As I mentioned in a previous post, I’ve been assigning large-scale collaborative writing projects in my mathematics classes. I’ve had my topology students write a textbook for their class, and this semester I’ve been doing the same in my discrete mathematics class. As I mentioned in that post, the approach has been very successful, but one area that needs work is the editing/revising processes. Some students are very reluctant to edit what has already been written. I think partly they are uneasy about editing the work of others, but partly they do not know how to revise/edit writing. So I’m trying a few new things this semester.
As I have in the past, I will give the students a document that I wrote called “The Nuts and Bolts of Writing Mathematics.” But now I’ve taken that document and turned it into a set of questions that the students should keep in mind while editing the document. (In fact, this checklist should work for any mathematical writing, not just collaborative writing.) You can download the pdf or view the HTML document below. (Note: If you have any suggestions for questions that I should add, please post them in the comments!)
I also plan to model good editing. I will give them a mathematical document (that I wrote) that needs a lot of revising, and we will spend some class time going through it, discussing how to revise it.
Finally, I’ve been reading this book on team writing. It discusses three ways to do team writing: face-to-face (you and I work together on the writing), divided (you do this, I do that), and layered (you look at it first, I look at it next). I think the layered approach will work best for my students. The book breaks up naturally into small parts—theorems and examples. For each problem I will practice the layered approach to writing and revising: Student 1 does the writing, student 2 does the editing, I give feedback, then student 3 does the final editing. (I may add one more layer of student editing before I see it.) I’ve created a Google Docs spreadsheet which gives, for each theorem/example, the names of the student writers and editors and the due dates for their work.
Editing mathematical writing: a checklist
The mathematical argument
- Is the mathematics correct?
- Is the argument easy to follow?
- Is there any extraneous information?
- Is the argument clear?
- Would it benefit from reordering the sentences?
- Is the level of detail appropriate for the audience?
- Are all proofs free of examples?
- Is the writing in first person plural? (Use “we,” not “I” or “one.”)
- Is the writing in the present tense? (Write “we find that,” not “we found that.”)
- Is the writing in the active voice? (Avoid “it was shown that.”)
- Are there symbols where there should be symbols and words where there should be words? (Use “x≤ 0,” not “x is ≤ zero” or “x is less than or equal to zero.”)
- Are the connecting words (thus, so, hence, therefore, moreover, furthermore, in addition, consequently, etc.) used appropriately and not repetitively?
- Is the writing free of flowery, imprecise, descriptive, and vague language?
- Are all mathematical expressions written in math mode? (We should see x, not x.)
- Is all text written in text mode? (We should see “such that,” not “suchthat.”)
- Are mathematical functions typeset correctly? (We should see sin(x), not sin(x).)
- Are the figures of high quality?
- Do they have captions?
- Does the text refer to them?
- Is the spelling, grammar, punctuation, capitalization, subject/verb agreement, sentence structure, etc. correct?
- Does the layout reflect the style of the rest of the document?
Note: do not be afraid to scratch an entire proof and start over. Sometimes completely rewriting an argument is better than trying to fix a poorly written one.