If writing stuff down helps you, do it. I do, and it helps me.
I'd suggest doing a few tactics puzzles a day, it will help you become familiar with common patterns and will help you recall the solutions faster when you come across it again later. Just as with learning a language, there are many ways to approach learning chess. Do what works for you.
I like to mix it up. I'll watch DVDs or YT lessons when I am a little more tired, I'll throw myself into a book when I have the energy, I'll analyse my games, do some tactics puzzles, or review previous stuff I've worked on, and of course, I'll play chess games!
I wouldn't stress about being slow at the notation - it becomes natural the more you use it, just like sheet music.
I am a beginner, I have been playing from time to time with friends since I was a child, but I never studied seriously. I enrolled for fun here on chess.com almost a year ago and have fun so far. A couple of months ago I decided I want to become better, to play more seriously, understanding in a deeper way the game of chess. I have bought some books, I usually look videos on youtube and, of course, I play also here.
My question is: How can one study chess? I am looking for suggestions about method. When reading a book, of course I set everything on the chessboard and I try to guess the right moves. But the point is that if I try the same puzzle a couple of days later I already forgot the solution. And I totally forget also the puzzle, meaning that I do not remember how to put the pieces in the initial position.
This it seems to me that I am wasting time, as I do not remember anything. I am really used to studying and learning (I do it for my job, as I am a mathematician working at university). I am really looking for method of learning.
At work, the best I can do is usually to write down stuff (theorems, proofs etc): the process of writing helps me in fixing stuff in my brain. Should I also write in chess? I am not totally used to notation (I know how to read it but I am slow and it takes me quite a lot). Could drawing diagrams be an idea? But how, is there any kind of software that could help me? I want to explicitly remark that I do not care about time, I mean it is not important to me to become a better chess player "in two weeks", I am just looking for an efficient way of learning.
I thank you in advance for your kind pieces of advice.