As a teaching assistant in a mathematics department, I consistently tell, and have professors around me tell, students NOT to write things down if they don't know anything.

If you are in the habit of writing things down with no idea whether or not they are true or false, relevant or irrelevant, you are (1) wasting the time of people who are grading and (2) losing track of whether or not you know something (especially if you're rewarded for it.)

It probably has much more to do with (1) than (2) though, just because grading 400 finals is exhausting enough without having to wade through a paragraph of meaningless scribbles every test.