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.
That is exactly what I am talking about too! And it is *blowing my mind* that you never had this experience. But like I said, that's why you went to grad school in this and I never did. :P Though I wanted to.
The "not teaching us what we needed to know" was only two classes, physics in my freshman year of college, and that's exactly why I was unable to continue with physics. I didn't have the ability to make up for any gaps in what they'd taught us. You obviously did.
That kind of thing never happened in high school physics, or I wouldn't have been able to try majoring in physics in college, and it never happened in math, which is why I was successful in getting a math degree and being a top student (we had mixed graduate/undergrad classes in college, and I regularly outperformed the graduate students in the same class).
When my physics prof asked why I was switching my major to math when it was math I was complaining about in his class, I told him, "It's because in math, first they teach you the math, then they test you on it! They never ever test you on something they haven't taught you. I didn't even know that was a thing! I want no part in it and I'm switching to math." Okay, I didn't use those exact words, those last two sentences were my emotions, but I did explain the facts in the first part.
So, again: the rest of us had to incrementally approach a problem over the course of multiple days. Because we had been taught all the relevant material, but it took a while to figure out which bits applied and to connect the dots. (I mean, lots of people gave up the same day and handed in what they had, but those were not the people who were majoring/went on to major in math/physics. People like me were somewhere in between "giving up on the same day because who cares" and "but I already know how to solve every problem": we got degrees in these subjects but did not manage advanced degrees.)
I would walk around campus tackling math problems in my head, I would meet up with a study group to tackle the same homework assignment more than once over the course of a week, I would fall asleep and wake up with the answer.
Now, would I have needed so many days to solve these problems/write these proofs if I'd had a good grasp of the concepts before being asked to work through a problem/proof beginning to end? Probably yes for some of them, for at least things like number theory, where the whole concept of "I know how to prove everything as soon as I sit down" is, again, blowing my mind, but far fewer. I would have been able to go farther in math, both on my own and in a classroom setting, and you might be looking at someone with an advanced degree in math today.
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 :) )
Actually, that might be your survivor bias at work again. ;) This was almost every single math homework assignment I had in college, minus some of the too-easy classes.
Now, I agree that they need to make it so that people like you *also* get challenging enough material before grad school, but that I think is a problem with the one-size-fits-all approach (which is a major thing that gets reformed in my imaginary quest to reform pedagogy).
![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
Re: Grad school
Date: 2023-01-14 01:40 pm (UTC)That is exactly what I am talking about too! And it is *blowing my mind* that you never had this experience. But like I said, that's why you went to grad school in this and I never did. :P Though I wanted to.
The "not teaching us what we needed to know" was only two classes, physics in my freshman year of college, and that's exactly why I was unable to continue with physics. I didn't have the ability to make up for any gaps in what they'd taught us. You obviously did.
That kind of thing never happened in high school physics, or I wouldn't have been able to try majoring in physics in college, and it never happened in math, which is why I was successful in getting a math degree and being a top student (we had mixed graduate/undergrad classes in college, and I regularly outperformed the graduate students in the same class).
When my physics prof asked why I was switching my major to math when it was math I was complaining about in his class, I told him, "It's because in math, first they teach you the math, then they test you on it! They never ever test you on something they haven't taught you. I didn't even know that was a thing! I want no part in it and I'm switching to math." Okay, I didn't use those exact words, those last two sentences were my emotions, but I did explain the facts in the first part.
So, again: the rest of us had to incrementally approach a problem over the course of multiple days. Because we had been taught all the relevant material, but it took a while to figure out which bits applied and to connect the dots. (I mean, lots of people gave up the same day and handed in what they had, but those were not the people who were majoring/went on to major in math/physics. People like me were somewhere in between "giving up on the same day because who cares" and "but I already know how to solve every problem": we got degrees in these subjects but did not manage advanced degrees.)
I would walk around campus tackling math problems in my head, I would meet up with a study group to tackle the same homework assignment more than once over the course of a week, I would fall asleep and wake up with the answer.
Now, would I have needed so many days to solve these problems/write these proofs if I'd had a good grasp of the concepts before being asked to work through a problem/proof beginning to end? Probably yes for some of them, for at least things like number theory, where the whole concept of "I know how to prove everything as soon as I sit down" is, again, blowing my mind, but far fewer. I would have been able to go farther in math, both on my own and in a classroom setting, and you might be looking at someone with an advanced degree in math today.
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 :) )
Actually, that might be your survivor bias at work again. ;) This was almost every single math homework assignment I had in college, minus some of the too-easy classes.
Now, I agree that they need to make it so that people like you *also* get challenging enough material before grad school, but that I think is a problem with the one-size-fits-all approach (which is a major thing that gets reformed in my imaginary quest to reform pedagogy).