I can't compose at the keyboard. I admire anyone who can, but I've found that if I try I either sit staring at the cursor blinking at me or I change one word for another that I've already rejected over and over again. For whatever reason, I do much better when I have paper and pen in hand. Heck, even this blog post started as notes scribbled in one of my many spiral pads.
In my notebooks I feel free to write whatever and however it occurs to me. Sometimes, when the synapses are firing nicely, the words tumble out in nearly final form, requiring only a bit of polish before adding them to the rest of the work. Sometimes I write the scene as it appears to me, sketched out in a fairly omniscient third person perspective (so far both novels are written in first person). And sometimes I talk to myself, making suggestions, proposing scenes, making corrections, and notes for further research.
I suppose I could do all of this electronically. I've used the review function in Word with my students, but if I had to wait for a computer to boot up every time a snippet of dialogue popped into my head in the middle of the night I'd forget what I wanted to say and it would be lost.
Looking at my notebooks, it's easy to see that writing is a process as our English teachers told us. There are additions, subtractions, word changes, rewrites of all sorts. I use highlighters to indicate which word or phrase I ultimately decide to use. When it's as perfect as I can make it, I finally type it into my computer, where I print out the file from time to time and edit it again.
I think the moral of the story is, use what works for you. Respect your process, no matter how hopelessly archaic it may seem to anyone else. After all, people have been writing on papyrus, parchment, and paper far longer than they have in pixels.