Are you struggling to learn? Let's discuss effective learning strategies.

[kant]

I don t know how other people do it, but i hate it. That is why i created this thread for me( perhaps people like me). I want to know your way to approach a book. do you like to question every sentence. do you try patiently to wait out every problem. do you try to work on the problem before working on the concepts? understand something means able to clearfy that something in your mind that goes not longer than a couple of sentences. It is to me the ultimate data compression algorithem. This sort of reminded me of how zen master do their mediation, or how chess master play cless. That is why i am interested in how people learn.

 

[brewnog]

I think your first question provides some insight into your problem; you parallel studying with learning. I've never really been able to learn just by sitting in a room with some books. I have to go and actually do something, either a lab or some simple experiments or even just trying to work through something myself. After 10 minutes in front of a book my brain is asleep.

Just try to find other ways to learn. I realize that some of your learning must come from textbooks, but try to see these as supplements to your learning, rather than the source and teacher.

 

[Azael]

I learn nothing from just reading a textbook. Especialy when its very mathematical. I just can not grasp that from reading alone. I have tried to very patiently read the chapter over and over to grasp it. But sometimes I can be stuck on a part of a page for a hour trying to understand what the hell they want to get across. My struggles with my one variable calculus textbook was epic.

Im like brewnog, after a few minutes of that I am struggling not to fall asleep. I learn nothing and end up frustrated and feeling retarded.

That is just a horrible waste of time for me, so nowdays I always get to work on the problems first thing after the lecture and check back to the relevant parts of the chapter/lecture notes when needed and when I am done with all the problems I read the chapter again if I have time. I usualy notice that after solving the problems I can grasp the chapter easily.

So I guess you could say that I start with the problem and end with the understanding :)

If I fail to grasp something despite all that I usualy try to look it up in different textbooks or ask my professor to try and explain it to me from a different point of view instead.

 

[reilly]

Even genius types have to work hard to learn. When I taught freshman physics at Tufts, I first told students to toss out their yellow marker pens. For most, learning requires a very direct, active approach. In particular, I suggested that students write out, while reading a text or lecture notes, what they think important in a notebook. Then go back and condense your first round of notes. That is, write your own textbook if you will. I learned this as a student, and passed it on as a professor.

Indeed, initially it is a great deal of work, but over time it becomes easier and easier. And, this approach means you'll have a relativiely easy time preparing for finals. Most of my students who tried this, found it to be very effective in all their courses, often going from being a C student to an A student.

And, always, ask questions in class. And, do the homework, do the homework, do the homework. ...

Best of luck,
Reilly Atkinson

 

[leright]

A lot of people claim that reading physics ans engineering books is very difficult and you cannot clearly and deeply understand what is being talked about, and it is true when one first starts out. But after practising reading such books it becomes easier to understand what is being talked about. Like everything, practice makes perfect.

I think it is very important for a person to thoroughly read the textbook (every page, and maybe twice for every page), and not simply rely on lectures and lecture notes.

 

[ircdan]

Math books have the property that the more you read them, the easier they become to read. When you read a math book, have a pencil next to you with paper, right down the definitions, think about what they mean as you right them down. Write down the theorems, the examples. If you feel like it try to prove the theorems without reading the proof in the book. If you don't feel like doing this, it's ok, read the theorem, sketch out the proof, make sure you understand every step. Then, go back and reprove it without looking at the proof in the book.

When you get to the problems, try all of them. If you get stuck, try harder, look at the theorems in the section, is there anything you can use? Maybe some of the ideas used in the proofs of the theorems can be used again also. Maybe there's an example where a similar idea was used. If you still can't figure it out go to another problem. Once you've done all the problems you could do, go back and try to do the ones you couldn't do. If you're still stuck, get help elsewhere, another book, google, or here.


Math is hard. I remember struggling to read my intermediate algebra book(while in college!) but yet last semester I was able to read through "almost all" of the first 6 chapters of my complex analysis book. It just takes lots of work. Goodluck.

 

[FrogPad]

:)

Math is hard. I remember struggling to read my intermediate algebra book(while in college!) but yet last semester I was able to read through "almost all" of the first 6 chapters of my complex analysis book. It just takes lots of work. Goodluck.

I couldn't agree with that statement more. I'm in the exact same boat (almost, I started reading a complex analysis book... but I don't have the time for it right now :( )I have always slacked my way through school until recently. I finally got sick of getting C's and B's, and decided it was time to shape up and "kill" school. I now get VERY mad when I get a B, and this is how I do it.

1) Go to every class.
Just get it through your head that you will go to every class. You can tell yourself that you won't do anything when you get there. You can tell yourself that you will text message people while in class. You can tell yourself anything you want, BUT go to class. Now what ends up happening is, that once I get there I just end up paying attention and turning my phone off.

2) Do every homework assignment.
Don't skip one. Make sure you finish EVERY assigned problem.

3) Make a list of what you think is important and look at it daily.
I make a list of important things to memorize and post it on the back of my door. I end up seeing that list OVER and OVER again, so I just memorize it. This requires a VERY SMALL amount of work. I prefer to write formulas in dark pen on bright paper so that it really stands out.

4) DO NOT WASTE TIME.
This is VERY important. Do not spend an hour on a single problem that was meant to only take 10 minutes of your time. Skip it, and go get help. Ask a classmate, go to the tutor center, go talk to the professor, come on this forum.

I just make it a point to follow steps 1-4 and it hasn't failed me since I started doing it. It's interesting... but for me, if I do these things better habits naturally occur. For example. A consequence of following step 4 has caused me to stop studying in my room. If I try to study in my room I end up watching a movie, sleeping, having a beer, going out with friends, etc... instead if I go to the library and study, I get more bang for my buck. If people call I tell them I'm at school so I can't do things. I can't watch movies. If I sleep, I only sleep for 5 minutes before someone wakes me up. It just keeps me in check. So if you are strict about rules you impose on yourself, others naturaly occur.

 

[Spirit]

Kant,

I don't want to quote what FrogPad wrote. However; He is saying CRITICAL points.

Again, it is critical.

And a third time: It is critical.

Dont want to sound repititative for no usage. But it is the method that got me rescued. I thank God for the Favor of getting much better grades now.

I said rescued becuase I did get a shcolarship at a University here [I am undergraduate student from outside the U.S.] and was almost about to lose it due to a drop in my grades. I analyzed the situation, and found the points of FrogPad at the heart of the probelm. And now its going strong up now.

And i may add: Be realistic about distractions. I honestly found my own that listening to music sometimes while studying was reducing my concetration big time, and i consume more time on the same amount of material.

Further more, my Laptop was an enemy to my books. Specialy of the internet browser is open.

My friends were not helping me in this problem by pressing to go out. However, now i am trying to let them even undertand why when i say to one of them ' I don't think you should stay with us that much this night, and go study' that i am not crossing his personal area, but i am giving an honest advise to a friend for her/his best specially if there is an exam that may drop his grade by a letter of two.. or even a homework that may add up so some dear points needed for a letter grade that is more than a letter grade in the long run.

At last, remind yourself always why you are studying, and what will happened if you got the grades you don't want, and how it will effect your life inthe long and the short run, and people around you that you love.

Yes, motivation by emotion is a strong support for mind actions, and the morale in the battlefields throughouts history is a one clear example of many arounds.

 

[0rthodontist]

I disagree with FrogPad's #4 though the rest is good advice. If the problem was meant to take 10 minutes and I'm spending an hour, then I must have been spending the time learning how to do something that I didn't know how to do, which is productive.

 

[jmcgraw]

I really like ircdan's advice. That's very similar to the way I've learned to read math.

 

[gazzo]

I disagree with FrogPad's #4 though the rest is good advice. If the problem was meant to take 10 minutes and I'm spending an hour, then I must have been spending the time learning how to do something that I didn't know how to do, which is productive.

It depends on how you're spending that hour... are you staring blankly at the problem hoping for something to pop into your head, or are you dissecting it into smaller parts, attempting it from different angles, laying out a plan of attack?

Or, as Polya suggests, confer with the pillow! Or if you don't have time for a nap, take a quick break.

And for the OP, just start exploring, seeing what works for you. What about group study? Don't be afraid to write on your books (assuming they're yours), if it helps!

One of my lecturers has a book in his office, that looked as if it had been soaked, with paged stuck together and ink running. When probed he confessed, that he is at his mathematical best when he is in the shower!

 

[turbo]

Tackle your problems early. Do not leave them until the last minute or they will own you. Tackle them early, and if they are tough, sleep on them. If you are like me, you will have lucid moments between the time when you stir and the time when you are fully awake, in which solutions present themselves, almost unbidden. Don't crowd your sleep time - you need to be relaxed and unconcerned about "getting up on time" for this to be productive. It works. In college, I kept a notepad by my bed to jot down good ideas.

 

[kdinser]

Go straight to the problems and try to work a few without reading a single page of the text. Try to get a real sense of what the problem is asking you to do. If it uses any words or terms you are unfamiliar with, look them up. Try some things that you know. Can you create a diff eq, a derivative, an integral? Is there a formula you can derive? Have you encountered a similar problem before, but find that this one is lacking some information that was provided before? What information is missing? How could you find that information? Look up the answer (not the solution) and try to work backwards to find out how they arrived at it.

I usually do this for 1 to 2 hours before I try to read the chapter.

edit: typo

 

[interested_learner]

people learn different ways...

People learn different ways. Some are hands on. They don't get much from a lecture or books. They need to actually be doing something. These people are really good in the lab. Other people are visual / abstract. These people get a lot from reading math books, but maybe aren't as good in the lab. Others are verbal. They get a lot from lectures.

Although, most of the advice above is good, keep in mind that each of the above persons is probably a different kind of learner than you are. You have to experiment and do what works for yourself. However, whatever kind of learner you are, you have to work. There is no way around that. The more time you spend solving problems (whether by pencil, programs on the computer or in the lab), the more you will learn.

 

[0rthodontist]

One thing that I think is very good to do is think about how you would do problems even if you don't do them on paper--see if you can get the whole idea of the problem, perhaps minus some specific calculation, just mentally. Or if it's a purely calculational problem, trying to do the whole thing mentally. Being able to remember and keep track of all the steps of a problem helps you see better how other problems might be done, and makes you more aware of what you're doing than if you're just looking at the last line you wrote and trying to turn it into the next line.

 

[leright]

One thing that I think is very good to do is think about how you would do problems even if you don't do them on paper--see if you can get the whole idea of the problem, perhaps minus some specific calculation, just mentally. Or if it's a purely calculational problem, trying to do the whole thing mentally. Being able to remember and keep track of all the steps of a problem helps you see better how other problems might be done, and makes you more aware of what you're doing than if you're just looking at the last line you wrote and trying to turn it into the next line.

I agree. Sometimes, actually planning out the solution of a problem without doing it is even better than actually doing the problem on paper because it forces you to PLAN, instead of just work through steps, and it helps you see the big picture of the solution, rather than just the minor details (which tend to get in the way, even if they are trivial). Also, using this method, you can "do" more problems, and then more complicated problems, and ultimately you learn much more in the end than if you actually calculate try to the answers to all problems.

I agree that doing the problem on paper makes you worry about individual steps and you only think about the step you're on and maybe the next step...often, all steps before the step you're on are lost. However, when you do plan out how you solve the problem in your head you see the big picture of the approach better. Often, students in physics and engineering forget about the big picture, and problems are just a list of 'steps' and calculations, and this results in lack of understanding.

 

[mathwonk]

i like reading books now, but did not in college. what worked for me then was discussing the stuff with a friend who was at about the same level as me. this made it more fun, more efficient, and we kept each other awake, and broke time by eating english muffins or whatever.

 

[mathwonk]

basically the main point is however do not give up, keep working whatever it takes.

 

[leright]

i like reading books now, but did not in college. what worked for me then was discussing the stuff with a friend who was at about the same level as me. this made it more fun, more efficient, and we kept each other awake, and broke time by eating english muffins or whatever.

I dunno, I personally enjoy reading engineering, math, and physics books, and I am an undergraduate, but most ugrads despise it for some reason.

 

[mathwonk]

you, have an advantage leright, AS you cAn teach yourself if you enjoy reADING BOOKS.

 

[mathwonk]

even now i do not like reading research papers, but that keeps me back, as i am slow to learn new developments. i prefer discussing mathematics with people.

if you are like me try to set up seminars where you present papers to others so you have a motivation to read them. perhaps this fall I will set up an opportunity to read john morgans exposition of perelmans work on poincare conjecture.