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Nobody even learns how to derive any formula in high school. The teacher might show it once (if even that), but then everyone just forgets it and applies the fo

Nobody even learns how to derive any formula in high school. The teacher might show it once (if even that), but then everyone just forgets it and applies the formula like a robot. Same with chain rule, integration by substitution, or anything really. People only learn how to apply it, and essentially never the idea behind it. In my class (which was focused on math) I had to explain to someone how the derivatives relate to the speed and acceleration of a car, something that should have been understood for 2 years now. And yet, she did completely fine in classes. Fairly good grades - not the best, because she had trouble with the later tasks that required more thinking, but the first 80% of every test she aced because she just practiced doing the same thing over and over again, without actually understanding any of it. Do I agree that this is a completely fine strategy for getting good grades? Sure. But you're gonna have a lot of catching up to do if you want to apply this knowledge to anything that isn't a text book task that was made up specifically for you without any context.

watwut 7y ago
We did formula derivation and proves - and we exactly sucked in solving exercises. The understanding of how it works did not translated to being able to solve problems. When I went to college and was ambitious in math class that required calculations, it sucked and I was loosing. Until someone recommended me book full of exercises and I started doing them including boring ones. That is why I say you need both. Knowing that derivation is related to speed or that integral is area under the curve does not help to solve the integral at hand.
- pingyong 7y ago
  You mention exercises first and problems second. I completely agree on exercises. It's not that you can't solve them, but obviously you're way faster when you've solved what is essentially the same exercise 50 times before. And school (and college) tests tend to be designed in a way where 80% of the time you do the same exercise you did before and you just gotta be fast. But for solving an actual problem, I would say that understanding is way more important. Because in actual problems you tend to spend most of your time transferring whatever information you have into solvable equations, and much less time (comparatively) solving those equations. So maybe my problem is more that tests aren't a great representation of real life problems, and less that homework doesn't prepare you well for tests.
  - watwut 7y ago
    It is not just speed. Speed difference shows up in simple exercises. When you have to solve complex calculations and need to think hard about small ones, you wont figure big one out. In homework we had equations and series that took hours till you figured it. On test, we had equations and series that took over 20 minutes to solve when you was smart and good. No because there were many of them, but because it was hard to figure out what to do and because it took multiple experiments to find it.
ozim 7y ago
Yeah but applying stuff to anything that is not a text book is not school responsibility but everyones on his own. It is like people blaming school for not teaching everything. There has to be some line because there is not enough time and money to teach people everything. Bad side is that a lot of people think that everything they learn at school is enough. No one is going to teach you how to live your life. No one is going to hold your hand while applying complex math stuff because people who can do that have better things to do and they have limited time.

watwut 7y ago

We did formula derivation and proves - and we exactly sucked in solving exercises. The understanding of how it works did not translated to being able to solve problems. When I went to college and was ambitious in math class that required calculations, it sucked and I was loosing. Until someone recommended me book full of exercises and I started doing them including boring ones. That is why I say you need both. Knowing that derivation is related to speed or that integral is area under the curve does not help to solve the integral at hand.

pingyong 7y ago
You mention exercises first and problems second. I completely agree on exercises. It's not that you can't solve them, but obviously you're way faster when you've solved what is essentially the same exercise 50 times before. And school (and college) tests tend to be designed in a way where 80% of the time you do the same exercise you did before and you just gotta be fast. But for solving an actual problem, I would say that understanding is way more important. Because in actual problems you tend to spend most of your time transferring whatever information you have into solvable equations, and much less time (comparatively) solving those equations. So maybe my problem is more that tests aren't a great representation of real life problems, and less that homework doesn't prepare you well for tests.
- watwut 7y ago
  It is not just speed. Speed difference shows up in simple exercises. When you have to solve complex calculations and need to think hard about small ones, you wont figure big one out. In homework we had equations and series that took hours till you figured it. On test, we had equations and series that took over 20 minutes to solve when you was smart and good. No because there were many of them, but because it was hard to figure out what to do and because it took multiple experiments to find it.

ozim 7y ago

Yeah but applying stuff to anything that is not a text book is not school responsibility but everyones on his own. It is like people blaming school for not teaching everything. There has to be some line because there is not enough time and money to teach people everything. Bad side is that a lot of people think that everything they learn at school is enough. No one is going to teach you how to live your life. No one is going to hold your hand while applying complex math stuff because people who can do that have better things to do and they have limited time.