18.821 | Spring 2013 | Undergraduate

Project Laboratory in Mathematics


Practice and Feedback

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In this section, Prof. Haynes Miller and Susan Ruff explain their use of practice presentations as well as how teams receive feedback on their presentations from both faculty and peers.

Students present informally during the mentor meetings and debriefings. When it is a team’s turn to present formally to the class, they first prepare by practicing with the help of their mentor for that project, the communication instructor, and the lead instructor. After the formal presentation to the class, the team receives completed feedback forms from peers and from the course staff.

Practice Presentations


Each presentation is preceded by a practice presentation three to five days before the in-class presentation.

Students are told to treat the practice presentation as though it were the final presentation. This encourages students to prepare appropriately. Practice presentations are typically attended by the group’s mentor for that project, the communication instructor, and the lead instructor. We schedule two hours for each practice session to allow ample time both for the one-hour presentation and for feedback and discussion.

Feedback on Practice Presentations

Students share the work of presenting in various ways. In Spring 2013, all teams gave presentations in which one student talked for the first third, another for the next third, and another for the final third. During the practice presentations, we would stop after each student’s part, and the whole group would discuss what we saw. Practice presentations were typically on Fridays, with the final in-class presentation happening on the subsequent Monday. The students would do a lot of work over the weekend. We were very pleased with how well the students picked up both the letter and the spirit of our critiques and put them into their final presentations. We loved doing the practice presentations with the students, helping them improve their presentations, and seeing the improvement from the practice to the final presentation in the class.

Typically Susan would write comments as the practice presentation progressed, and then give these comments to the students at the end of the practice presentation.


Over the years, instructors have approached practice presentations and final presentations in different ways. Here are some variations that have been tried:

  • A mini conference at the end of the semester. One year, we concentrated all the talks into a mini “conference” at the end of the term. One disadvantage was that students couldn’t learn from their classmates’ talks in time to improve their own. Another was that because the whole class only met together for the start-of-term workshops and for presentations, the class did not meet as a whole group for most of the semester, and the students didn’t really interact with any classmates other than those in their teams.
  • Slide-based talks. It can be challenging to get students to put adequate effort into a presentation, especially if it is a chalk and blackboard talk. One semester, we insisted on slide presentations, which forced students to do a certain amount of preparation and improved the overall quality of presentations. This puts a burden of learning the slide presentation technology (often Beamer) on students, and does not reflect current practice in many areas of mathematics.
  • Give practice presentation comments after the whole group has presented. In the past, we sometimes had the entire team give the presentation before giving feedback, rather than after each person presented his or her part. This allowed us to see the transitions and overall structure of the presentation before formulating comments. The converse practice, of interrupting presentations repeatedly for comments, does not work well; it is discouraging, it fails to let students get into the swing of their presentation, and students do not have the chance to absorb suggestions.

Peer Feedback

In Spring 2013, students were asked to give written feedback on their classmates’ presentations.

Students made comments in the following categories:

  • What did you particularly like about the presentation?
  • Which part of the presentation was most difficult to follow?
  • What advice do you have for the presenters for the future?

The students had the option of signing the response form on the front, if they were willing to let others see their names attached to their comments, or they could sign the form on the back, if they didn’t want their names attached to their comments. At the end of class, we collected these sheets, scanned the fronts, sent them to the presenters, and posted them on the course website. Most students chose to have their name visible, and the comments were generally quite constructive and astute. We do not have quantitative evidence on the impact of these forms, but we had the feeling that they helped students be more engaged in their classmates’ talks and reflective about what makes a good talk. We hope the feedback was useful both to the presenters and to groups that presented later in the semester.

Select Student Response Sheets for Sample Presentation (PDF) (Courtesy of MIT students. Used with permission.)

The peer response sheets also served as an indication of attendance. Ten percent of the presentation grade was allocated to an attendance mark. Attendance was in fact quite high, and students often wrote to Haynes in advance if they had to be absent. In one case a student watched a flip-cam recording of a presentation he had to miss. We think the high attendance was largely a function of the high quality of the presentations, since all the teams gave very good presentations.

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