Writing in Math: Wait, this isn’t English Class

By Hudson Harper

A math professor once walked into a graduate course I was enrolled in, fuming about the latest proofs we had submitted. It wasn’t because anyone had plagiarized their solutions, and it wasn’t because the students just didn’t get it. No, it was because the professor was “sick and tired” of comma splices. He then proceeded to take the first 20 minutes of lecture to show us a YouTube video on comma splices and showed specific examples from our work to demonstrate just how egregious our grammar was. At the time, I was a little confused as to why a math professor with limited lecture time would take such a large chunk of a class to emphasize just one example of misused grammar. However, I finally understood when I started teaching math.

I couldn’t read my students’ work! And it’s not a mystery as to why. If you simply do a Google image search for the word “Math,” you’re likely to find stock photos of chalk boards full of equations, symbols, and drawings. I hate to admit it, but I’m guilty of spreading this image of math as well.

Me “Doing Math” for a Trendy Profile Photo

Me “Doing Math” for a Trendy Profile Photo

However, I challenge anyone to read the math in this photo in a coherent way. The only way you would be able to make any sense out of my work is if you already knew a good bit about and had experience with the math I was working on. Unfortunately, this hodgepodge of symbols, drawings, and general nonsense is the most common way that math is presented in secondary education by teachers and students alike. And it’s understandable why it’s this way when procedures and algorithms are emphasized over mathematical thinking.

Thanks to my professor who yelled at me about comma splices and my experiences as a math teacher, I am more intentional about the way mathematics is communicated in my courses. So first off, you will never find me during class at a board like the one in the photo. More importantly though, my students are forced, I mean taught, to write… a lot. This writing can take several forms. The most common is a formal or informal explanation/proof of an idea a student has. However, students in my class will write reflections on their mathematical thinking, draw annotated diagrams to demonstrate difficult concepts, and even from time to time write papers. Yes, the humanities aren’t the only subjects that can assign essays!

My students will also engage in peer review. They’ll revise drafts. They’ll think about the ways in which grammar affects math just as much as a misplaced mathematical symbol. They’ll identify expressions as clauses and equations as sentences with subjects, verbs, and predicate nominatives. At the end of the day, I want my students to go out into the world and be able to reproduce and explain their work for others. As a first step though, I’ll make sure that I can read the work they submit, and point out the occasional comma splice.