Could you help me about my mathematics note-taking skill?

[bacte2013]

Dear Physics Forum friends,

I am a rising college junior in US with a major in mathematics. I recently noticed a problem in my note-taking skill in the mathematics, both from the textbooks and lectures. When I was a microbiology major, I wrote extensive amount of notes from my books and lectures since I had to memorize all of them. I followed this trend and took extensive notes from my math books and professors' lectures. The problem with my note-taking skill is that I basically copy down almost everything from my books. For example, I am currently studying Apostol's Mathematical Analysis; what I am doing is that I copy down the theorems, proofs (including my footnotes), authors's remarks & motivation, and examples. I tried to copy them on my own words, but the result is that I basically copy down verbatim with little change in the grammars. I started to realized that I should not take such exhaustive notes since the textbooks contain exact materials from my notebooks, but I cannot overcome the feeling that I need to make my own version of books, by taking notes from them, and the fear of memory loss. Also I tried to take as much notes as possible from the professors's lectures. What I realized is that I copy down the exact words from my professors, and I often lost the concentration to focus on lectures and absorb the materials. I also lost my concentration whenever I take the notes from my books since I need to divert my attention from books to notebooks.

I am currently thinking about various alternative strategies, which are followings:

1) Taking notes within the textbook using the blank space of books and the Post-It: Take notes about interesting remarks, confusion about the exposition and examples, and my own interesting ideas or approach to the proofs and examples.

2) Taking notes on a separate notebook but only copying the information from 1).

3) Do not take any notes and try to absorb the materials from the books: I noticed that I usually learn the best by reading. Use the lecture to supplement the textbook reading and to gain different perspective.

Could you help me out by commenting about my strategies and/or share your note-taking skills? I am quite embarrassed about my note-taking problem.

 

[axmls]

To me, there's no harm in copying (almost) everything the professor says or that's in the book. For many people, taking notes isn't about having something to study--the act of writing the things down helps entrench the information into your mind, even if you don't end up looking at the notes afterwards.

 

[DEvens]

All I can tell you for sure is, your number 1) is not a good plan. You will find it hard to learn that way, hard to study from such notes, and you will render your texts of zero value if you ever decide to sell them. And the half-life of a post-it note on a text is probably about 5 days.

There are several ideas about notes.

One idea, as axmls has suggested, is the physical process of taking notes helps impress the information on your brain. For many people the learning process is most efficient if you engage multiple information paths. If you listen to the lecture, look at what the prof puts on the board, and write it down, then the multiple pathways interacting tend to make a longer lasting more complete memory. At least for most people.

Another idea about notes is an efficient study aid. So you want to be sure to get the information from the classes that is not in the texts. Or that is presented differently. And you want to record it in a way you can personally understand quickly to remind you of the content you want for assignments and exams.

You can tweak this during your assignments. If your notes don't help you with assignments, try to figure out what is wrong with them. Too much detail? Not enough? The wrong kind of detail? Adjust your notes so they help with assignments. Adjust your note taking so that they help with mid-term exams. That will help you adjust so that your exam knowledge is as good as you can make it. When you get your marked assignments back, or your mid-term exams, look at them and look at your notes. What notes would it have helped to have when you were studying for that exam? What notes would have helped when you were doing that assignment?

Acting as a tape recorder is probably not efficient nor desirable. Probably you want to try to understand the lesson and record your understanding. And enough of the content of the class so you can quickly reconstruct your understanding later. Or record the points you DON"T understand so you can work to understand them later. Either by reading the text or asking the prof or the TA or your co-students for assistance.

The classes I worked the hardest on, because I needed to or because I enjoyed them the most, were the ones where I worked the hardest on my notes. I would make quick notes in class. Then I would recopy them neatly very soon after the class. I would add extra info to fill in the holes, maybe doing a few sample problems along the way to illustrate the issues. Maybe put a few page refs to things in the text. Sometimes I would even have two sets of notes, one for exam prep study and another for doing homework assignments.

 

[bacte2013]

To me, there's no harm in copying (almost) everything the professor says or that's in the book. For many people, taking notes isn't about having something to study--the act of writing the things down helps entrench the information into your mind, even if you don't end up looking at the notes afterwards.

That is very interesting point. I thought people write notes so they can keep the record which they can refer nicely than books...So the whole point is to aid the learning process rather than keeping a separate, referencing record.

 

[bacte2013]

All I can tell you for sure is, your number 1) is not a good plan. You will find it hard to learn that way, hard to study from such notes, and you will render your texts of zero value if you ever decide to sell them. And the half-life of a post-it note on a text is probably about 5 days.

There are several ideas about notes.

One idea, as axmls has suggested, is the physical process of taking notes helps impress the information on your brain. For many people the learning process is most efficient if you engage multiple information paths. If you listen to the lecture, look at what the prof puts on the board, and write it down, then the multiple pathways interacting tend to make a longer lasting more complete memory. At least for most people.

Another idea about notes is an efficient study aid. So you want to be sure to get the information from the classes that is not in the texts. Or that is presented differently. And you want to record it in a way you can personally understand quickly to remind you of the content you want for assignments and exams.

You can tweak this during your assignments. If your notes don't help you with assignments, try to figure out what is wrong with them. Too much detail? Not enough? The wrong kind of detail? Adjust your notes so they help with assignments. Adjust your note taking so that they help with mid-term exams. That will help you adjust so that your exam knowledge is as good as you can make it. When you get your marked assignments back, or your mid-term exams, look at them and look at your notes. What notes would it have helped to have when you were studying for that exam? What notes would have helped when you were doing that assignment?

Acting as a tape recorder is probably not efficient nor desirable. Probably you want to try to understand the lesson and record your understanding. And enough of the content of the class so you can quickly reconstruct your understanding later. Or record the points you DON"T understand so you can work to understand them later. Either by reading the text or asking the prof or the TA or your co-students for assistance.

The classes I worked the hardest on, because I needed to or because I enjoyed them the most, were the ones where I worked the hardest on my notes. I would make quick notes in class. Then I would recopy them neatly very soon after the class. I would add extra info to fill in the holes, maybe doing a few sample problems along the way to illustrate the issues. Maybe put a few page refs to things in the text. Sometimes I would even have two sets of notes, one for exam prep study and another for doing homework assignments.

Thank you very much for the detailed advice. I noticed that my math books contain just right amount of information, neither too verbose nor too concise. That characteristics made me to struggle in note taking since every materials presented in the books seem very important and non-trivial. The note-taking also has been interfering with my attempts to solve the problems since the time required for the note taking consumes most of my allocated time. I am actually considering mixing 1 and 3, focus on reading the books and hearing the lectures, and only copy down thematerials that are treated in different approach or perspective, interesting ideas, or other ideas that popped into my mind.