I’m interpreting eli_sennesh as claiming that even if the elasticity model is true, believing in it is demoralizing and thus will reduce one’s elasticity,
Actually, I think both personal capacity/elasticity and morale/drive are more like real numbers than like booleans, and that since they’re both factors in your actually doing/learning math, there seems to me (just based on observation) to be a very large range of values for the two variables where you can leverage one to make up for a lack of the other in order to get more math done.
I also think that the elasticity/ability variable does not dictate a hard limit on how much math you can learn, but instead on how quickly you learn it.
To pin myself down to concrete predictions, I don’t think, for instance, that most people are incapable of learning, say, beginning multivariable calculus (without any serious analysis, the engineers’ version). I do think that many people have so little innate ability that they cannot learn it quickly enough to pass a math, science, or engineering degree in four years. I just think they can probably learn the material if they repeat certain courses twice over and wind up taking seven years. What we normally consider being Bad At Math simply means being so slow to learn math that it would take decades to learn what more talented students can digest in mere years.
Neither innate ability nor drive, in my view, draws a hard “line in the sand” that dictates an impassable limit. They simply dictate where the “price curve” of pedagogical resource trade-offs will fall; we can always educate more people further if we have the resources to invest and can expect a positive return.
(To further pin myself to concrete experience, I have a dyslexic friend from undergrad who faced exactly this trouble with programming. Because the university and his family knew he was dyslexic, he was allowed to take five years to finish his undergraduate degree in Computer Science, and he used quite a lot of personal grit and drive to ensure he studied enough to pass in those five years. If I recall, he came out with just about a 3.10/4.00 GPA, or somewhere thereabouts—not excellent but respectable. Today he works as a software engineer for Cisco and earns a healthy salary, because the university and his parents decided the extra resources were worth allowing/investing to let him learn the fundamentals at the pace his studying efforts could carry him.)
Actually, I think both personal capacity/elasticity and morale/drive are more like real numbers than like booleans, and that since they’re both factors in your actually doing/learning math, there seems to me (just based on observation) to be a very large range of values for the two variables where you can leverage one to make up for a lack of the other in order to get more math done.
I also think that the elasticity/ability variable does not dictate a hard limit on how much math you can learn, but instead on how quickly you learn it.
To pin myself down to concrete predictions, I don’t think, for instance, that most people are incapable of learning, say, beginning multivariable calculus (without any serious analysis, the engineers’ version). I do think that many people have so little innate ability that they cannot learn it quickly enough to pass a math, science, or engineering degree in four years. I just think they can probably learn the material if they repeat certain courses twice over and wind up taking seven years. What we normally consider being Bad At Math simply means being so slow to learn math that it would take decades to learn what more talented students can digest in mere years.
Neither innate ability nor drive, in my view, draws a hard “line in the sand” that dictates an impassable limit. They simply dictate where the “price curve” of pedagogical resource trade-offs will fall; we can always educate more people further if we have the resources to invest and can expect a positive return.
(To further pin myself to concrete experience, I have a dyslexic friend from undergrad who faced exactly this trouble with programming. Because the university and his family knew he was dyslexic, he was allowed to take five years to finish his undergraduate degree in Computer Science, and he used quite a lot of personal grit and drive to ensure he studied enough to pass in those five years. If I recall, he came out with just about a 3.10/4.00 GPA, or somewhere thereabouts—not excellent but respectable. Today he works as a software engineer for Cisco and earns a healthy salary, because the university and his parents decided the extra resources were worth allowing/investing to let him learn the fundamentals at the pace his studying efforts could carry him.)