This list from the JMM 2013 Minicourse Teaching and Assessing Mathematical Communication characterizes effective writing of future teachers of mathematics.
- Is the math correct?
- Is the writing clear and intuitive?
- Is there a coherent flow of ideas with a logical progression?
- Does it explain “why” and not just “how” (conceptual, not just procedural)?
- Are tricky areas and potential confusions addressed?
- Are examples used to clarify ideas?
- Is the full generality of the concepts acknowledged?
- Is the writing scaffolded? Is the writing grounded?
- Is the writing precise, concise, but complete?
Mechanics of good writing
- Is there proper grammar, spelling, punctuation, complete sentences?
- Is the mathematics integrated with the writing?
- Is the presentation of mathematics easily readable (e.g are equations offset and aligned)?
- Are precise definitions of terms used? Is the terminology used correctly? Is the notation correct and proper?
- Is vocabulary introduced as (or before) it is used?
- Are any diagrams labeled clearly?
- Appropriate targeting
- Is the vocabulary appropriate to the target audience?
- Is the level of detail appropriate to the the target audience?
- Is the problem (or explanation) motivated and set in context for the target audience?
- Is the work insightful?
- Is it unique?