Solving Physics Problems: 1 vs. 2

[gimak]

Which is a better way to do physics?

1) Do a complicated problem, spend hours and hours on that single problem until you solve it.

2) Try to do the complicated problem for 5-10 minutes; look at the answer and try to understand the answer for 5-10 more minutes. Then, move onto another problem?

Thanks,

(Not trolling, serious.)

 

[Vanadium 50]

Which is a better way to learn to lift weights?

1) Lift weights
2) Watch someone else lift weights?

 

[Phycisists]

Which is a better way to learn to lift weights?

1) Lift weights
2) Watch someone else lift weights?

What if you observe how someone solve a problem, and then do it yourself? In that case looking at the answer and understanding the process itself. Is that good? Or does it remove the persons independence making it difficult for further learning?

 

[jtbell]

What if you observe how someone solve a problem, and then do it yourself? In that case looking at the answer and understanding the process itself. Is that good?

At the very beginning of learning a new topic, I would say yes. That's why textbooks have worked examples, and why lecturers do examples in class and explain their methods. But you need to move to the point of independence as soon as you can.

At some point you have to take the training wheels off your bicycle, so to speak.

 

[gimak]

replying

Ok guys,

Thanks for your posts! The reasons is I sometimes spend 2-3 hours on a single problem (in physics 1: classical mechanics). I sometimes think that those hours are wasted b/c I've heard spending hours and hours on a single problem is time gone down the drain. Based on my own personality, I think that I should spend 15-20 minutes thinking INTENSELY on a single problem, then move on if I can't solve it. Then, a couple of hours later I can come back to it.

I guess the key point here is to do enough problems until you don't need the solutions to those problems anymore and that you've totally mastered the topic.

Let me know what you think.

 

[micromass]

Ok guys,

Thanks for your posts! The reasons is I sometimes spend 2-3 hours on a single problem (in physics 1: classical mechanics). I sometimes think that those hours are wasted b/c I've heard spending hours and hours on a single problem is time gone down the drain. Based on my own personality, I think that I should spend 15-20 minutes thinking INTENSELY on a single problem, then move on if I can't solve it. Then, a couple of hours later I can come back to it.

Thinking 2-3 hours on a difficult problem is pretty normal and you'll have to get used to this. It's definitely not wasted time, you learn more than you think. Of course, if the problems are meant to be simple and you're doing 2-3 hours on them, then that's not a very good sign. Maybe you didn't understand the theory well enough then.

I basically agree with jtbell. When you first learn a topic, watch how other people approach the problems in order to be comfortable with the basic techniques. But you should rapidly start attempting to do things on your own.

I guess the key point here is to do enough problems until you don't need the solutions to those problems anymore and that you've totally mastered the topic.

This might not be totally relevant here. But I think nobody has ever totally mastered a topic. There's always more to learn.

 

[gimak]

response

Which is a better way to learn to lift weights?

1) Lift weights
2) Watch someone else lift weights?

I guess you need to watch someone life weights to learn the technique. However, at some point you have to lift weights. I guess you need both, but mostly #1.

I am doing #1. However, my question is which is the correct way to do #1. Is spending hours and hours on a single problem time wasted? What do you think of my new method?

 

[micromass]

I guess you need to watch someone life weights to learn the technique. However, at some point you have to lift weights. I guess you need both, but mostly #1.

I am doing #1. However, my question is which is the correct way to do #1. Is spending hours and hours on a single problem time wasted? What do you think of my new method?

It depends. The weight lifting analogy is really spot on because there are many bad and harmful ways to lift weights. In the same way, there are bad ways of thinking about and solving physics problems.

Usually, when somebody lifts weights, they will have some kind of trainer and coach at first who will see whether they are not doing too much or too little and who will give all kinds of advice. I think the same should happen with doing physics and math. Somebody should see if you're approaching the problems the right way, whether you're not doing too much, and other stuff.

 

[porcupine137]

Which is a better way to do physics?

1) Do a complicated problem, spend hours and hours on that single problem until you solve it.

2) Try to do the complicated problem for 5-10 minutes; look at the answer and try to understand the answer for 5-10 more minutes. Then, move onto another problem?

Thanks,

(Not trolling, serious.)

1. spend a decent amount of time, if need be give up and go to some other problems, then return to the problem problem and try again, if need be look at answer and try to understand it (but beware falling into the trap of going there too quickly, too often, do the hours and hours thing at least here and there if need be, but OTOH you can't totally bog down, not at first, so you have to make a careful balancing of it all, it can be a trap to just want to get it solved and waste forever on it and want it completed before moving on and it can be a trap to just turn to the answers too easily and too often.)

for physics 1 mechanics you probably don't want to be getting bogged down for 2-3 hours too often all the time, if that is happening for more than 0-2 per week that might be a sign that something is going wrong (unless it's some honors type intro physics class and they are giving out a number of really tough ones each week)

 

[porcupine137]

Ok guys,

Thanks for your posts! The reasons is I sometimes spend 2-3 hours on a single problem (in physics 1: classical mechanics). I sometimes think that those hours are wasted b/c I've heard spending hours and hours on a single problem is time gone down the drain. Based on my own personality, I think that I should spend 15-20 minutes thinking INTENSELY on a single problem, then move on if I can't solve it. Then, a couple of hours later I can come back to it.

I guess the key point here is to do enough problems until you don't need the solutions to those problems anymore and that you've totally mastered the topic.

Let me know what you think.

Yeah that sounds good and it's actually largely what I just suggested hah.

 

[porcupine137]

It depends a bit upon the problem too, sometimes they are just bogged down messes and spending forever one like that might be more of a waste of time in some situations. Or some little sub-part of a problem might not be the sort of thing to bother forever about.

And it depends upon the text used, some intro physics classes use texts where not all that many problems are 2-3 hour types, but some intro courses tend to offer deeper, more complex problems at times where it might be normal to have some problems take some thinking over for a while, quite possibly for hours. It might be that a problem or two each week is meant to take many people some hours. It might pay to see how long others are taking, etc.

 

[Lavabug]

I am surprised no one has brought up a third option: picking easier exercises appropriate for one's skill level. Allow me to stretch the weight lifting analogy even further: start with the empty barbell, make sure you can go through the motions properly, then progressively add weight to it... A masterful snatch and clean and jerk comes through years of practice.

You aren't going to solve a 3D rigid body dynamics problem with complicated geometries if you don't have hundreds of basic kinematics and statics problems under your belt, have solved for moments of inertia several times, etc. Getting stuck for hours on end on one problem without even being able to start it might signify you have some ground work to do. Take a step back, go back a chapter or even consult a more basic text and make sure you can handle the basics with proficiency. If you're taking something beyond intro physics, say thermodynamics, can you solve any problem on the topic pulled at random from your intro physics textbook? If not, work on that first.

I did lots of back tracking like this in undergrad (and probably will be doing more of it) and it was always tremendously useful.

Watching someone else solve a problem might help on occasion, but IME no two people think the same. You have to develop your own approaches to problem-solving through practice, trial and error, and fully undestanding why your wrong answer cannot make physical sense. Your skill can only improve.

 

[Jorriss]

Which is a better way to learn to lift weights?

1) Lift weights
2) Watch someone else lift weights?

This is a great analogy because clearly one would do 2) (in conjunction with a person who is experienced) first in order to learn to lift weights or else they would risk injury! What kind of person would lift weights without watching it done first afterall?

 

[vela]

Thanks for your posts! The reasons is I sometimes spend 2-3 hours on a single problem (in physics 1: classical mechanics). I sometimes think that those hours are wasted b/c I've heard spending hours and hours on a single problem is time gone down the drain.

Is this an introductory physics course? It sounds like it since it's called Physics 1. If that's the case, then you are very likely wasting a lot of time if you're commonly spending 2 to 3 hours on a single problem. The problem, as I see it, is that you don't know how to learn effectively yet, so you spend a lot of time not really making any progress.

That doesn't mean that after 20 minutes, you should look at the solutions. What you need to do is figure out where you're getting stuck and how to fix that. Perhaps, as Lavabug suggests, you're simply not ready to tackle the complicated problem and need to do easier exercises to get the basics down. Maybe you need to read your textbook again. Now that you've thought about the problem, you might understand the significance of a passage in the text that you had overlooked before. Perhaps it would help to discuss the problem with a classmate. You need to do something to make more effective use of your time.

The reason referring to the solutions is often a bad idea is that it's very easy to convince yourself that you understand the material simply because the solutions made sense to you. Many times I've heard students say, "I didn't have time to do the homework, but I looked at the solutions and understood them," and then they do poorly on the exam. The only thing surprising is that the students were so naive to think that that was enough.

 

[mooncrater]

what i do-
read the solutions when you don't understand the problem...
but if you understand the problem try to solve it
but when you come across a point when you realize that all your weapons are worthless at the point of time ...
see the solutions.
this is what a great person said.( well, i said it)

 

[Choppy]

I'm not sure there's an absolute answer to a question like this that applies universally.

In my experience you have to chose a strategy. If you're happy with the results you get, keep doing it. If you're not, try something else.

Personally, I find I learn the most when I wrestle with questions. But there's also a law of diminishing returns that comes into effect. I don't have an infinite amount of time.

 

[Arsenic&Lace]

With regards to strategy 1, trying to work a problem until it is solved in one setting is very difficult if the problem is a serious one. It is much more efficient to begin the assignment as soon as possible and work each or most problems until you hit diminishing returns, then stop and do something else, perhaps returning to it later in the day or waiting until tomorrow. The brain is a physical system and takes a finite amount of time to absorb and get to grips with a problem.

Diminishing returns can be identified as the time when frustration really kicks in. When you can no longer remain calm and focused, something is wrong, and diminishing returns may be it (or something else, on occasion).

Strategy 2 will have consequences in the future, so avoid it.

 

[gimak]

With regards to strategy 1, trying to work a problem until it is solved in one setting is very difficult if the problem is a serious one. It is much more efficient to begin the assignment as soon as possible and work each or most problems until you hit diminishing returns, then stop and do something else, perhaps returning to it later in the day or waiting until tomorrow. The brain is a physical system and takes a finite amount of time to absorb and get to grips with a problem.

Diminishing returns can be identified as the time when frustration really kicks in. When you can no longer remain calm and focused, something is wrong, and diminishing returns may be it (or something else, on occasion).

Strategy 2 will have consequences in the future, so avoid it.

What this user said definitely resonated with me. Maybe I should look into the past to answer my questions. Years ago, I was doing mental math. I was trying to figure out how to multiply 23*67 in my head for instance. Recently I figured out that 23*67=(20+3)*(70-3). After years and years of doing mental math, I only recently figured it out.

Perhaps the solution lies in combining the two approaches mentioned above. I'll try the following method:

1) Spend 10-20 minutes on a problem.
2) Go on to the next problem. However, I'll try sleeping on the problem for a day or two and reading various book excerpts to look at the problem in various ways.
3) If I still can't solve the problem, only then will I look at the solutions.

I think that this method will fit very well with my nature. I naturally like thinking about how things work. This method is a conglomeration of different advice in different posts. Thanks!

 

[Fredrik]

Over the years I have come to disagree with the view that it's a good idea to spend ridiculous amounts of time on most of the problems that you're unable to solve quickly. You should obviously work out some hard problems for yourself once in a while, but if you do this too much, you simply won't be able to get through the amount of material that you're studying in a reasonable amount of time.

You will certainly learn something valuable when you solve a hard problem for yourself, but you will also lose time that you could have used to learn something new. So I don't think it's a great idea to spend too much time being "stuck".

 

[AlephZero]

Over the years I have come to disagree with the view that it's a good idea to spend ridiculous amounts of time on most of the problems that you're unable to solve quickly.

I agree. Spending "hours and hours" achieving nothing on a problem that should take a few minutes maximum is wasting your time. In that situation, the thing you need to learn is how to figure out why you are stuck, and then how to overcome that general difficulty, not just look at the answer for that particular problem.

For example if the problem is math proof and you "can't even get started", most likely either you don't know the definitions of the things you are given, or you don't understand what you are meant to prove. Staring at a blank piece of paper for "hours and hours" won't fix those problems. And you are more likely to learn something that is generally useful by reviewing a section of your textbook, rather than just looking up the answer to that particular problem.

 

[ZombieFeynman]

I agree with most of the responses in this thread. My advice that I give students when teaching intro physics is to:

1. Review class notes
2. Carefully read the book, taking additional notes alongside.
3. Work the example problems in the book with the book open.
4. Attempt to do the problems in the book which have answers in the back. Allow yourself to refer to the book and your notes if you need to look something up. Check your answers after you attempt the problem, but not before.
5. Work the problems in the book without answers in the back. Only use resources you'd have available in a test environment, such as an equation sheet.
6. Attempt to make up your own problems and then solve them.

I don't think it's possible for someone who has the prerequisite knowledge for a class to consistently study this way and not do well.

When I was an undergraduate, I didn't always study this way, but when I did I always got As.

 

[Arsenic&Lace]

Over the years I have come to disagree with the view that it's a good idea to spend ridiculous amounts of time on most of the problems that you're unable to solve quickly. You should obviously work out some hard problems for yourself once in a while, but if you do this too much, you simply won't be able to get through the amount of material that you're studying in a reasonable amount of time.

You will certainly learn something valuable when you solve a hard problem for yourself, but you will also lose time that you could have used to learn something new. So I don't think it's a great idea to spend too much time being "stuck".

I more or less agree with this. The danger comes from devoting too much time to a hard problem at the expense of other problems.

However I think with relatively minimal expenditure one can spend a bit of time here and there on various projects and yet still maintain reasonable productivity. Devoting a bit of time every now and then to hard problems and solving them over a much longer time scale than easier problems is probably good for you. But the dividends paid by instead spending this time on research are significantly greater, so as an individual becomes much busier it is likely, as you state, not a very useful usage of time.

More problematically, I think that solving a serious problem can be modeled by surpassing an energy barrier; the more difficult the problem, the steeper the barriers, and therefore there is a lower bound on how much effort can be put into a problem without it being completely futile. Another inference one can make from this "model" is that a problem needs to be continually attended or it will roll back and progress will be lost (I have certainly had the problem where I return to a challenge after a period of time and need to reinvent the wheel because I have forgotten what I was doing).