Ah, that's a very good question and has a longer answer than you might expect.
In high school, I had a pretty unassailable self-esteem. I knew I was really good, and although there were a few people better than me at math in the state, I was definitely of the "all right, let's see if I can take you next time!" mindset. (With the exceptions of the two guys who were, I believe, top 5 and top 1 in the nation their senior years, which were my sophomore and junior year respectively. We all knew that they were untouchable. And I knew it was likely I wouldn't beat the guy who was #1 at all the math competitions in my state my year, but it was more of a "but why not try?" sort of thing.) And yep, I did do things like try to make sure I knew the answers to things I got wrong or didn't know how to do because I knew that would make me better for next time. (I will say that it did not occur to me to practice in addition to that -- but I would have if I had known to do so; I was pretty dumb about this kind of thing until I failed quals in grad school the first time because of it, at which point I had to learn in a hurry.) I would have totally considered myself as having a growth mindset during this time (though in retrospect it's clear that I did base a good deal of my identity on being good at math contests, in a fixed-mindset kind of way).
Then I went to college, and a) was confronted by a number of people who were (sometimes arguably, sometimes inarguably) better at math and math contests than I, and b) had classes that I didn't just breeze through. (I got good grades, they just weren't trivially easy for me any more.) Then I took the Putnam, and did really badly. I mean, even at the time I understood it wasn't that bad for a sophomore who hadn't really done stuff at that level before! (1) But interestingly, that time it just destroyed me in terms of technical competitions. I gave up. I avoided the Putnam, and tried to avoid technical competitions in general from then on.
D went through a similar path, where he bombed the Putnam the first time, but then his response was something more along the lines of, "huh, these are interesting problems! I should do more of them!" (Now, I should say his university did not have such a density of highly-ranked people that mine did, but I don't think it would have made a difference.) He then went on to score in the Putnam top 100 his junior and senior years of college. (I didn't know this until now, actually -- I had never really thought about it before, but just now I thought, "I bet he scored well enough that it was recorded," and just found this out by doing a google search, lol.) He still does math competition problems for fun, and as you can imagine he's done them for so many years now that he's really good at it. While I never learned how to do math contest problems at that level.
E. knows these stories (except for the top 100 thing, which I just now found out), and I constantly tell her she should be more like D and less like me in this particular respect :) (This is a message that resonates with her, as she likes very much thinking that she can do things better than her mom.)
(1) A couple of my upperclassman friends at the time (who were male) tried to reassure me by saying that when they first took the Putnam, they'd done even worse than I had. And we had a bet going that all three of our scores added together would be higher than our third friend, and we won that bet, and those guys did a lot of affectionate mocking and trash-talking to Third Friend -- which was of course immensely tongue-in-cheek, because of course Third Friend had done (almost) three times as well as we had. (I think our total score came to more points than was possible to get; Third Friend was in the top 5.) The thing I'm trying to get across here is that my friends treated the Putnam like a game that they'd play again and hopefully improve and do better at the next time, but which said nothing about them intrinsically as people, even if they weren't particularly good at it. (I believe neither of these guys scored in the top 100, although I remember one of them doing reasonably well.) Which is (mostly) how I treated math competitions in high school, but not this time.
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Re: Another book rec
Date: 2022-06-30 03:35 pm (UTC)In high school, I had a pretty unassailable self-esteem. I knew I was really good, and although there were a few people better than me at math in the state, I was definitely of the "all right, let's see if I can take you next time!" mindset. (With the exceptions of the two guys who were, I believe, top 5 and top 1 in the nation their senior years, which were my sophomore and junior year respectively. We all knew that they were untouchable. And I knew it was likely I wouldn't beat the guy who was #1 at all the math competitions in my state my year, but it was more of a "but why not try?" sort of thing.) And yep, I did do things like try to make sure I knew the answers to things I got wrong or didn't know how to do because I knew that would make me better for next time. (I will say that it did not occur to me to practice in addition to that -- but I would have if I had known to do so; I was pretty dumb about this kind of thing until I failed quals in grad school the first time because of it, at which point I had to learn in a hurry.) I would have totally considered myself as having a growth mindset during this time (though in retrospect it's clear that I did base a good deal of my identity on being good at math contests, in a fixed-mindset kind of way).
Then I went to college, and a) was confronted by a number of people who were (sometimes arguably, sometimes inarguably) better at math and math contests than I, and b) had classes that I didn't just breeze through. (I got good grades, they just weren't trivially easy for me any more.) Then I took the Putnam, and did really badly. I mean, even at the time I understood it wasn't that bad for a sophomore who hadn't really done stuff at that level before! (1) But interestingly, that time it just destroyed me in terms of technical competitions. I gave up. I avoided the Putnam, and tried to avoid technical competitions in general from then on.
D went through a similar path, where he bombed the Putnam the first time, but then his response was something more along the lines of, "huh, these are interesting problems! I should do more of them!" (Now, I should say his university did not have such a density of highly-ranked people that mine did, but I don't think it would have made a difference.) He then went on to score in the Putnam top 100 his junior and senior years of college. (I didn't know this until now, actually -- I had never really thought about it before, but just now I thought, "I bet he scored well enough that it was recorded," and just found this out by doing a google search, lol.) He still does math competition problems for fun, and as you can imagine he's done them for so many years now that he's really good at it. While I never learned how to do math contest problems at that level.
E. knows these stories (except for the top 100 thing, which I just now found out), and I constantly tell her she should be more like D and less like me in this particular respect :) (This is a message that resonates with her, as she likes very much thinking that she can do things better than her mom.)
(1) A couple of my upperclassman friends at the time (who were male) tried to reassure me by saying that when they first took the Putnam, they'd done even worse than I had. And we had a bet going that all three of our scores added together would be higher than our third friend, and we won that bet, and those guys did a lot of affectionate mocking and trash-talking to Third Friend -- which was of course immensely tongue-in-cheek, because of course Third Friend had done (almost) three times as well as we had. (I think our total score came to more points than was possible to get; Third Friend was in the top 5.) The thing I'm trying to get across here is that my friends treated the Putnam like a game that they'd play again and hopefully improve and do better at the next time, but which said nothing about them intrinsically as people, even if they weren't particularly good at it. (I believe neither of these guys scored in the top 100, although I remember one of them doing reasonably well.) Which is (mostly) how I treated math competitions in high school, but not this time.