TITLE: How to take the most of math lectures in college?
QUESTION [20 upvotes]: I am trying to become more effective in my study habits and in my case, I feel that attending classes is a huge waste of my time. The lecturer just keeps writing formulas on the board and to be honest, I am simply too busy just rewriting all those symbols to really understand what is being taught. I only really understand when I slowly go through the textbook and do the exercises.
Perhaps it is just my learning style, but I have the impression that only one or two students are really following the math lectures (and they are probably the ones who carefully read the material before the lecture), and the rest are just a bunch of robots attending because they have been told that they have to, or are afraid to miss some important hints for the exam. But I feel that spending that much time in class just to get an edge in an exam is quite ineffective.
It seems to point out that the best way to take advantage of the lectures is to get acquainted with the material first. But I am not sure if this is the most effective way to go. Isn't that more time consuming this way because once you understand the concept from the book, you would not need another hour to expose the same concepts and examples again. And reading a book is much more time consuming than an lecture. Or does it really help to reinforce the material and fill some gaps in understanding? Hard to say. 
So, is a lecture meant mostly as a complement or substitute for reading the textbook?
Do I have to admit that I am too stupid to follow the lectures and write what is on the board at the same time?

REPLY [2 votes]: I was in your shoes. During my first semester of calculus I took notes diligently and did well in the class, but I would occasionally look up at a proof and be dazed by what it meant. During my second & third semesters of calculus I had a different instructor with a different teaching style. He didn't just teach the concepts of calculus, he also taught the history of the concept. Who discovered and formalized these ideas and how they came about their discoveries. In these classes I learned to take less notes (the stories surely weren't going to be on any exam). The stories however gave unparallelled context as to how each concept was conceived, what problem space it addressed, and how it was to be applied. 
Ever since then, I have never taken notes in math lectures shy of a few important equalities. I find diligently taking notes heavily distracts from understanding the big picture: 

How do these new concepts relate to previously understood concepts?
What do these new concepts build on top of?
What makes this new concept unique?

These things are hard to focus on when you brain is busily processing then next line of chalk on the board.
I would attend lectures without any expectation of taking notes. Follow the lecturer's dialog on the subject. Scribble down only those concepts which seem most important. Then go home skim through the book reading in depth only the sections which you did not grasp from the lecture. Attending the lecture will make reading through the book much easier.