by Simon Xu

Writing and mathematics may seem orthogonal to each other, especially to students who are taking their first heavily proof-based course. Even for some more experienced math students, including myself, who might have sensed some degree of similarities between these disciplines, it can be difficult to articulate a precise relationship. In our class WIPP 7001, Pedagogy of Writing in the Disciplines, I had the fortune to find Caroline Yoon’s insightful article, “The Writing Mathematician,” in which the author offered a few writing-mathematics metaphors. One of them that resonates with me the most is the metaphor of “writing as proving.” Yoon writes, “Academic writing is like a proof that performs dialogic role in the way it addresses and seeks to convince a public.” At first glance, this is simply a metaphor about academic writing, but it also highlights the aspect of proof-writing that many beginning students tend to omit: the aspect of audience. As much as we think that mathematical proofs are meant to capture perfect, stone-cold logical deduction, they’re still read by other people. They’re still meant to convince other people (who tend to be very skeptical). The importance of writing then comes into the picture very naturally. An effective proof requires clear communication between the author and the audience.

As much as we think that mathematical proofs are meant to capture perfect, stone-cold logical deduction, they’re still read by other people.

Perhaps one of the most important takeaways from my experience taking WIPP 7001 is that coaching writing should be thought of as an ongoing dialogue between students and the writing coach. One of the most important measures we implemented in our course is a rewrite-and-resubmit process, in which students get a chance to receive feedback from me and to revise their writing accordingly. I quickly realized that because this course might be my students’ first exposure to formal proof writing, and because the assignments are turned in on a weekly basis, it is more practical to first focus on the mechanics of proof writing. This is the part of mathematical study that really resembles learning the grammar of a foreign language. For example, words like “imply” and “if” have specific logical meanings in mathematics, and misuse of these technical words can lead to confusion on the part of the readers. One strategy that I found especially helpful in familiarizing students with this jargon and style is to ask them to imitate proofs in the textbook. These proofs are written by professional mathematicians, and more importantly, the intended audience for these writings are precisely beginning students such as themselves.

Over the semester, most students do seem to have grown more comfortable with using a formal mathematical language. If I have the chance to teach and/or grade a course in the future where students are more mature mathematically, I plan to build on this foundation by focusing more on other aspects of proof writing, such as the organization of a proof.

This dialogue of coaching writing also really benefits me as a writer. It gives me the perspective of a reader and a clearer sense of what writing style is working and what style is not working. It helps me to reflect upon my own writing and to realize potential ways of improving my own work.