Building insight on a particular topic

[pakmingki]

Im in high school now taking AP calc AB, AP phys C mechanics, and AP chem, and the typical english/social studies classes. I am doing this cause i like math and science. My dream schedule would have been AP calc BC, AP phys C and B, AP chem, AP bio, and probably AP stats or envi sci. This is because i like math and science.

Most of the times, whenever there is in any of my math or science classes, i can usually cram the night before and still ace the test. But, there are some times where i can study every night for a week before the test, and do poorly. I believe this has to do with "insight" on the topic. the reason why i can do well o tests with little studying is because i already have natural insight on that topic, and i would say the reason why i do ****ty on some tests is because i do not have insight.

I can't really explain what my view of insight is explicitly, so i will give some examples.

on my calculus quiz today, i really did not have insight, and in order to solve certain problems, i had to refer back to specific examples we did previously and think about which concept applies to the problem. The question was "dy/dx = 1/sqrt(4-x^2) find the general solution." the only reason why i knew how to do that was because just a few days before, our teacher lead us thruogh basically the exact same problem, just with different numbers. Now, if we had not done an example problem like that i would definitely not have been able to do that problem. And this is the reason why i think insight is so important. No matter how many example problems you go through, there will always be more and more problems which you haven't had an example of, and you are guaranteed to run into this situation, and you are guaranteed to screw up big time.

In chemistry, i usually have the most natural insight, and i hardly ever do any practice problems and ace the tests, because my deep insight allows me to just instincly know which concept applies to a problem instead of thinking about it, and i just instincly know how to set up problems i have never seen before.

In physics, i usually have to work on it. A few months ago on our test on work and conservation of mechanical energy, i studied for 2 weeks and got like a 20 percent on the test. A week later, the teacher offered a retake. By that time, my insight somehow increased (im sure it had something to do with studying like 3 hours a day) and i aced the retake. On the retake, there was a free response question which i had never encountered, but because i had that insight, i just instinctly knew how to set it up.


Now, i was wondering if you guys have this sort of thing, and I am trying to find a way i could build that concrete insight faster, so i don't have to take retakes (retakes are always after school, and plus my teachers always give only like 90% or 95% of the grade earned on the retake, as an incentive to do well the first time)

 

[Dr Transport]

Insight comes from practice, practice and practise. Years of experience is also a key to having insight into how to solve problems. I have been doing quantum mechanics for twenty years and I have a lot of insight into how to attack problems, the same goes for electromagnetics etc... The more you work at a subject the more you will learn it and you will develop little tricks to allow you to make progress.

 

[dontbesilly]

Sounds to me like you are talking about the difference between doing something mechanically and actually understanding it. This is something that comes up a lot in my BC Calculus class. My classmates often have problems with certain things because they simply are not taught to understand things. I swear high school math is more devoted to learning an infinite number of problem solving algorithms (if this do this) than actually gaining an understanding of the subject. The only way I've found of avoiding this trap is to read the textbook.