"Writing to Learn" is a 1988 book by William Zinsser, in which he makes the argument that all college courses across the whole curriculum should feature writing as a part of their core emphasis. You can browse through the book at the publisher's web site, or pick up a copy from Amazon for as little as a penny plus postage. (Even good books lose their resale value after being in print as textbooks for 20+ years.)
Zinssner of course did not even contemplate blogging as a form, though he did write and edit for newspapers and for the Yale alumni magazine. Of that last experience he writes:
I never stopped to ask: "Who is the typical Yale alumnus? Who am I editing for?" One of my principles is that there is no typical anybody; every reader is different. I edit for myself and I write for myself. I assume that if I consider something interesting or funny, a certain number of other people will too. If they don't, they have to inalienable rights - they can fire the editor and they can stop reading the writer. Meanwhile I draw on two sources of energy that I commend to anyone trying to survive this vulnerable craft: confidence and ego. If you don't have confidence in what you are doing you might as well not do it. (p. 25)
When you are learning something new to you, or when you are taking something that you know and teaching it to others, there is no better way to capture that effort than writing regularly and routinely. It makes you put into words the things that you know, and makes you find the words to describe what you don't know. Zinsser's "Writing to Learn" is a good book-length call for writing throughout the college curriculum, and it's worth picking up and leafing through at your local library to see if you want to add it to your own "books about writing" bookshelf.