Efficiently Learning & Retaining Course Material

[Miike012]

The way I study is I read through the course book and while I read I write down everything that I feel is important, but this takes a lot of time and its not very effective.

Typically the things I will write down are:
1.Theorems
2.Proofs
3.Equations- and how they arrived at the equation
4.Graphs and pictures

To me learning the above info is important but I would like some advice. I know this question will have a different answer for every individual but what is the best way to learn and understand a subject and retain the information? I don't just want to retain it for test day I would like to develop an understanding of the material to where it is easily recalled years later.

Also should I not worry so much about writing all the information down and just read through the book then work the homework problems?

 

[espen180]

It sounds like you are studying mathematics. If so, just copying the book onto your notes will not teach you the material. As others have stated in previous threads, you have to be active in your learning. Question the material, think independently. When seeing a new theorem, questions you can ask yourself are for example:
-Is the converse true? If not, why? Can you find a counterexample? What conditions are needed (if any) to make the converse hold (if possible)?
-Why are the assumptions in the theorem neccesary? Can they be relaxed?
-Can you find an alternative (shorter?) proof?

There questions can be very hard depending on the subject matter, but you can answer them, you are well on your way towards an intimate understanding of the material. In short, more than taking notes or doing problems, you have to ponder the material!

 

[20Tauri]

If I could figure out how to retain information beyond the exams I'd have it made--as it is, I'm lucky if I remember the beginning of the class when I'm taking the final. I think doing lots of practice problems helps, but if you want to remember something, math is pretty much use it or lose it. If you're not revisiting the material from time to time, you will likely forget it, even if you understood it quite well.

 

[genericusrnme]

I'd say go beyond the material you're trying to study and see it unified with other concepts. If go ahead and work on harder material you'll look back at the things you were struggling with in your exams as trivialities for the most part.