Assessing students’ writing and providing them with feedback they can learn from takes a long time, a lot of thought, and is one of the biggest challenges the instructors face in this class. Below, Michel Goemans, Peter Shor, Lorenzo Orecchia, and Susan Ruff share a variety of strategies they use to engage in this work.
We involve everyone on the teaching team, from the lead faculty member to the undergraduate graders, in assessing students’ work. We’ve found that it is very important to manage workload, so we try to limit the number of papers per team member to 12-18. If we assess more than that, the quality of our comments suffers. When the papers are longer, such as the term papers, we have students submit their papers in two batches so that one person is only grading between 6 and 9 papers per week. We give ourselves one week to grade each assignment.
Norming meetings are sessions in which all the instructors and staff members sit in one room to discuss students’ writing. There is a norming meeting for each assignment. Susan provides participants with a grading rubric, which is based on how easy a paper is to read and understand. Each instructor comes to the session having already assessed a handful of student papers. We then compare how we assessed students’ work, attempting to come to a consensus. We share a spectrum of student work so that we “norm” our assessments of assignments that are strong, moderately successful, and weak. This process is very time-consuming—often lasting one or two hours per session, which does not include the grading instructors do after the meeting—but extremely helpful.
What is interesting for us, as instructors, is how clearly the norming meetings reveal the nuanced aspects of mathematical communication that we attempt to convey to students. That is, the norming meetings are spaces in which instructors advocate particular styles of writing and of communicating mathematical understanding; the subjective nature of communication in mathematics—something that people outside of or new to the field often fail to understand—becomes very apparent, very quickly!
What we’ve learned about giving feedback is that it’s typically better to focus on a few main issues in each student's writing rather than to highlight all areas for improvement. Moreover, what we focus on depends on the quality of the piece. For example, typos might be a big issue in a paper that is well composed, while we might not even discuss typos in a paper that has many structural errors. We try to focus on what we consider to be the main issues in students’ writing. We also provide summaries of our comments to help students distinguish critical areas for improvement from less important ones.
We believe that it’s very important to be constructive when giving feedback. We try to point out what students are doing well in their writing, as well as aspects of their writing that should be improved. When we discuss papers that need a lot of improvement during our norming meetings, we also talk about the positive comments we can honestly provide. We do this to ensure that students keep doing the things they are doing well. We also do this to make sure that students don’t come away from the class with the feeling that they’re doomed to be poor writers forever. We want to convey our sincere belief that students can improve their writing abilities.
Simple things like wording comments about the paper instead of about the student can help convey our belief that students can become better writers. Noting that a paragraph tries to make too many points at once and that it might be helpful to break it apart is very different than saying “it would really help if you could focus your thoughts.” It’s important that our comments be constructive because students really do care about their writing.