Peer Review of Mathematical Essays

Question

Background

I find that the best way for my mathematical modeling class to understand the modeling process is by having the experience of modeling some real world situation of their group's choosing. I have a number of strategies so that the project topics are interesting and of the right scope to be doable in the amount of time allotted. One of two main deliverables that I require is a 16–20 page paper about their model, focusing heavily on the evaluation of the model. (See here for Project Description and Project Expectations.)

One day of the semester, I ask the students to submit a final draft to peer review. The groups bring in three copies of their paper and the students spend the 75-minute class period reading and commenting on their peers' papers. I give the students directed questions to address about the papers. (See here for Peer Review Sheet.) The goal of this peer review process is to give the students a chance to improve upon their drafts before submitting them to me for grading a few weeks later.

I feel that I have set up the Peer Review process for success but every year there are issues with the process. For example, some groups get peer comments that their paper needs only minimal revisions but when I read the paper, it is clear that the main focus of the paper is not the model or the paper does a bad job with model evaluation. This leads to frustration and disappointment with the grades that I assign, especially with all the effort that I know that the students put into the project. (I do allow for a second revision to improve their grade afterward.) I feel that the peer review process is not doing its intended job to improve the quality of the paper and giving a false sense of security.

Question

Do you have any suggestions for ensuring success in the Peer Review process?

Answer 1

Here's my perspective as a project manager.

Weighting the different sections

It would help to break down the 16-20 pages into sections with page guidelines, e.g.:

• 2 p. Introduction
• 3 p. Assumptions
• 3 p. Results
• 3 p. Discussion: Strengths
• 3 p. Discussion: Weaknesses and Expected Errors
• 3 p. Discussion: Future Research
• 1 p. Conclusion

This keeps the units of guidance under 5 pages long. (Also, you have lengths in a mixture of pages, paragraphs and words, so it would help to standardize.)

Revised Questions on Content

For each 3-page section of the paper, provide at least one question. This will help ensure that both the papers and the feedback have the right emphasis.

Content #3: It may help to focus on clarity over length. "Did the paper explain the model’s assumptions clearly? What other assumptions are important?" And then ask the same about the errors, in a different question.

Content #4: Identifying gross overstatements asks for too much judgment. "What are the boldest claims in the paper? Are they adequately supported?"

Other questions to remove

Overview #2, what to expand: You may not need this if you have questions on each individual part identified above.

Overview #3, redundancy and fluff: I wouldn't worry about this so long as the first draft is of the right length and the final draft is complete. Students may explain one thing twice because they don't realize that two things are the same.

Structure #3, style: This requires a vocabulary that you probably wouldn't develop in a math class. The authors can decide for themselves which criticisms can be met by changing their style.

I hope this helps -- let us know how it goes next time!

Answer 2

The "peer review" term is really misleading, what it is really about (at least for the first papers you submit) is having someone experienced read and comment on the text. Basic understandability and other gross characteristics can be assessed by class mates, finer points only by a TA or teacher. You'd need to combine both methods. Having their text read by classmates (and seeing their mistakes firsthand) should help both parts, probably as a required step to be certified somehow as really done, but not part of the grade.