Helping Students Learn to Write Mathematics Papers

In this section, Dr. Snowden describes some aspects of mathematical writing that students needed to learn as well as the role of a revision cycle in improving student writing.

The Writing Requirement in Undergraduate Math Seminars

One requirement of undergraduate math seminar classes is that students write and revise a math paper roughly 10 pages long. Through this process, students are expected to learn more about how mathematicians write.

In this particular class, students were required to write an expository final paper on a specific topic related to the course. I came up with a list of possible topics and put it on the class webpage to give the students ideas. I didn't require them to use one of these topics, but I think everyone did. Students had to choose a topic 5 weeks into the semester, hand in a draft 10 weeks into the semester, and then hand in the final paper 12 weeks into the semester.

Learning to Write Like a Mathematician

Students learned about structuring mathematical papers. A lot of first drafts read like high school essays.

— Dr. Snowden

On the technical side, students who had never used TeX, a typesetting system used by mathematicians, learned how to use it to write this paper.

We also helped students learn about proper mathematical syntax and conventions in mathematical writing. As part of this effort, I wrote a short document about things they should and shouldn't do in LaTeX (PDF) just to provide a general stylistic guideline.

Beyond that, students learned about structuring mathematical papers. A lot of first drafts read like high school essays. I'd see, for example, summative conclusion sections, which just don't appear in academic math papers.

All of these kinds of things—how would they know beforehand? It's just the culture of how math people write papers.

The writing instructor for the course, Susan Ruff, came to class once, spoke briefly about writing, and gave the students a handout about some basic guiding principles.

Using a Revision Cycle to Improve Student Writing

The students submitted first drafts two weeks before the final paper was due. Susan helped me come up with criteria on how to evaluate the papers, and then we both read their drafts and commented on them in detail. I gave the class a document describing common mistakes in their first drafts (PDF).

Throughout the whole process, I met with students who wanted to or felt like they needed to, and we talked about ideas for how to structure their papers.