Mathematical Communication is a developing collection of resources for engaging students in writing and speaking about mathematics, whether for the purpose of learning mathematics or of learning to communicate as mathematicians.

Peer critique on writing

There are many reasons to have students give each other feedback on their writing, but students are likely to require some guidance to give effective peer critique, and coordinating critique requires some planning.

Advantages of peer critique

  • Students learn from seeing effective practices modeled by other students as well as from seeing pitfalls they’d like to avoid.
  • Struggling to understand a peer’s writing emphasizes for students the importance of writing clearly.
  • Writing recommendations for improvement helps students to clarify their own understanding of how to write well.
  • Students often learn from their peers’ comments that their writing isn’t as clear as they think it is. This feedback is often more powerful from a peer than from an instructor.
  • Having students provide critiques may reduce your reading workload. If students review each others’ first drafts, then when you review their second drafts, the quality will have improved somewhat so reading is likely to be faster.
  • Collaborating with peers prepares students for the “real world,” in which those who want feedback must solicit it from peers.

Guiding peer critique

Although peer critique has many benefits, it can be stressful for the students. A respectful atmosphere is important. Here are a few ways to provide guidance:

  • Guidance can be given in lecture: see this lesson plan for a peer critique recitation from M.I.T.’s communication-intensive offering of Real Analysis
  • Guidance can be given in a handout: see these handouts from M.I.T.’s Principles of Applied Mathematics and Mia Minnes’ Seminar in Mathematical Logic at M.I.T..
  • The first round of feedback can receive comments as well as a grade (see this rubric from Real Analysis), while all subsequent peer critique could be graded without comment. (Grading peer critique is much faster than grading a paper.)
  • Students may learn mathematical concepts and effective strategies of communication from their peers. That’s a good thing! If an author wants to use material from a peer’s paper in his or her own paper, guidance may be needed for how to do so appropriately. For example, tell students about Acknowledgements sections and show them some examples; and/or teach good note-taking/attribution habits by assigning students to note down what they learned from their peer’s paper.
  • MIT’s Writing Across the Curriculum has created a video about peer critique for students
  • “Abstract Algebra and the Conversation of Humankind” by Tatu, Yuster, McMahon, and Miller-Brown discusses the authors’ efforts to support student proof-writing in an abstract algebra course using peer review and undergraduate writing consultants.


  • If peers don’t yet know each other, giving feedback in person helps them to develop a collegial relationship that ensures respectful feedback. Discussing comments in person also ensures that the comments are understood. Yet it’s difficult to read and respond to a paper “on the spot,” and it’s often helpful to the teacher to have a written record of the critique. These desires may conflict.
    • One option is for the peers to talk when papers are distributed for review: each author should describe the kinds of feedback desired. Peers can read and respond to a small part of the paper “on the spot” to begin to develop a collegial relationship. As homework, the critique is completed in written form, and comments are discussed in the following class.
    • Another option if the teacher doesn’t need a written record is for peers to read the paper before class, jotting notes to themselves, and then give feedback in class.
    • If peers have already developed a collegial relationship, then talking in person first is not necessary: the critique may be written outside of class and be discussed in the following class.
    • Conducting critique entirely outside class has been attempted in a large class at MIT. Although the quality of the critiques appeared to instructors to be acceptable, students reported that paper-only critiques were unhelpful.
  • Pairing peers works well, but using groups of three or larger has the advantage that authors can see the degree of consensus about the various comments. In groups, each student should ideally read the papers of all other members of the group so all can participate in the discussion.
  • Students are better at critiquing clarity than correctness, so even when peers are providing comments, you may want to briefly review the papers for correctness.
  • Peer critique is most effective if students have written on different topics: a reader relatively unfamiliar with the content can better assess whether the author communicates clearly.
  • If students read the papers outside of class and then discuss comments in class, plan what you will do if a student’s peer(s) don’t make it to class. You might provide on-the-spot feedback yourself. If two or more students are left peer-less, they could verbally summarize their papers to each other: the challenge of summarizing verbally may help the author discover better ways to explain, and the classmate’s questions may signal parts of the paper that need clarification as well.
  • When students discuss comments in class, it will be necessary to have a copy of the paper to refer to.
  • When sharing students’ papers, try to minimize the temptation/opportunity for violations of academic integrity. It may be wise to ensure that each student can see only the one or two papers to be critiqued, and only after they’ve submitted their own drafts. It can work well to wait until drafts are submitted, and then tell the students who they should email their drafts to. (e.g., place on-time students in groups of 3 and have each student email their paper to the other two members of the group; late students are then grouped together once they submit their papers)
  • The website Calibrate Peer Review (CPR) can facilitate peer rating of writing. Students begin by entering their writing into the CPR interface. Then they see and rate a few sample responses and can calibrate their ratings by comparing against those supplied by their instructor. After the calibration step, peers rate each other’s writing. The text entry interface uses html for formatting. This is a peer rating system, not a peer commenting system.
  • Students can use the free version of Adobe Acrobat Reader DC to write comments directly on PDF documents.

General resources & research (not specific to mathematics)

  • How can I get the most out of peer review? The WAC Clearinghouse
  • MIT’s Writing Across the Curriculum has created “No One Writes Alone: Peer Review in the Classroom,” a pair of videos, one for students and the other for teachers.
  • Eli Review offers a tool that facilitates teacher-mentored peer critique and revision. The website also provides guidance for giving effective feedback and for designing effective peer critique assignments.
  • Bishop, J., and M. Verleger, “Feedback effects: Comparing the change resulting from peer and TA feedback to student solutions of Model-Eliciting Activities,” 2012 Frontiers in Education Conference Proceedings (pdf)
    Student revisions show greater change if peer feedback is given before TA feedback than if the order is reversed. (Abstract) The entire proceedings is available (free) as a pdf through the FIE 2012 website.
  • Reynolds, J., and V. Russell, “Can You Hear Us Now?: A comparison of peer review quality when students give audio versus written feedback,” The WAC Journal, Vol. 19: August 2008, pp. 29-44.
    This study of first-year composition students found that the quality of digitally-recorded audio peer feedback was higher than for written peer feedback, but that students preferred giving and receiving written feedback.
  • Holmes, C., “Read-Around Groups: Low-Stakes and High-Impact Writing in First-Year Composition,” a Nov. 13, 2014 blog post in The Writing Campus, George Mason University.
    Caitlin Holmes describes a low-stakes activity she uses to enable students to see and discuss the writing of their peers.
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