How important is mastery of course material?

[eddotman]

Hi everyone,

So, I'm currently in my second year (undergrad) of university studying nanoscience/physics in Canada. I try to think about my future career fairly often, so that I can do my best to make good decisions. However, I'm beginning to get the feeling that I'm not truly "mastering" the material that I learn in my physics courses. That terminology is vague, so I'll try to clarify what I mean.

Looking back at high school, I'm quite sure that I mastered the material in my math/physics courses. If someone walked up to me on the street and said, "Hey, do this integral of a high school-difficulty-level single-variable function" or "Solve this projectile motion problem," then I'd respond, "Yeah, no problem."

Now, with my university course material, although I'm doing fine in the courses (80s or 90s, so I can't really complain), I feel like if someone came up to me and asked the same type of textbook-style question, I might not be able to do it so easily. In other words, I feel like I'm sort of scraping by, even though my marks seem to say otherwise. I feel like I know the material, but I don't yet feel that it's truly internalized.

So, I guess my question is, is this an issue worth worrying over? Since physics is cumulative, do you think that by 3rd year, all of my second year material will feel internalized and I'll feel the same way about 3rd year courses (i.e. is this feeling I get just a result of newly-learned non-intuitive material)? And perhaps most importantly, would it benefit my career in the long run if I devoted a lot of time to solving as many textbook-style problems as possible (not necessarily to any benefit of my course mark), or would my time be better spent elsewhere?

 

[Acut]

It's impossible not to forget the details if you haven't used a particular knowledge for a long time.

Usually, I don't remember the precise formula, but I'm able to reconstruct it. Or, at least, I know what the guiding idea was.

Also, bear in mind that in real life, unlike tests, you can always look it up.

If I were in your shoes, I wouldn't be worried. But I would do the text problems anyways, since I tend to gain more insight or look things at a different angle when I do them a long time after I've seen the theory.

 

[Nano-Passion]

Well what physics and math classes do you have now?

I personally think an understanding of course material is very important. The general principles in math and physics are of course the most important because they are cumulative subjects. You need to have a good understanding of the math and physics in order to make a contribution of your field. Just look at what experiments/technology/experimental ideas that people have made. Things such as -http://www.youtube.com/watch?v=mA98ZBdkW0M - for example.

Above all though, I believe creativity is the most important, along with being able to visualize things. Personally, I sometimes ponder about the physics and math of having different technology and how I might construct it. Unfortunately though I don't have the resources nor expertise to pursue that, but its always a nice daydream.

One very important thing that you need to do is be creative to think of other things that would help in the field of nano science. You then need to have a pretty solid understanding of how things work or else your creativeness will be of waste. Often your creativeness can lead you astray, but its your knowledge that will keep it from going off on a tangent. Its importance is evident when you see rather creative people state that they found the "ultimate theory of everything."

If your creative and lacking knowledge, you will fail. But if you have both, then your potential is perpetual with respect to your knowledge. If you think about physics and math outside of college in everyday life/applications and think beyond.. then you might be on the right road.

 

[eddotman]

Well what physics and math classes do you have now?

I personally think an understanding of course material is very important. The general principles in math and physics are of course the most important because they are cumulative subjects. You need to have a good understanding of the math and physics in order to make a contribution of your field. Just look at what experiments/technology/experimental ideas that people have made. Things such as -http://www.youtube.com/watch?v=mA98ZBdkW0M - for example.

Above all though, I believe creativity is the most important, along with being able to visualize things. Personally, I sometimes ponder about the physics and math of having different technology and how I might construct it. Unfortunately though I don't have the resources nor expertise to pursue that, but its always a nice daydream.

One very important thing that you need to do is be creative to think of other things that would help in the field of nano science. You then need to have a pretty solid understanding of how things work or else your creativeness will be of waste. Often your creativeness can lead you astray, but its your knowledge that will keep it from going off on a tangent. Its importance is evident when you see rather creative people state that they found the "ultimate theory of everything."

My current classes for this year are as follows.

Semester 1:

Advanced Calculus 1
Mechanics 1
Electricity and Magnetism 1
Synthesis of Nanomaterials
Structure and Bonding
Linear Algebra 1

Semester 2:

Complex Analysis
Mechanics 2
Electricity & Magnetism 2
Analysis of Nanomaterials
Structure and Spectroscopy
Differential Equations 1


I agree that understanding the course material is important. I'm fairly confident that I understand the course material in all my courses, but I think there's a difference between merely understanding something and mastering it. By understanding my course material, I mean that I can get all the concepts, write the tests, do the assignments, etc. But I certainly can't do all the textbook problems with ease, nor can I say that all of the techniques taught in the course come to me instinctively yet. Basically, I'm wondering if it's important to try to push the rigour of my understanding beyond what my courses demand.

As for your points on creativity, well, I can't say that I know whether or not I'm creative, having no good way of measuring it.

 

[Nano-Passion]

My current classes for this year are as follows.

Semester 1:

Advanced Calculus 1
Mechanics 1
Electricity and Magnetism 1
Synthesis of Nanomaterials
Structure and Bonding
Linear Algebra 1

Semester 2:

Complex Analysis
Mechanics 2
Electricity & Magnetism 2
Analysis of Nanomaterials
Structure and Spectroscopy
Differential Equations 1I agree that understanding the course material is important. I'm fairly confident that I understand the course material in all my courses, but I think there's a difference between merely understanding something and mastering it. By understanding my course material, I mean that I can get all the concepts, write the tests, do the assignments, etc. But I certainly can't do all the textbook problems with ease, nor can I say that all of the techniques taught in the course come to me instinctively yet. Basically, I'm wondering if it's important to try to push the rigour of my understanding beyond what my courses demand.

As for your points on creativity, well, I can't say that I know whether or not I'm creative, having no good way of measuring it.

If you started thinking about how you would change some technology/ impact nano science today then I would call that creativity; regardless of whether your reasoning behind it was solid. The knowledge will come with time.

And mastering the material is pretty important. But one thing I hate about language is that its very vague, particularly adjectives! Mastering with respect to what? Right now I can do all the problems in my physics book with relative ease, and I would consider that mastering the material. But I don't attempt the "challenge problems" at the end of the chapter. If you can't do the very hard problems [again a relative term] then wouldn't say that you didn't master the material. If you can't do the standard 1-50 problem in the physics book then I would say there might be a loop in your understanding. Your responsibility is to fill all these holes. I don't want you to think that you should do the standard problems effortlessly, that doesn't mean anything else then that would indicate your not really learning. But if you are pretty comfortable with doing problems and fill in the holes of your understanding then I would say that you mastered the given material.

 

[nucl34rgg]

You have to be able to solve some problems cold, but it is rare for anyone to have "mastered" topics like E&M (upper division) fresh out of undergrad. Even professors who teach E&M have to think a little and refer back to things to solve some of the harder problems.

This doesn't apply to math. In a sense, math, or at least pure math, is one of the few areas where you should really make sure you fully get what's going on in a course before proceeding, since everything literally builds directly upon what you just learned.