Saturday, September 05, 2009

How to Learn Math from the Book

It is only recently that I've been able to learn math from a textbook without enormous mental strain. Even a year ago, I don't think I could. And the difference isn't that I've gotten smarter in the past year - it's that I've had to read and understand such difficult material that, through sheer desperation, I learned how.

The key (for me) is to write down what the book says.

Seriously. If the book has a definition, write it. Axioms, copy them out. Theorems, reproduce them on your paper word for word. If there is a proof, write it out, trying to understand each line. (If you don't understand it, just copy it down anyway.)

This seems like it wouldn't work. If you don't understand something when you read it, how can copying it help? I think it's very simple - writing is slow, so it forces you to read the words over and over at a very slow rate.

What about the parts you still don't understand? Again, for me, writing is key. Write down your questions, confusions, and speculation. You may very well answer your questions as you write.

This won't help with math that is too advanced for you to possibly understand, but it's awesome for math that you would understand if someone explained it to you. Of course, it requires work, so no wonder it took me 34 years to figure out. (Yes, I never, ever took notes from a book until recently.)


Sally said...

This is part of the reason that going to math class often helps even if your instructor is sort of bad - going through the motions of writing the stuff down does help. (It does not help when your instructor is bad in the sense that he doesn't use the blackboard. I had one like that and it still boggles my mind.) I think this is also why your math teachers encourage you to work all the proofs, examples, etc., as you go through the book.

Tam said...

You had a math teacher who didn't write things on the board?! How is that possible? What did he/she do instead?

Sally said...

This was the infamously horrible stats class at Rice - the one in which the professor decided not to use a book either, despite a particular book and general syllabus having been standard for that class for years. His approach appeared to be to talk about things most people did not understand and then assign some problems that were quite beyond the material we were supposed to cover.