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Learning the meanings of things without learning how to do them leaves you powerless to do anything with that knowledge. It's very easy to walk around saying "w

by Retra 7y ago

Learning the meanings of things without learning how to do them leaves you powerless to do anything with that knowledge. It's very easy to walk around saying "we could solve problem X with technique Y", but if you don't actually know how to do Y, then you're just conjecturing fruitlessly. For instance, here you're talking about "memorizing how to manually integrate a 5th degree polynomial" as if that's something anyone who knows calculus actually does. What it really sounds like is that you don't want to put effort into things. Giving you easier classes isn't going to solve your problem. Granted, you'll want a broader understanding of things, but the best way to get that is often to actually learn as many details as possible over the long term, not by watching teaser trailers and being told that's the whole plot.

bootlooped 7y ago
I'm pretty sure I manually integrated (and differentiated) polynomials that large in my calculus classes. As for the "you don't want to put effort into things", I did put in the effort, I took the classes in question and graduated. I just happen think that particular effort was a waste of time. There's always a deeper or shallower understanding to be had of a subject. Finding what is appropriate for a given task is the question.
- Retra 7y ago
  You don't have to talk about integrating higher degree polynomials, because a polynomial is just a sum of monomials, and you just end up integrating monomials over and over again. If you can integrate a single monomial, you can integrate all polynomials. That makes your objection seem weak, as though you don't know how to integrate, and you're just imagining that it is hard. That undermines your point because there are actually things in math that are hard, but you'd be woefully unprepared to understand them if you don't see the value in memorizing the absolutely trivial stuff. It's like a child saying "I don't want to be forced to memorize the shapes of the letters, because that's not what makes a good writer." Does a good writer sit around looking up letter shapes in a diagram all day because they can't be bothered to remember them? Either way, the optimal solution is the same: do the task over and over again until you are so familiar with it that you can recall it from memory. Memorization is a necessary part of learning.

by Retra 7y ago

bootlooped 7y ago

I'm pretty sure I manually integrated (and differentiated) polynomials that large in my calculus classes. As for the "you don't want to put effort into things", I did put in the effort, I took the classes in question and graduated. I just happen think that particular effort was a waste of time. There's always a deeper or shallower understanding to be had of a subject. Finding what is appropriate for a given task is the question.

Retra 7y ago
You don't have to talk about integrating higher degree polynomials, because a polynomial is just a sum of monomials, and you just end up integrating monomials over and over again. If you can integrate a single monomial, you can integrate all polynomials. That makes your objection seem weak, as though you don't know how to integrate, and you're just imagining that it is hard. That undermines your point because there are actually things in math that are hard, but you'd be woefully unprepared to understand them if you don't see the value in memorizing the absolutely trivial stuff. It's like a child saying "I don't want to be forced to memorize the shapes of the letters, because that's not what makes a good writer." Does a good writer sit around looking up letter shapes in a diagram all day because they can't be bothered to remember them? Either way, the optimal solution is the same: do the task over and over again until you are so familiar with it that you can recall it from memory. Memorization is a necessary part of learning.