For me I'd say the most important influences towards improving my writing came from one particular course in high school (modern european history) where the homework was all short essays and paragraph-ish long answers to a bunch of questions/topics and heavy participation in usenet during my college years.
With papers it's too easy to fall into a pattern of satisficing, because the bar is set pretty low, even in college, and the exercises are mostly unrealistic. But when you have to spend time trying to communicate complicated subjects to real human beings or to make detailed arguments then you have to step up your skills substantially.
I'm pretty sure there is some underlying difference and it would be good to know what it is - I was diagnosed with dyslexia when I was 14, which never really felt like a satisfying answer, though I do have some dyslexic-ish symptoms (I tend to spell phonetically when I'm very tired and often type word-correct anagrams - like "never really left like a satisfying answer", above).
What I have going for me is that I'm a pretty good public speaker. The moment I picture myself behind a podium in front of an audience, ideas organize themselves into coherent patterns. It's a skill that's been honed over many weekends of debate practice.
My writing process now looks like this:
1. Identify thesis 2. Give a speech 3. Take bulleted notes 4. Give the speech again 5. Revise bulleted notes 6. If satisfied with structure begin expanding bullets into sentences and paragraphs.