Understanding Concepts as opposed to Memorizing concepts.

[The Dagda]

With intelligence your probably starting out at a certain level due to your genes, so if you're not that bright chances are you aren't going to win a nobel prize, but memorization has little to do with intelligence, it is a learned ability, and being able to apply it is most certainly something to do with intelligence. That said as with anything in the brain its something that can be improved with practice, even if you aren't the brightest, you can still excel if you apply yourself. This is just common sense, and as someone else mentioned common sense and intelligence are two things that are seldom related in a proportional measure. I think given the right attitude even the most mediocre of students can succeed, assuming they're not blighted with being remedial.

 

[rogerharris]

Dont forget Einstein style creative visualization of abstract concepts is very helpful. Einstein imagined he was riding on a beam of light and apparently this gave him a breakthrough. Many of his ideas were derived from visual spatial thought. I read an article that a lot of science breakthroughs have occurred in dreams. Maybe practising visualization helps with this. I dunno. I only ever had these dream insights, when i was working round the clock on a problem sleeping in my study. Many scientists probably dream about more basic survival problems, like dealing with colleages, meeting deadlines etc.

If you can create visual analogies like setting up different components of a complex problem as players on some kind of stage this may be useful. You will probably have to drop the analogy, but they can be usefull to get hooks into a problem. Sometimes the shift in mental focus helps the brain jump a stage up in understanding.

 

[The Dagda]

Dont forget Einstein style creative visualization of abstract concepts is very helpful. Einstein imagined he was riding on a beam of light and apparently this gave him a breakthrough. Many of his ideas were derived from visual spatial thought. I read an article that a lot of science breakthroughs have occurred in dreams. Maybe practising visualization helps with this. I dunno. I only ever had these dream insights, when i was working round the clock on a problem sleeping in my study. Many scientists probably dream about more basic survival problems, like dealing with colleages, meeting deadlines etc.

If you can create visual analogies like setting up different components of a complex problem as players on some kind of stage this may be useful. You will probably have to drop the analogy, but they can be usefull to get hooks into a problem. Sometimes the shift in mental focus helps the brain jump a stage up in understanding.

Very true, but the way people visualise things is very different from person to person and relies on visualisation skills, again something that can be trained. Is anyone noticing a pattern here. People talk about each other as if they will be the same person at age 14 as at age 36, which is why often when you meet someone 20 odd years later you find out they weren't as dumb or as bright as you thought. What happens in between is up to anyone to train. Of course you have certain things you will be good at inherently, memorisation is not one of mine, although once its in it tends to stay. My strength is visualisation. Just make sure you appeal to your strengths and fortify your weaknesses with practice or some method or another that works for you; it's really not rocket science, unless of course you are doing rocket science, then it is rocket science obviously.

 

[zhentil]

You obviously missed *my* point also :

Somewhere someone has an explanation of the line integral's geometric and physical meaning. Go over *that* until you can recite and explain each step.

Or try to discover that yourself. Somewhere, somehow, people are coming up with new research. I would bet good money that they're not doing any memorization whatsoever. My professors fully admit to not remembering long equations (e.g. kernels in PDE, transformation laws for general tensors, etc.). They certainly don't make an attempt to memorize them; they just look them up in a book when they need to.

 

[se7en]

Well I took my first physics midterm yesterday and it was very intense. Most of the equations that were needed were not given, which means that we had to derive them from the ones that were given. But that's not the part that posed the greatest challenge. A large part of the exam was conceptually based and I felt that I was well prepared for this part. Unfortunately, the questions required us to "twist" concepts and apply them them in certain situations which I had a hard time doing. I am 99.9% that I knew ALL the concepts being tested but I just couldn't utilize them in the way that would help me answer the question. How do you guys study in order to prevent gaps in your understanding of concepts so that when you do come around questions like these you are able to answer them? The word problems did not really pose any difficulty because I solved so many of them through practice...

 

[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...