Here is a list of tips I check for each paragraph whenever I write anything:

  1. Each paragraph is about a single concrete and coherent idea
    1. Does the first sentence of the paragraph introduce this idea?
    2. Do all subsequent sentences in the paragraph further clarify the first sentence?
    3. Did I use transitional words to establish logical relationships between sentences?
    4. Did I write anything like, “Next, we …”? If so, remove. The structure of the paragraphs should flow into one another.
    5. Did I sequence light to heavy: so the earlier sentences that start light/succinct, follow-up with “heavy” details?
    6. Does the last sentence of every paragraph link it to next paragraph?
  2. Tense
    1. Is the tense consistent within each paragraph (results are past tense)?
    2. Is it past tense only for things that you or other people did previously?
    3. Are there any passive tense phrases (e.g., “it can be shown”)? If so, revise to active tense.
  3. Any time you introduce a new concept
    1. Have other people discussed this concept? If so, did you use familiar notation/naming conventions? If not, have you clarifed/justified the difference?
    2. If you’ve introduced 1 new concept, have you used the name of that topic consistently? And did you never use any other term (to bury the concept in their mind)?
    3. When introducing a novel concept/word/equation/notation/etc., did you explain it before usage, rather than after (else the reader will not understand when reading it, and we don’t want that)?

See this youtube video for details.

I realize this is actually 12 things to check. I’m ok with that.