Self Evaluation in Self Education

[CosmicKitten]

I have been studying physics and math on my own for ever a year now, and I am not sure about when I am ready to move on to something higher. How do you know when you 'get' something?

Is it when you can look at all of the problems and figure out instantly how to do them just intuitively, without even looking up the formulas or even bringing them up into memory? I have gotten to that point with some problems.

In particular, lately I have been reviewing material (ODE's) I had studied cursorily almost a year ago, and although I don't remember everything explicitly, as I work on it and briefly read through solved problems it pops back into my head even fresher than when I was first studying it. Does that mean I don't need review?

Is it supposed to be challenging just to understand the concepts? Because that is never an issue with me if I pay attention and it's a well-written text.

I've also been studying electromagnetics out of Schaum's, and I like the way they have shown me how to set integrals up with the differentials and vector notation and everything. That was not only not shown in my last electromagnetics class but not required to know, I think? It was a comm. college class and very poorly taught and boring...

 

[Jorriss]

I don't believe there is a criteria for when one 'gets' a subject.

But then I don't know if there is any subject in physics I would say I really get, and the criteria would certainly be something other than an instantaneous ability to answer all textbook problems. I still can't answer especially challenging freshman problems instantly, but I can pretty much solve any I have come across given some time, does that qualify as understanding?

Is it supposed to be challenging just to understand the concepts? Because that is never an issue with me if I pay attention and it's a well-written text.

How do you measure understanding concepts?

 

[micromass]

There is no such thing as finally understanding everything. The more you look at something, the more you will understand it. I can look at a freshman calculus course and still discover things I didn't knew before.

In my opinion, you will need to keep reviewing. If you don't review something, then you will eventually forget it. That doesn't mean you should keep reading a chapter on derivatives over and over until the end of time. But it does mean that you should be aware that your ability to calculate derivatives will diminish slowly over time. So if you really need to calculate them, then you should review those things.

Also, you claim to understand the concepts. I think you should realize that people don't understand the concepts after many years practicing. You might understand them at a certain level and be able to work with them, but there's always a deeper level of understanding that you can have.

 

[CosmicKitten]

There is no such thing as finally understanding everything. The more you look at something, the more you will understand it. I can look at a freshman calculus course and still discover things I didn't knew before.

In my opinion, you will need to keep reviewing. If you don't review something, then you will eventually forget it. That doesn't mean you should keep reading a chapter on derivatives over and over until the end of time. But it does mean that you should be aware that your ability to calculate derivatives will diminish slowly over time. So if you really need to calculate them, then you should review those things.

Also, you claim to understand the concepts. I think you should realize that people don't understand the concepts after many years practicing. You might understand them at a certain level and be able to work with them, but there's always a deeper level of understanding that you can have.

I don't forget things without reviewing. It's part of being autistic, I think. As a matter of fact with time they sort of ferment in my mind and I understand them on a different level... but probably because I think in terms of math and science to constantly give myself practice and so such concepts never get rusty. In my particular case, I believe it would be like saying my ability to talk or use English language would diminish over time.

As an example, when I first took math and science courses in college (second semester, because I transferred from a comm. college that did not have any calculus classes or calculus based physics classes) I scored as high as they would allow you to on the math placement exam, despite having not taken a math class in two and a half years, while I had several classmates that were engineering majors that had to retake trig when they entered college despite being fresh out of high school and some having taken multiple calculus courses in high school to boot. Also, I got an A without even studying or doing the homework, I could figure out the problems using pure logic and dregs of high school physics in the time I was given to take the test. I was one of probably only two students that got an A; most of the other students would have failed if the teacher didn't generously curve the grade for them.

Also, by understanding I don't mean as thoroughly as you mention; I simply mean enough to move on to something else (which would likely bring greater understanding if you're ready for it). At which point am I stifling myself and need to bring the level up?

 

[CosmicKitten]

I don't believe there is a criteria for when one 'gets' a subject.

But then I don't know if there is any subject in physics I would say I really get, and the criteria would certainly be something other than an instantaneous ability to answer all textbook problems. I still can't answer especially challenging freshman problems instantly, but I can pretty much solve any I have come across given some time, does that qualify as understanding?


How do you measure understanding concepts?

I would imagine by taking a test?

I used to be a very good test taker but my last half-semester in college would seem to show otherwise.

I could probably solve all the problems on the test given enough time... but since it's a test you don't get that much time.

So apparently understanding enough means you must be able to answer them all in less than two hours or however long the exam is...