in Crime" (which I have also done, for whole classes even, with varying degrees of success in actually learning and retaining things), but in both cases it's still "once I know the material then I can solve the problem." (I mean, I guess it's... helpful in some ways... that I got crash courses in teaching myself things?)
I'm talking about the kind of problem where you do know everything you need to know to solve the problem, you just don't know yet how to put it together, and you have to keep thinking about it and trying different things and playing with it, many of which might not work. Or where you might not see how to do the whole problem, but you might see how to do a little part, and you have to play around with that part, then maybe once you've done that part you can see how to do another part, but you won't be able to see it until then.
I had a little of that in college, but the pedagogical system of classwork isn't really set up to foster that (except maybe in Sweden :) )
Re: Grad school
Well, not until college, certainly, except that I used to do the USAMTS which really did give you weeks to play around. But I got a different idea from what you've previously said: I got the impression that it took you a week to do the problems because you hadn't been taught the material you needed to solve the problem.
This is not what I'm talking about. I mean, yes, I've had plenty of problems like that too, especially in college, and, sure, they took me the entire week to solve, but that's not interesting or useful to me pedagogically because the solutions are either "beg the TA to teach us what we need to know to solve the problem" (which I have done) or "learn this thing by myself or with the help of B, College Partner in Crime" (which I have also done, for whole classes even, with varying degrees of success in actually learning and retaining things), but in both cases it's still "once I know the material then I can solve the problem." (I mean, I guess it's... helpful in some ways... that I got crash courses in teaching myself things?)
I'm talking about the kind of problem where you do know everything you need to know to solve the problem, you just don't know yet how to put it together, and you have to keep thinking about it and trying different things and playing with it, many of which might not work. Or where you might not see how to do the whole problem, but you might see how to do a little part, and you have to play around with that part, then maybe once you've done that part you can see how to do another part, but you won't be able to see it until then.
I had a little of that in college, but the pedagogical system of classwork isn't really set up to foster that (except maybe in Sweden :) )