I don’t think that he would have gotten a grade below C in calculus if he had spent all waking hours talking about calculus with me for 6 months.
Of course he would have gotten an A. The difference between being good and bad at math is whether you need to “spent all waking hours talking about calculus” to get an A.
Of course he would have gotten an A. The difference between being good and bad at math is whether you need to “spent all waking hours talking about calculus” to get an A.
Extrapolating from 1 course is silly. I worked like a demon to do mediocre (low Bs) in both calc 1 and physics 1, but somewhere towards the end of my freshman year of college something fell into place for me. By my first year of grad school I was breezing through quantum field theory and math methods for string theory courses with minimal effort.
Fascinating… do you have any idea what might have “fallen in to place”? (I’m always eager to learn from people who became good, as opposed to people who were always good or always bad, because I figure the people who became good have the most to tell us about whatever components of being good are non-innate. For example, Elon Musk thinks he’s been highly driven ever since he was a kid, which suggests that he doesn’t have much to teach others about motivation.)
Well, one thing was definitely changed was my approach to the coursework. I started taking a lot of notes as a memory aid, but then when I worked through problems I relied on what I remembered and refused to look things up in the text book or my notes. This forced me to figure out ways to solve problems in ways that made sense to me- it was really slow going at first but I slowly built up my own bag of tricks.
Interesting. I think I’ve read research suggesting that answering questions is significantly better for learning than just reading material (similar to how Anki asks you questions instead of just telling you things).
Val at CFAR likes to make the point that if you look at what students in a typical math class are actually practicing during class, they are practicing copying off the blackboard. In the same way maybe what most people are “actually practicing” when they do math homework is flipping though the textbook until they find an example problem that looks analogous to the one they’re working on and imitating the structure of the example problem solution in order to do their homework.
In the same way maybe what most people are “actually practicing” when they do math homework is flipping though the textbook until they find an example problem that looks analogous to the one they’re working on and imitating the structure of the example problem solution in order to do their homework.
Consider that you’re given a magic formula (the derivative) to determine the vertex of a quadratic equation when learning how to graph equations. That nonsense is how mathematics is -taught-. It shouldn’t surprise us when students adopt the “magic pattern” approach to problem-solving. (And my own experience is that most of the teachers are following magic patterns they don’t understand themselves, anyways.)
In the same way maybe what most people are “actually practicing” when they do math homework is flipping though the textbook until they find an example problem that looks analogous to the one they’re working on and imitating the structure of the example problem solution in order to do their homework.
That would explain why story problems seem to be perceived as hard by average students at the high school level. I remember being confused by that, since mathematically they were usually the easiest problems in a set—but they wouldn’t be trivially pattern-matched to sample problems.
Of course he would have gotten an A. The difference between being good and bad at math is whether you need to “spent all waking hours talking about calculus” to get an A.
Extrapolating from 1 course is silly. I worked like a demon to do mediocre (low Bs) in both calc 1 and physics 1, but somewhere towards the end of my freshman year of college something fell into place for me. By my first year of grad school I was breezing through quantum field theory and math methods for string theory courses with minimal effort.
Fascinating… do you have any idea what might have “fallen in to place”? (I’m always eager to learn from people who became good, as opposed to people who were always good or always bad, because I figure the people who became good have the most to tell us about whatever components of being good are non-innate. For example, Elon Musk thinks he’s been highly driven ever since he was a kid, which suggests that he doesn’t have much to teach others about motivation.)
Well, one thing was definitely changed was my approach to the coursework. I started taking a lot of notes as a memory aid, but then when I worked through problems I relied on what I remembered and refused to look things up in the text book or my notes. This forced me to figure out ways to solve problems in ways that made sense to me- it was really slow going at first but I slowly built up my own bag of tricks.
Interesting. I think I’ve read research suggesting that answering questions is significantly better for learning than just reading material (similar to how Anki asks you questions instead of just telling you things).
Val at CFAR likes to make the point that if you look at what students in a typical math class are actually practicing during class, they are practicing copying off the blackboard. In the same way maybe what most people are “actually practicing” when they do math homework is flipping though the textbook until they find an example problem that looks analogous to the one they’re working on and imitating the structure of the example problem solution in order to do their homework.
Consider that you’re given a magic formula (the derivative) to determine the vertex of a quadratic equation when learning how to graph equations. That nonsense is how mathematics is -taught-. It shouldn’t surprise us when students adopt the “magic pattern” approach to problem-solving. (And my own experience is that most of the teachers are following magic patterns they don’t understand themselves, anyways.)
That would explain why story problems seem to be perceived as hard by average students at the high school level. I remember being confused by that, since mathematically they were usually the easiest problems in a set—but they wouldn’t be trivially pattern-matched to sample problems.
That’s true. I’ve seen this go both ways, too. Though the priors are against a turn of events like yours, it does happen.
You seem to be nitpicking over a semantic issue at this point. With considerable due respect, you have better things to do.
OK, sorry, didn’t mean to upset you. Disengaging.
I wasn’t offended :-).