Guidelines for Peer Review in Math


Robert Cowen

The aim of your review is to help the author of the paper produce a better final draft. In order to do that criticism must be constructive and specific. (“This is a lousy paper,” is neither constructive nor specific!)  To start, try to figure out what the author wants to accomplish and write this down as best you can in your own words, as the first part of the review.  Something like, “In this paper, Joe Rice, investigates the 5x + 7 problem, a variation of the 3x +1 problem. He is able to show that……….” If you aren’t clear on what the author wants to accomplish, say so and point out where the difficulties occur.  Next answer the following questions in writing as part of your written review.

  1. Is there an introduction or abstract that motivates the reader to read the rest of the paper?
  2. Does this introduction sufficiently explain the relation of problem at hand to other, better known problems?
  3. Are the results correct? Check the programs provided to see that they do what they claim. Can they be improved or shortened?
  4. Are the results that are claimed as general as they could be or could more be obtained with essentially the same methods.
  5. Are the results presented as well as possible? If not, how can the presentation be improved?
  6. Are the diagrams, charts, etc., effective? Do they present too much or too little information? How can they be improved?
  7. Is the English employed effective? Point out, on the manuscript, places that need work. In particular, are the paragraphs well designed and are there proper transitions from one paragraph to the next?
  8. Is there a conclusion? Is it justified by the preceding work?  Does it indicate what further work might  be done by the author or by others?

When you meet with your author, exchange written reviews. Read the reviews and then discuss them. In general, authors need to follow all of the reviewer’s recommendations; however if they disagree with a specific recommendation, they can elect not to follow it; however, they then must give their  reason, in writing to the “Editor” (their instructor).

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