Understanding Concepts as opposed to Memorizing concepts.

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In summary, it is important to remember the important concepts, but it is also important to apply them to real-world examples.
  • #1
se7en
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All throughout high school I was able to memorize the most important concepts and that would be enough to produce great test results. I am now in my second semester of college and the questions posed by the professor are more thought provoking and require much more knowledge ABOUT the main concepts rather than what they are. I usually study with 1 or 2 friends so I wouldn't really consider it a "study group", but I find that there are always holes in my knowledge about what we are studying and it seems that they are making connections between concepts that I am not picking up on. Fortunately, they fill in the gaps of my knowledge for me by explaining them to me. I know this is due to my lack of practice for adequate study habits. So how can I increase my understanding of concepts and in the process make connects between them?
 
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  • #2
You are taught to memorize concepts because it has been shown that it is an effective method for scoring well on tests in a short period of time. The side effect of this method is that in the long run, you retain next to nothing and your critical thinking skills are... well... non-existent.

I refuse to memorize even to this day because it's such a waste of time. People do it because humans love instant gratification. Memorize as much as you can, and score decent on tests (or sometimes good), but the long term effects are BAD! Kind of why people buy big new cars even if they can't afford it. Humans are addicted to instant gratification.

It's really ironic because new teacher's are taught NOT to do that... but told secretly to do it. And what's even more ironic, most new teacher's go through university learning using this memorize everything method. They finish university knowing nothing. Hence, this explains why most teachers in elementary and high school know very little of the topic they are actually teaching. True facts.
 
  • #3
JasonRox said:
You are taught to memorize concepts because it has been shown that it is an effective method for scoring well on tests in a short period of time. The side effect of this method is that in the long run, you retain next to nothing and your critical thinking skills are... well... non-existent.

I refuse to memorize even to this day because it's such a waste of time. People do it because humans love instant gratification. Memorize as much as you can, and score decent on tests (or sometimes good), but the long term effects are BAD! Kind of why people buy big new cars even if they can't afford it. Humans are addicted to instant gratification.

It's really ironic because new teacher's are taught NOT to do that... but told secretly to do it. And what's even more ironic, most new teacher's go through university learning using this memorize everything method. They finish university knowing nothing. Hence, this explains why most teachers in elementary and high school know very little of the topic they are actually teaching. True facts.

If you get the chance, look into the Indian university (college?) system. It appears to be two-tiered, with those in the upper tier getting a broad, well-grounded education while those in the lower tier (there's a name for this tier but I can't recall or find it) memorize and regurgitate lots of facts. The end result is graduates who understand few of the essentials about their fields and that appears to be severely limiting India's industrialization efforts.

Can you say "No child left behind"?
 
  • #4
Memorization has its place. For example, all need to begin somewhere when a new concept is learned. THe concept of energy for example is highly complex, but it needs to begin with the acceptance of a conventional definition, "the ability to do work." Immediately after that, the concept drifts from the simple definition with tautologies (the definition of work? it's "the mechanical transfer of energy." and what's energy?...") and paradoxes ("The energy that is unavailable for work, etc).

The full concept is only learned after the superficial accepted facts and definitions are set in place, and then those facts and definitions get pushed around through critical thinking and experiencing varied examples.

One way of encouraging "going deeper" is to take any memorized definition, and ask why? or how? Go to any memorized law of physics and then look at any phenomenon and connect the two: How is a volcanic eruption consistent with the second law of thermodynamics? Apply gauss' laws to the operation of a magnetic tape player.

It is very difficult to apply things to a law if you do not remember what the law says. The act of "memorization" seems to be an act of futility, while simply "remembering the important stuff" is a necessity.

What's the difference? sometimes it's hard to say. As a high school teacher, I try to avoid the command "memorize" when giving assignments to students. I do however make it a point that they MUST remember that the word "spontaneous" makes or breaks the 2nd law. THe exact wording is not important, but the law itself is very important.
 
  • #5
JasonRox said:
You are taught to memorize concepts because it has been shown that it is an effective method for scoring well on tests in a short period of time. The side effect of this method is that in the long run, you retain next to nothing and your critical thinking skills are... well... non-existent.

I refuse to memorize even to this day because it's such a waste of time. People do it because humans love instant gratification. Memorize as much as you can, and score decent on tests (or sometimes good), but the long term effects are BAD! Kind of why people buy big new cars even if they can't afford it. Humans are addicted to instant gratification.

It's really ironic because new teacher's are taught NOT to do that... but told secretly to do it. And what's even more ironic, most new teacher's go through university learning using this memorize everything method. They finish university knowing nothing. Hence, this explains why most teachers in elementary and high school know very little of the topic they are actually teaching. True facts.

Sadly over hear it's become more about passing tests than understanding things, unsurprisingly we now have the worst standard of education in Europe outside of the Eastern bloc.

Basically our system has been so degraded that our qualifications up to and including sometimes degree are not as rigorous as they used to be. Luckily the sciences and maths still tend to be ok, at least at degree level. Critical thinking is not just for arts students. Obviously memorising facts is all part of the process, but in my experience, they tend to throw curve balls in exams at degree level, that test your ability to apply certain concepts to situations that might not always be that obvious. If you know why something works and can manipulate it rather than just knowing x, then you can apply it more generally.
 
  • #7
@ Dagda, TVP45 and se7en

This is becoming the case world over.

>With the population boom, there's more competition.

>More the competition, less attention every student is going to get and more the importance is going to be paid to test scores and competitive exams like the Olympiads. You could do thousands of sums (which is very difficult of course) and get through to the next level of the these exams without understanding very much.

>That is where the question comes in: how do we design a system which incorporates more than just numbers and grades on paper? We need a system wherein a person is not reduced to to ink on paper and rather someone with potential to think for himself.
 
  • #8
anirudh215 said:
@ Dagda, TVP45 and se7en

This is becoming the case world over.

>With the population boom, there's more competition.

>More the competition, less attention every student is going to get and more the importance is going to be paid to test scores and competitive exams like the Olympiads. You could do thousands of sums (which is very difficult of course) and get through to the next level of the these exams without understanding very much.

I don't buy that our population has been stagnant for 20 years, as have many European countries, the standard of education in countries like Sweden, Norway, France, Germany etc is excellent, it's not class sizes it's government spending and where it goes. There's a reason the US has an even worse education than the UK, which sits square at the bottom of European league tables and that is investment in proper education methods. The US I think blew it when they tried the testing method as well, but then their educational standard pre University has always been poor for reasons not just related to expenditure.

>That is where the question comes in: how do we design a system which incorporates more than just numbers and grades on paper? We need a system wherein a person is not reduced to to ink on paper and rather someone with potential to think for himself.

Precisely, we look at the better performers to see what we can learn from them.
 
  • #9
Why not develop both abilities? The smartest people are able to memorise tonnes in short periods of time as well as develop deep understandings of topics. A good pianist is able to memorise his pieces as well as interpret them prodigiously. I feel that we should neglect neither since a good memory and a good understanding reinforce one another.
 
  • #10
@ Dagda

That is true. The government expenditure and the private school boards have also become shoddy and corrupt. Have you read "Surely You're Joking Mr.Feynman"? In that book, Feynman refers to his experiences in Mexico. I feel that is similar to what you are talking about. Correct?
 
  • #11
I have to second Chi Meson's response. The way to fill in the holes is to become more actively engaged in a subject by asking how and why. Essentially you have to go beyond the course work and apply each concept in an independent manner to a new problem. From there, understanding naturally evolves.

Another argument in favour of memorization is that it can save you time in having to look things up.
 
  • #12
You may not have time to understand everything before moving on, so you may be forced to memorize.That's fine. Field's medallist Timothy Gowers recommends it in Mathematics: A Very Short Introduction. His example is a^ma^n = a^m+n. Many high school students cannot understand why. Gowers says it is fine just to memorise. You may need it as a basis for understanding other mathematics, and don't have time to talk it out with your chums. In college you may look at it again and understand why it works in a flash. So understanding may eventualy flower, meanwhile memorisation is 'good enough' -- and may always be good enough...
 
  • #13
anirudh215 said:
@ Dagda

That is true. The government expenditure and the private school boards have also become shoddy and corrupt. Have you read "Surely You're Joking Mr.Feynman"? In that book, Feynman refers to his experiences in Mexico. I feel that is similar to what you are talking about. Correct?

I think we're on the same page. Although I think maybe Obama is the president to tackle the issue of education, which is obviously a minefield and not an easy problem to solve. Over here I just think we should abandon the testing kids 4 or 5 times until they leave, it patently doesn't work and we need to tackle the fundamentals.
 
  • #14
JasonRox said:
You are taught to memorize concepts because it has been shown that it is an effective method for scoring well on tests in a short period of time. The side effect of this method is that in the long run, you retain next to nothing and your critical thinking skills are... well... non-existent.

I refuse to memorize even to this day because it's such a waste of time. People do it because humans love instant gratification. Memorize as much as you can, and score decent on tests (or sometimes good), but the long term effects are BAD! Kind of why people buy big new cars even if they can't afford it. Humans are addicted to instant gratification.

It's really ironic because new teacher's are taught NOT to do that... but told secretly to do it. And what's even more ironic, most new teacher's go through university learning using this memorize everything method. They finish university knowing nothing. Hence, this explains why most teachers in elementary and high school know very little of the topic they are actually teaching. True facts.

Memorization is critical in any field. Try passing a graduate level qualifying exam in electrodynamics without memorizing Maxwell's equations. It's impossible.
 
  • #15
I find that simply reading and listening to lectures is the most difficult way to learn concepts. Even taking notes seems to only help with the memorization aspect (though I agree that memorization serves an important, if secondary purpose).

The best way to learn, in my experience, is by actively engaging questions. That's basically the role of problem sets in textbooks: you don't fully understand something until you can apply it (actually, you don't fully understand it until you can teach it).

Nevertheless, it is sometimes necessary to memorize something even when that is not ideal (just to pass a test, maybe). But it is still important, I think, to struggle with the concept first. If you come away with some vague understanding of why something works the way it does, you'll be better off and have a better chance of understanding it the next time you come across it.
 
  • #16
TVP45 said:
If you get the chance, look into the Indian university (college?) system. It appears to be two-tiered, with those in the upper tier getting a broad, well-grounded education while those in the lower tier (there's a name for this tier but I can't recall or find it) memorize and regurgitate lots of facts. The end result is graduates who understand few of the essentials about their fields and that appears to be severely limiting India's industrialization efforts.

I feel sad that it is true. But there are no tiers here, its same all the way. Students are taught to secure marks, by hook or by crook, in the end, only marks matter. This tendency goes beyond any control by the time student reaches class XII. I dunno, its sort of inbuilt in us.
Memorizing is the best way to score, no doubt. But it isn't the right way.

Sadly I have gone through the system & its depressing, my college ranks 8th in engineering college rankings in India. The only exam in India which has the ability to separate the best from nearly best, is the IIT-JEE, & that too because it asks physics questions from irodov's physics text. And sadly, students here don't prefer going to that extent & rely heavily on tuition(mugging) for such exams.
 
  • #17
Brian_C said:
Memorization is critical in any field. Try passing a graduate level qualifying exam in electrodynamics without memorizing Maxwell's equations. It's impossible.

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
 
  • #18
Chi Meson said:
Memorization has its place. For example, all need to begin somewhere when a new concept is learned. THe concept of energy for example is highly complex, but it needs to begin with the acceptance of a conventional definition, "the ability to do work." Immediately after that, the concept drifts from the simple definition with tautologies (the definition of work? it's "the mechanical transfer of energy." and what's energy?...") and paradoxes ("The energy that is unavailable for work, etc).

The full concept is only learned after the superficial accepted facts and definitions are set in place, and then those facts and definitions get pushed around through critical thinking and experiencing varied examples.

One way of encouraging "going deeper" is to take any memorized definition, and ask why? or how? Go to any memorized law of physics and then look at any phenomenon and connect the two: How is a volcanic eruption consistent with the second law of thermodynamics? Apply gauss' laws to the operation of a magnetic tape player.

It is very difficult to apply things to a law if you do not remember what the law says. The act of "memorization" seems to be an act of futility, while simply "remembering the important stuff" is a necessity.

What's the difference? sometimes it's hard to say. As a high school teacher, I try to avoid the command "memorize" when giving assignments to students. I do however make it a point that they MUST remember that the word "spontaneous" makes or breaks the 2nd law. THe exact wording is not important, but the law itself is very important.

I have heard it 1000 times. There are N(N tends to alot) things which are to be memorized, eg whatever you said in the post. But the point is not at all about those things, students mostly drag this opportunity to memorize to topics which are meant to be understood deeply.
 
  • #19
Although I think I know what your folks mean (ank_gl and Jason specifically) when you say you don't "memorize," but you simply can't get anywhere if you don't remember anything. No equation can be derived if you don't start from an initial set of memorized equations. The point you are making, I believe, is that you don't bother with the laborious process of memorization (flash cards, hours of repetition, etc.)

Some folks have an advantage in that area. As I said before, you can't get far unless a "toolbox" of fundamental facts are well within you mental grasp, and some people simply remember stuff without "memorization."

In education, I have one strong opinion: there is no one method of learning. WHenever educational systems try to endorse a single method (phonics vs whole language for example), the end result is unsuccessful.

While the act of memorization as a sole method of learning is (as we all agree) is erroneous if not damaging, the contrary position of demanding that nothing ever be memorized is just as erroneous (yet not as damaging).

As I am teaching an unit in Energy and Thermodynamics right now, I am demanding that my students know the definitions of the key words, and what the Laws say. IF I only et it alone ant that, then I would be a poor teacher indeed.

But when I ask them on a test, next wednesday to consider a scenario where a ball jumps up into the air after receiving a blast of heat and noise, I expect them to explain which law was violated, and of course, why. IF they don't know what each law says, they will not be able to take the next step of using it to analyze the scenario.

In the obvious comparison of learning an new language, please do not tell me that you can do so without memorizing new words. IF you learn by "total immersion," then you might not be aware of the act of the memorization process, but it will happen passively. I can say , however, from when I learned to speak German, the words that I can recall to this day (20 years later) are those words that I actively memorized (flash cards, etc). The vocab that I picked up passively seemed to be the first to go with disuse.

Summary: memorization has it's place. It should not be the dominant part of learning anything, but should not be eschewed in a reactionary response to the evils of overdependence on memorization.

Side note: I had a student in my AP class last year. 'Twas a sad case. THis student had obviously been getting excellent grades due to brute memorization. Then as a high school senior in an advanced physics class, when they finally got questions where the answer was not in the textbook, they would simply start writing something. The answers would be true, and full of details, and nearly perfectly word for word right out of the book, but it was totally wrong as an answer to the question. This student hated, hated, hated me for the first half of the year. By the end of the year, I think I walked on water in their eyes.

Pedagogic metaphor time:
What good is a library without books on the shelf? What good are the books if you don't read them? Why bother reading them If you don't write one yourself? (Someone else came up with that one.)
 
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  • #20
ank_gl said:
I have heard it 1000 times. There are N(N tends to alot) things which are to be memorized, eg whatever you said in the post. But the point is not at all about those things, students mostly drag this opportunity to memorize to topics which are meant to be understood deeply.

One cannot memorize "deep understanding." That is futile, i think we agree. Definitions, laws, models, examples, and (in our topic) schematics of famous experiments should be "on recall" in the memories of those going forth in their field. If this requires active memorization, so be it. Yet one must not allow that to be more than the initial step in "deep understanding."

If you are successful in your field without ever "memorizing anything," then you are lucky to be gifted with a keen memory. If your analytic skills are matched with your recall, then you will go farther than most other people would be capable. That is as it should be.
 
  • #21
Of course you can't get anywhere memorizing nothing. Hence, in mathematics, you have to memorize a lot. You have to know what compactness is, what paracompact is, what a number field is and so on.

Sometimes you have to memorize the trick to a proof.

But it's important to understand the trick and how it makes things work. Not to memorize the entire proof itself. That's not necessary.
 
  • #22
JasonRox said:
You are taught to memorize concepts because it has been shown that it is an effective method for scoring well on tests in a short period of time...
My mother saw this when she supervised student teaching (She was a Prof. of Ed.) It frustrated the teachers who knew it was wrong but had no choice but to spend nearly half the school year drilling for standardized tests. This is one of the reasons the average teacher changes professions after five years. Pay is important but most of those who go into education do so for the love of it. The current public system quickly turns that love to hate.

The root of the problem is publicly funded education which demands objective standards of quality assessment. The only form one can use is standardized tests. This sounds fine but one must remember the classroom is not a factory assembly line and children are not engine blocks upon which one can apply objective quality control.

Rather the mind is a process and the paradigm for good education is the professional educator. The teacher doesn't "work on" students he interacts with them and guides them. Similarly the teacher should be assessed and trained by senior peers and professionally trained principles and superintendents who interact with him and guide him in his professional development.

Originally standardized tests were a tool for the educator to spot areas needing remediation or unusual talents needing special attention. Now this has been turned on its head and the tests are used to evaluate the teacher's and school's effectiveness. The teacher must drill the student in the tests for the sake of school funding and national scores.

I think it comes down to the object vs. process paradigms a la A. N. Whitehead. (Also an issue in classical vs. quantum physics.) You can't describe the goal of a well educated child solely in objective terms. It must be a case by case judgment made by professionally trained educator and interested parent.

Consider the parallel with medicine. You don't want doctors trying to get your vital signs to conform to a scorecard of standardized values. You want the doctor to diagnose, treat, and re-evaluate in a perpetual cycle to promote health as guided by his professional judgement and experience. The doctor interacts with his patient seeing if one method of treatment is effective and then reassessing either the method of treatment or his diagnosis as he judges the patients response. He uses tests as a tool to diagnose and assess treatment.

Now consider what will happen to the profession of medicine if we socialize it, centrally fund it, and demand objective number standards to evaluate the quality of our physicians. Will we find doctors trying to get their numbers up rather than getting their patients well? Will surgeons decide not to operate on older patients and more profoundly ill since this will affect their statistics? Will hospitals implicitly encourage misdiagnosis so that they can get more funding or so that the patient can qualify for procedures which they need but which doesn't fit the centrally dictated standards? (Consider the explosion of "learning disorders" in our schools.)

I shudder to think where we are heading in both our education system and our medical system if the current trends continue. I say if we must fund these through taxes (a separate argument) then we need to put the choices back in the hands of those with an immediate interest in the quality of the outcome. The patient in the case of medicine and the parent in the case of education. As to curriculum and methodology that choice should be placed back in the hands of the educator whom then answers to the parent.

There can be no freedom without the freedom to make the wrong choices and there can be no improvement in the quality of education unless this freedom (and responsibility) is returned to the parent and educator.

Why the political left opposes vouchers can only be that they fear loosing control over what is taught and how...which is exactly what needs to happen. For quality to prevail that control needs to be in the hands of the parents.

(And there is no more a Separation of Church and State issue with church based schools than there are when a person on welfare puts a few dollars in the church offering because it is the individual not the state making that choice.
[EDIT: Did a little digging and it seems that the Supreme Court agrees with me on this point.]
)
 
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  • #23
Chi Meson said:
One cannot memorize "deep understanding." That is futile, i think we agree. Definitions, laws, models, examples, and (in our topic) schematics of famous experiments should be "on recall" in the memories of those going forth in their field. If this requires active memorization, so be it. Yet one must not allow that to be more than the initial step in "deep understanding."

If you are successful in your field without ever "memorizing anything," then you are lucky to be gifted with a keen memory. If your analytic skills are matched with your recall, then you will go farther than most other people would be capable. That is as it should be.

I love this statement. Is there a way to develop your analytical thought processes to match your recall ability?
 
  • #24
se7en said:
I love this statement. Is there a way to develop your analytical thought processes to match your recall ability?
I think everyone can do it, if there are no time limits in the exam.
 
  • #25
se7en said:
I love this statement. Is there a way to develop your analytical thought processes to match your recall ability?

Of course, the brain isn't hard wired, you can train it to do what every you like, blah, blah, blah. Why people end up resigning themselves to whatever there insecurities tell them is there ultimate smartness is beyond me. Hell if you're smart and you try to make up for your shortcomings, and even if your not, you can get smarter. Intelligence isn't set in stone, it never has been, and IQ tests are a joke. You can get further than anyone else, even if you aren't the sharpest most memory able, most creative most eh.. Why bother society makes labels of us all, try listening to this low IQ jerk.



Pfft this guy doesn't even have the IQ of the smartest people in the world, 127? I have a smarter IQ than that, but am I smarter than him, good God no.
 
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  • #26
127 is 'good enough'. Someone did the research and found that you can succeed in physics with IQ 120 --but you need to be able to get on with your supervisor. It's not what you know, but who you know (see Gladwell's latest book for details. Wassit called again: Outliers? Blah - wish my memory was better).
 
  • #27
I think an interesting way to harness your memorization capabilities for a greater understanding of a topic is to memorize the *explanations* that are given to you. E.g. work through a very intricate mathematical proof over and over again until you can reproduce it (and explain it as you go along). In the end you have technically just "memorized" something, but you will find that the process forced you to make a lot of the connections you are talking about.
 
  • #28
shaggymoods said:
I think an interesting way to harness your memorization capabilities for a greater understanding of a topic is to memorize the *explanations* that are given to you. E.g. work through a very intricate mathematical proof over and over again until you can reproduce it (and explain it as you go along). In the end you have technically just "memorized" something, but you will find that the process forced you to make a lot of the connections you are talking about.
You are missing the point completely.

take an example, work is defined as the line integral of the force over the path.
Memorizing = knowing how to calculate integralF.dr(i don't know latex)
Understanding = knowing what is its geometrical & physical meaning.

Of course, one just knows some basic things, that isn't memorizing, that is applying as little basics to as large problem as possible. This is what all scientists tend to do, they tend to generalize things, so as all cases can be simply analyzed using one single theory(well not ONLY one theory, but some basic concepts & relations)
 
  • #29
There is room for both-memorization and derivation
 
  • #30
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.
 
  • #31
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.
 
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  • #32
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.
 
  • #33
rogerharris said:
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.
 
  • #34
shaggymoods said:
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.
 
  • #35
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...
 

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