Understanding Concepts as opposed to Memorizing concepts.

[zhentil]

Could you explain what you mean by "twist?" Does this involve deriving new concepts, or does it mean using the old concepts to answer unfamiliar questions?

 

[se7en]

Could you explain what you mean by "twist?" Does this involve deriving new concepts, or does it mean using the old concepts to answer unfamiliar questions?

It would be the latter. Using old concepts to answer unfamiliar questions.

 

[Bourbaki1123]

I wonder how logic, abstract(non-constructivist) mathematics and computer science play into the scheme of visualization/geometric intuition = Understanding. Clearly there is something beyond memorization in deriving logical and mathematical conclusions and in answering problems dealing with finite/discrete/recursive concepts.

There is a divide, I think, in understanding based upon the object of consideration. I think there is necessarily an appeal to a more linguistic intuition in some problems which require facility with logical concepts that allow for little visual input. If it were the case that all processes were visual in nature, then of course such concepts as infinity which are not rooted in observation would be not existent as they do not occur in nature but are processes which can be deduced from nature. There is a combination of linguistic clarity and visual clarity which begets understanding, but in order for us to draw and express linguistic conclusions we have to have linguistic facts which are memorized either by experience or consciously and so too for visual processes.

The benefit of a public education is an typically economic one, intellectually it is a detriment. You cannot get a reasonable job without a high school diploma, you cannot get a good job without a college degree; this is what we are taught. More and more our degrees are seen as expensive pieces of paper, and college grads are not viewed in the way that the were 30-40 years ago, and with good reason. Now that those who have gone through the system and seen how broken it is are in positions of power and they do not recognize the college degree as having nearly the weight that their predecessors did.

 

[zhentil]

It would be the latter. Using old concepts to answer unfamiliar questions.

I would say that this is a fair test of understanding concepts. Otherwise, aren't they just testing whether you remember how to do problems?

 

[Raizy]

I don't know anything about Maxwell's equation, & I sure don't underestimate it. But saying that memorizing is critical is not right, its upto the paper setter to set a paper which test the brain, not the memory.
I never memorized any equation, if I need it, i derive it myself in exam.

Memorizing = Cheating

Yeah they should have something called "smart" open book tests EVERY TIME. Where even though it was an open book test, you would still have to study to understand the concepts. Or else you'll end up studying during the testing exam and take the entire testing time to understand some explanation. And to supplement there should be a nice chunk of marks that require you to think.

 

[se7en]

I would say that this is a fair test of understanding concepts. Otherwise, aren't they just testing whether you remember how to do problems?

not exactly. The questions are usually ones that I(we as a class) have not seen before. But some seem better at being able to apply the concepts and relate concepts in order to answer the question. I know this isn't a problem that the whole class is having, but these types of questions separate the As from the Bs and I'm more than not in the latter category...

 

[mbisCool]

Are you sure you are truly understanding the material and not simply doing the problems? It is quite common for an exam to involve questions like the ones you describe. Simply memorizing the material and techniques alone won't get you through the more difficult exam questions.

 

[se7en]

Are you sure you are truly understanding the material and not simply doing the problems? It is quite common for an exam to involve questions like the ones you describe. Simply memorizing the material and techniques alone won't get you through the more difficult exam questions.

yeah maybe I'm am just not truly understanding the material.

 

[ank_gl]

yeah maybe I'm am just not truly understanding the material.

Who is to judge it then? Well no one, only you can know if you are understanding it. If you feel satisfied by the level of judgment you have for some concept, then its fine. Personally I try to relate things to physical world(talking about mechanical engineering), if I am able to reason out a phenomenon by using my understanding of the topic, i feel satisfied.

If you are willing, do NOT read the derivations for something first, try to apply the basics to the problem & try to reach for the solution. Don't bother if you end up with an incorrect result, DO try a bit before just reading out some derivation, atleast it won't feel like hey, I can never be a Newton, he thought of those things by himself, & I am just learning his work.

And I am surprised how, literally, people are not understanding the point raised by OP. OP asks whether to be opportunistic by memorizing or doing it the harder(longer?) way.For example, if two boys are writing an exam, one of em knows all the formulas & solves all the problems, he ll be awarded full marks, on the other hand, the other boy is short on memory package, & he resorts to deriving the formulas needed & ends up with 3 unanswered questions at the end of the exam, he ll be getting lesser marks, but he deserved more than that, at least a bonus for using his brain. It isn't fair to assume that the first boy didn't knew the derivations, he might have, but the question paper didn't trick him enough to use his analytical skills to answer(which is usually the case with many exams).

 

[se7en]

Who is to judge it then? Well no one, only you can know if you are understanding it. If you feel satisfied by the level of judgment you have for some concept, then its fine. Personally I try to relate things to physical world(talking about mechanical engineering), if I am able to reason out a phenomenon by using my understanding of the topic, i feel satisfied.

If you are willing, do NOT read the derivations for something first, try to apply the basics to the problem & try to reach for the solution. Don't bother if you end up with an incorrect result, DO try a bit before just reading out some derivation, atleast it won't feel like hey, I can never be a Newton, he thought of those things by himself, & I am just learning his work.

And I am surprised how, literally, people are not understanding the point raised by OP. OP asks whether to be opportunistic by memorizing or doing it the harder(longer?) way.For example, if two boys are writing an exam, one of em knows all the formulas & solves all the problems, he ll be awarded full marks, on the other hand, the other boy is short on memory package, & he resorts to deriving the formulas needed & ends up with 3 unanswered questions at the end of the exam, he ll be getting lesser marks, but he deserved more than that, at least a bonus for using his brain. It isn't fair to assume that the first boy didn't knew the derivations, he might have, but the question paper didn't trick him enough to use his analytical skills to answer(which is usually the case with many exams).

Thanks! I'll try that method out! I appreciate it...