If I spend my free time solving practice problems will I get the highest grades?

reree17

I enjoy solving practice problems for any subject, especially maths and physics. It's challenging for me and I like a challenge, I could solve practice problems for the rest of the day without a problem, morning until night, which some may think is weird. Anyway, I hate reading textbooks in general. I retain information from it pretty quickly, but I always struggled applying the information to questions. So some suggested I do more practice problems. I tried some out and I really like doing them, be it from the textbook, online, past papers etc. When I get answers wrong, I go back to the question, observe what went wrong, then solve it again to get the right answer. It has really helped.

Currently I get good grades, but I'm not getting as high as I would like to. (Mostly A's, 1 B, some A*'s), I'm aiming for mostly A*'s. I feel that what was holding me back from achieving this was my inability to apply knowledge to questions and new situations even when I have a very good memory.

So So say I have 14 hours of free time on weekends, if I spent maybe two hours on the Internet, two hours watching tv, two/three hours in total looking at the textbook for a bit of background knowledge and to learn how to do new questions, then 6 hours doing practice questions. Then on school days, 2 hours of practice questions. Do you think this is a good idea and do you think following this I will be on track to get mostly A*'s, or even all A*'s? Thanks!

(I will give myself some days off of course to relax. And before you suggest me going outside, I do already lol. I'm just very interested in my studies, that's all.)

QuarkCharmer

It certainly is a true statement that practice makes perfect, but I think another important aspect in doing well is understanding the concepts behind the material. I like to make sure that I understand how to solve a problem, the concepts in work behind solving it, and then I take to the practice problems.

A thing that I have noticed about book/course questions, is that alot of times they are the same as the homework questions or other examples, and practicing all of the "types" of questions you may encounter only goes so far. It's best to know the logic behind the questions rather than just being able to rapidly solve the same problems with slightly different variables.

clope023

Perfect practice makes perfect, bad practice just makes you good at doing the same bad thing.

I disagree very strongly with this notion that putting effort into solving problems only makes you good at regurgitating the algorithm required to come up with the answer, understanding why steps were taken and the concepts behind those steps while solving the problem often leads to better insights into the material as a whole.

bcrowell

Just watch out that you don't shortchange your conceptual understanding. In physics, there is a phenomenon that is well documented in the pedagogical literature, which is that conceptual understanding is often only very loosely correlated with problem-solving ability.

DrummingAtom

Can you please explain this more?

The reason I ask is because it happened to me last semester. I could rip through difficult problems on the homework and tests but then the conceptual multiple choice questions on the test crushed me. I rarely felt that I plug and chugged through problems either. I would even derive the equations on my own and felt very comfortable with using math as the language. But then on the test a question that I remember well was "What does the acceleration graph of a ball falling from a ledge and bouncing on the ground look like?" would trip me up.

Throughout the semester I did get better at the conceptual part but it didn't really feel like I was doing any "work" when I practiced those problems which was why I neglected them early on.

Sorry if this sounds naive, but in the upper level physics classes is the conceptual part stressed more or less than the intro classes? I've talked to some upper class physics majors and they seem to say that they get lost in the math so much that the conceptual part becomes even more confusing. That worries me a bit because I want a strong foundation when I start those classes. Thanks for any help.

zif.

Practice always helps.


Now some advice for choosing which problems to practice...

Start by skimming through the questions you're choosing from. Make note of which ones you feel good about and know how to solve.

You won't be practicing those ones.


I don't remember who pointed it out to me, but it really blew my mind when I realized I was avoiding studying the questions I had trouble with. I'd just spend a couple hours working through problems that I enjoyed and then considered it good study time.

reree17

Sorry for late reply. Thanks for help all. But how exactly does one understand difficult concepts? I've tried applying to reality and visualizing, looking for answers within textbooks etc. nothing helps.

Klockan3

It is hard to say, if there was a direct answer then it would be applied to education all over the world already. The only thing I can say is that it helps thinking about the concepts for a long time. Reading a textbook doesn't give you understanding, neither do solving problems. What gives understanding is thinking and thinking alone. Of course in order to think you need a basis to start from which is why you might read the book or solve some problems, but you need to remember to think about what everything does and what everything means when you read/solve or it wont build any understanding.

And you can solve problems without thinking things through, that is how this happens:
What you guys need to remember though that students have no clue about which ways teaches them the most efficient. Instead they study in ways which makes them feel like they accomplish things. In reality sitting and thinking about a concept for an hour might give much more than solving 2 problems, but it always feels better to solve those two problems instead.

clope023

God, you love that excluded middle.

Klockan3

The point isn't that things like solving problems wont help your understanding, the point is that it is easy to solve problems without garnering any understanding from it. If we take your post before this one, we see that you agree with this notion:
Now, people who solve problems and still don't understand obviously needs another approach. I'd say that the biggest hindrance for understanding is that people refuse to think, they fall into doing mindless churning since that is easier and more reliable. For those cases I try to get them to take a step back, take a deep breath and start thinking about what they actually do without being distracted by any problem.

Frion

That's a gross oversimplification. People at every level struggle with problems. Do you mean to say that all the professional mathematicians who are stumped by this or that problem simply refuse to think? You're taking a big leap by claiming to understand the state of mind of others.

People struggle to solve problems for various reasons. Some people simply don't have a sufficiently clear recall of the relevant equations. If a student forgot Taylor's Remainder Theorem, he would be in the worst position to realize its relevance to the problem he is struggling with. At other times it has to do with a subtle misunderstanding of the problem statement. One example is symbolic confusion which often happens to beginning math students (common one is confusing set with n-tuple). At other times it's a lack in fundamentals. A student who calculated the wrong eigenvalues might miss out on an key observation needed to solve the next stage of the problem.

It is not even clear what understanding is. Do you clearly perceive the meaning of what you're doing because you've 'understood' it or because you've gotten used to it? How can any person reliably free himself of hindsight bias?

Klockan3

I didn't say anything that goes against the notion that everyone struggles with problems, nor did I state anywhere that I had this ultimate solution which would make everything easy.
This however is a valid retort, yes "understanding" is a very fuzzy concept which cannot be properly defined. If I could state exactly what "understanding" is then people would be cramming it already. I would say that the more concepts you have properly associated with a given concept the better you understand said concept. Doesn't have to be concepts you learned at school but different things learned during your immense amount of time in this world.

You don't build many such connections by any other means than thinking for yourself, the books and problems aren't tailored for how you see things and for your knowledge. Instead they are made for some fictive student who don't know anything but what was taught in the prerequisites and who thinks like the author of the book.

This is something which is impossible to do away with completely, you can only mitigate it to an extent. I would argue that doing countless practice problems only makes it worse, you garner familiarity without making many new connections. In my experience it isn't those who do the most problems who have the best understanding instead it is those who do a minimal amount of problems and still do well. If you understand the concepts then you would also realize that you don't have to do that many problems since most of them are roughly the same anyway.

Geezer

Really? I don't think I've ever heard that before. I was always under the impression that the more problems you do, the deeper your conceptual understanding becomes; that is, with each little "twist" or change to a problem type comes a test to see if you can understand how to deal with the new information/constraint.

Klockan3

Look at this and 15 minutes forward from this point:
http://www.youtube.com/watch?feature...Pj8GgI#t=1686s

The deal is that you get a better understanding on how to solve problems the more you solve problems but how good you are at solving problems doesn't say much about how well you really understand the concepts. The reverse isn't true however, if you are good with the conceptual understanding you are also quite good at the problem solving bit, people who say that they understood but flunked since they are bad problem solvers are in almost every case just overestimating their own understanding.

Geezer

Thanks for the link.

I watched the entirety of Dr. Mazur's talk. Very interesting, very illuminating. I'm glad I took the time to watch it all.