Hope this isn’t too off-topic, but I wonder if you have any ideas about why that is.
The main impediment to many far-mode thinkers learning hard (post-calculus) math is the drill and drudgery involved. If you’re going to learn hard math, it seems you should, by all means, learn it deeply. That’s not the obstacle. The obstacle is that to learn math deeply, you must first learn a lot of it rotely—at least the way it’s taught.
In the far-distant past, when I was in school, learning elementary calculus meant rote drilling on techniques of solving integrals. Is this still the case? Is it inevitable, or is it the result of methods of education?
The main reason “smart people” avoid math isn’t that they want to avoid depth; rather, what is, at least for some of them, drudgery. Math, more than any subject I know of, seems to require a very high level of sheer diligence to get to the point where you can start thinking about it deeply. Is this inevitable?
Hope this isn’t too off-topic, but I wonder if you have any ideas about why that is.
I think that the point is that more people are capable of routine tasks than of conceptual understanding, and that educational institutions want lots of people to do well in math class on account of a desire for (the appearance of) egalitarianism.
In the far-distant past, when I was in school, learning elementary calculus meant rote drilling on techniques of solving integrals. Is this still the case?
What time period was this? (No need to answer if you’d prefer not to :-) )
Math, more than any subject I know of, seems to require a very high level of sheer diligence to get to the point where you can start thinking about it deeply. Is this inevitable?
Some diligence is necessary, but not as much as it appears based on standard pedagogy. I wish that I could substantiate this in a few lines. If you say something about what math you know/remember, I might be able to point you to some helpful references.
In the far-distant past, when I was in school, learning elementary calculus meant rote drilling on techniques of solving integrals. Is this still the case? Is it inevitable, or is it the result of methods of education?
Some degree of this is probably inevitable. Integration in particular has no closed solution (unlike differentiation), so there really is no one general method you can apply to all problems. All you can do is remember a bag of tricks. While for differentiation, a few general rules allow you to integrate all elementary and trigonometric functions, and that’s pretty much all you encounter in school.
Hope this isn’t too off-topic, but I wonder if you have any ideas about why that is.
The main impediment to many far-mode thinkers learning hard (post-calculus) math is the drill and drudgery involved. If you’re going to learn hard math, it seems you should, by all means, learn it deeply. That’s not the obstacle. The obstacle is that to learn math deeply, you must first learn a lot of it rotely—at least the way it’s taught.
In the far-distant past, when I was in school, learning elementary calculus meant rote drilling on techniques of solving integrals. Is this still the case? Is it inevitable, or is it the result of methods of education?
The main reason “smart people” avoid math isn’t that they want to avoid depth; rather, what is, at least for some of them, drudgery. Math, more than any subject I know of, seems to require a very high level of sheer diligence to get to the point where you can start thinking about it deeply. Is this inevitable?
I think that the point is that more people are capable of routine tasks than of conceptual understanding, and that educational institutions want lots of people to do well in math class on account of a desire for (the appearance of) egalitarianism.
What time period was this? (No need to answer if you’d prefer not to :-) )
Some diligence is necessary, but not as much as it appears based on standard pedagogy. I wish that I could substantiate this in a few lines. If you say something about what math you know/remember, I might be able to point you to some helpful references.
Some degree of this is probably inevitable. Integration in particular has no closed solution (unlike differentiation), so there really is no one general method you can apply to all problems. All you can do is remember a bag of tricks. While for differentiation, a few general rules allow you to integrate all elementary and trigonometric functions, and that’s pretty much all you encounter in school.