How Do You Take Effective Notes When Learning Mathematics?

[jmjlt88]

I am curious about the note taking strategies implemented by others on this board. I am referring to notes taken while reading (as opposed to notes taken during a lecture). As I progress further in my studies, I am noticing that I learn the material best when my notes become somewhat of a textbook. For instance, I will first read the section in a cursory way, taking note of what seems at first glance to be the “big idea.” Then, I will work through the section carefully with pencil and paper; I will try to work out all the details and fill in all the gaps. Finally, I will start from beginning and handwrite a “textbook section” on the material to a hypothetical struggling student. This is a very time consuming process, and I doubt this approach would work well with a full course load; however, I hasten to add that the exercises at the end of the section have never seem so easy! I would love to read input from others concerning their note taking habits and strategies.

 

[micromass]

What you are describing is essentially the way I always study. It works very well for me. If I don't write extensive notes, then I understand it much less.

 

[halo31]

That is quite a time consuming way. What I do is skim the section first to get a good highlight of the section. Then I will reread the section this time but much more in depth. What really helps is stopping at every definition and theorem and to try proving it on your own (try to fiddle around for about 10-20 minutes with it). If you don't get anywhere then you can read part of the proof and try to finish the proof on your own. Then go to the problems and try to do most of them if not all of them (struggling on the ones you can't do is a good thing and if you don't get it don't beat your head against the wall. Just set the problem(s) aside and ponder about it in your free time. Eventually you will figure it out. ). Then a few days later go back to the same section and reprove the theorems and definitions. If you can then you have mastered the material.

 

[drizzle]

I used to do my own 'textbook' for major subjects in high school, math and science. This way not only helped me to understand the material well, but I also didn't have to study much for the exams. It was so concise yet informative, and it included all possible related matters so I won't have to get back to the book. They also were so precious to me that I couldn't throw away--eventually I did. However, it wasn't my method for college, as you said, it's time consuming. But i's a good way to establish a strong background for any discipline, especially for those who rely on self study.

 

[QuarkCharmer]

I used to do my own 'textbook' for major subjects in high school, math and science. This way not only helped me to understand the material well, but I also didn't have to study much for the exams. It was so concise yet informative, and it included all possible related matters so I won't have to get back to the book. They also were so precious to me that I couldn't throw away--eventually I did. However, it wasn't my method for college, as you said, it's time consuming. But i's a good way to establish a strong background for any discipline, especially for those who rely on self study.

This is also the Quarkcharmer method. I have dozens of notebooks which read like my own written textbook, omitting only information that I find obvious. It works great for me. I keep a scrap paper to work out problems or try something out as I am working through a text, then when I am satisfied that I understand the section I transcribe it into the notebook.

 

[hsetennis]

What you are describing is essentially the way I always study. It works very well for me. If I don't write extensive notes, then I understand it much less.

I absolutely agree that this works best. The specific structure of the notes varies depending on the type of class; however, the materials I use are the same:

- 0.7mm mechanical pencil, wide-ruled perforated 3-hole punched paper (best combination)
- dry-erase marker and whiteboard (or a window if I feel inspired )
*if I'm on the go, I keep a fine-tip marker and a sheet protector with a blank piece of paper as a makeshift dry-erase
- a well-tabulated 3-ring binder with pop-out folders to organize all my notes and homework

I first walk through each and every step of the textbook/video by working it out on my whiteboard, rather than scratch paper, because it's much easier to erase my work. If it's a solution-based course, then I essentially reproduce the examples that are worked out in the textbook. If it's a proof-based course, I write out every theorem and accompanying example but opt out of writing out the whole proof or just the details of the proof.

 

[meuphemia]

I agree; extensive notes are key for me too.

I have thought about getting a LiveScribe sort of pen that records my audio as I write. I can then upload my notes and have a digital copy which includes my explanations at key points. The only bad part is that LS itself requires the use of Evernote which wouldn't work for me, but when this is sorted it may help decrease the amount of writing!

 

[jbunniii]

"[Serge] Lang liked to say that the best way to learn a new topic is to write a book about it."

http://www.ams.org/notices/200605/fea-lang.pdf

(Of course, it was also said that "Serge Lang writes great books badly." )

 

[mfZero]

I've started doing this as well, but my notes are written in LaTeX instead of by hand.

That way I'll always have backups that are written nicely and neatly, not in my own sloppy handwriting.

 

[mickybob]

I am curious about the note taking strategies implemented by others on this board. I am referring to notes taken while reading (as opposed to notes taken during a lecture). As I progress further in my studies, I am noticing that I learn the material best when my notes become somewhat of a textbook. For instance, I will first read the section in a cursory way, taking note of what seems at first glance to be the “big idea.” Then, I will work through the section carefully with pencil and paper; I will try to work out all the details and fill in all the gaps. Finally, I will start from beginning and handwrite a “textbook section” on the material to a hypothetical struggling student. This is a very time consuming process, and I doubt this approach would work well with a full course load; however, I hasten to add that the exercises at the end of the section have never seem so easy! I would love to read input from others concerning their note taking habits and strategies.

I've always found that having to write or explain something to someone else is one good way of making sure you understand it.

Practicing solving problems is the other main way of doing it.

The worst way is just to read it.

If you're time-poor then I'd saying working on problems is the most time-efficient way of learning material - I've passed exams using only that technique in the past.

 

[espen180]

I always write extensive notes. In some courses I write them by hand, in other I typeset them in Latex. It depends on what kind of notes they are, whether they are written linearly or not, etc. This is very helpful especially when there is no single textbook that fits the whole course.

I wish I had time to clean up my notes and typeset them, but sadly I don't.