I’m an Applied Mathematics Professor, and Improving My Students’ Writing Ability Matters

Credit: iStock.com/Lamaip
Credit: iStock.com/Lamaip
In my experience, most students have difficulty translating their ideas to acceptable prose. It’s my belief that it’s the responsibility of every professor—including mathematics professors—to try to enhance the writing abilities of their students. Writing is a fundamental skill, one common to all disciplines. Many of my students will not need the mathematics I teach them in their professional working lives. But they will depend on the writing skills I help them to develop.

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In my experience, most students have difficulty translating their ideas to acceptable prose. It’s my belief that it’s the responsibility of every professor—including mathematics professors—to try to enhance the writing abilities of their students. Writing is a fundamental skill, one common to all disciplines. Many of my students will not need the mathematics I teach them in their professional working lives. But they will depend on the writing skills I help them to develop.

Not much has changed since Merrill Sheils wrote “Why Johnny Can’t Write” nearly half a century ago. It’s not news that a large percentage of high school students do not write well. This is consistent with education ministry testing results pretty much across the globe. For example, The Nation’s Report Card: Writing 2011 reports that only 27 percent of US 12th-graders perform at or above the level “proficient.” It’s also consistent with the views of many of my university colleagues who have bemoaned student writing skills for years.

Of course, writing is an incredibly difficult skill to learn. And it’s as difficult to teach. But, in my experience, there are a few things instructors should try to do with students. One is to explain why writing is important. Another is to show them how to revise their work with individual feedback if possible.

It’s an approach I’ve tried in the trenches, and it has some merit. It has the flavor of what Mike Rose describes in his wonderful book Lives at the Boundary (1989). Rose taught writing at UCLA for many years. His one-on-one, compassionate approach was informed by the assumption that writing is an extremely difficult skill to master but one required for a student to be able to enter into the conversation on ideas.

I teach applied mathematics, and in my senior undergraduate elective courses, largely case-based, I ask students to present their recommendations and supporting arguments in written reports to a fictional senior decision-maker. My students are in one of two groups. They are either very good writers or they struggle. For those who struggle, I have no complaint about the general logic of their writing. Their arguments are usually good. Where they are weak is in writing a grammatically correct sentence to express the particular idea they want to convey.

Let me give you some examples. At the beginning of these courses, I am interested in finding out what students read for pleasure. Usually, a student who reads can also write. So, I ask them to write at most a page double-spaced. The following sentence is from one of those submissions and is representative of the difficulty some students have:

I also enjoy reading autobiographies of people including Kurt Cobain, Andre Agassi, and Anthony Kiedis, lead singer for the red hot chilli peppers.

When I read this sentence, I understand the idea the student wants to convey. But it’s poorly written. Or take this sentence, where the student is explaining why she prefers periodicals and newspapers to books:

I like reading articles because they are short, to the point, and I get a lot of information.

Again, I understand the idea, but the sentence is not grammatically correct.

The ignition point

I’ve asked my students who can write how they learned. Invariably they can trace their development to a single person, usually a teacher or a parent. I’ve also asked a number of good professional writers the same question, and they, too, point to a single person. Lewis Lapham, the American editor and essayist, learned from a graduate student at Yale. They would meet at Mory’s, and the grad student would go over Lapham’s work, sentence by sentence, explaining his errors and then how to fix them. The poster boy is the American writer Stephen King. While in high school, he worked for his hometown newspaper as a sports reporter. The editor was a fellow named Gould who turned out to be an inspiration to King:

I took my fair share of English Lit classes in my two remaining years at Lisbon, and my fair share of composition, fiction, and poetry classes in college, but John Gould taught me more than any of them, and in no more than ten minutes. (King 2000, 56)

What Gould did was take the first article King wrote and edit it with a black marker. At one point in the article King wrote that a particular basketball scoring record had stood “since the years of Korea.” Gould looked at King and asked what year the record had been set. King responded 1953. With that, Gould struck out “the years of Korea” and substituted “1953.” To King, this was a revelation. As he writes in his book, “Why . . . didn’t English teachers ever do this?” (57).

At some point, a student will decide that it’s important to learn to write. I term this the ignition point, the point where the student moves to a new glide path, one where they will take over the responsibility for learning to write. At this point, students start to see the logic of writing. They begin to write second and third drafts of their own accord. They begin to read attentively, trying to understand what makes good sentences good. And most importantly, they develop a new attitude: they begin to take pride in their writing by refusing to issue substandard prose to a reader.

In my view, our teaching objective ought to be to get students to this ignition point. But how do we do this? The short answer is that I don’t know. But, as I remarked above, I think there are a few things instructors can try.

Most of my students don’t think that writing is important. For these students, I make sure to take some time in class to explain that writing is a fundamental technology that enables us to discover ideas we otherwise couldn’t. I’m currently writing a book titled Why Writing Matters that makes this precise point. Most students take the neurocentric view that they need only their heads and some effort to come to ideas. As the extended mind literature makes clear, nothing could be further from the truth.  (See Donald 1993, 2010; Hutchins 1995; Clark and Chalmers 1998.) I try to make the point that writing is a 5,000-year-old technology that has done absolute wonders for us.

The second thing to try, if possible, is Mike Rose’s one-on-one approach, and I’ll discuss my variation of it in the next section.

My variation of the “Rose” approach

I consider myself lucky because I don’t have large classes. Generally, I have 10–15 students in my senior elective courses, and this enables me to provide detailed feedback on each sentence a student writes. I realize that most colleagues will have many more students, and this makes detailed feedback impossible. But there are ways to scale to a classroom, and I’ll explain these shortly.

I make my editorial suggestions to students directly in the Word files they submit. For example, take the first sentence above:

I also enjoy reading autobiographies of people including Kurt Cobain, Andre Agassi, and Anthony Kiedis, lead singer for the red hot chilli peppers.

Here is the feedback I gave that student:

Is the word “reading” necessary? If you reread the sentence without it, you’ll see it’s not. It’s understood that an autobiography will be read. My first rule of rewriting is to get rid of words not required and, where possible, to rewrite with fewer words.

Are the words “of people” required? They aren’t. Autobiographies are always about people.

Should you capitalize “red hot chilli peppers”? Yes. Proper names are normally capitalized.

Is “chilli” spelled correctly? No, it’s not. The correct spelling is “chili.”

Did you mean to write “autobiographies” or “biographies”? Kurt Cobain did not write an autobiography, but Charles Cross has written the biography Heavier Than Heaven.

Here’s the sentence with these suggested corrections:

I also enjoy biographies including Kurt Cobain, Andre Agassi, and Anthony Kiedis, lead singer for the Red Hot Chili Peppers.

The sentence is still not right. I think you meant to write that you enjoy biographies and recently you’ve read those of Kurt Cobain, Andre Agassi, and Anthony Kiedis? Furthermore, why did you explain who Kiedis is but not the others? A writer needs to appreciate his audience. I may be an old fat professor, but I like rock music and I know who Anthony Kiedis is. When you explain who he is, it’s mildly insulting because you’re intimating you don’t think I know.  

With these considerations, you might rewrite as follows:

I also enjoy biographies. Recently, I’ve read a biography of Kurt Cobain, and the autobiographies of Andre Agassi and Anthony Kiedis.

I think these two sentences express the idea you intended.

Dear reader, no doubt you are thinking that, for my part, this is a lot of work. It is. But I consider it to be the most important work I do. Furthermore, as time has passed, I’ve gotten a lot quicker at it. Each poor sentence is a puzzle that you have to solve. And like anything you work at, you usually get better over time.

As you can see, the fixes I suggest usually boil down to logic. For example, when a student writes “autobiographies of people,” you can simply point out the redundancy. Most students see this easily. After you point out a number of these logic issues, they begin to “get it.” Maybe it doesn’t come as quickly as the road-to-Damascus lightning bolt that Stephen King experienced. But most students will eventually see that sentence writing is an exercise in logic.

The other critical aspect of this approach is how you assign a grade. In my courses, a student will be writing a series of case submissions. Each submission is, at best, two pages double-spaced. What I first do is get their submissions to the point where their prose meets my standard. This sometimes takes two to three drafts, with each successive draft taking less time to evaluate. It’s over these drafts that I can also ask the student to consider any weaknesses in their logic or argument. Once I get the final draft, I then assign a final grade, which is usually 100 percent. The only students who do not get 100 percent are those who do not do the required redrafting. In these cases, I tell students that their maximum grade will be 70 percent and they’ll only get that if they have a strong argument. Most students are prepared to redraft for two reasons. First, they feel they are improving their writing, and second, they get higher marks. The other part of my evaluation is to give praise to a good student sentence when I see one. This really boosts a student’s morale and confidence.

One way to scale this approach is to have the whole class look at a poor sentence and try to fix it. I call this activity Mr. Fixit Sentence Repair Exercises. As students develop a better idea of what I am looking for, they really “get into” these exercises. You can do three to four sentences in 10 minutes so it doesn’t take up too much class time. And if you do it twice per week for 14 weeks, you end up showing students how to fix well over 100 sentences. Recently, my colleague Doug Delaney (History, RMC), my son David (a web developer), and I have started a Substack site, Sentence Logic, which takes this Mr. Fixit approach. We take actual student sentences and show, in detail, how to fix them. By studying these fixes, a student will begin to appreciate the logic of sentence revision.

Another way I scale is with an end-of-term essay. I ask my students to write a five- to eight-page essay on a specific problem based on the subject matter of my course. Students are required to find an editor for this essay and they must submit their editor’s name and email address with the essay. I warn students that any mistake in grammar or usage will result in their maximum possible mark going from 100 percent to 70 percent. I tell them I will not assign an A or B grade to any essay that is not impeccably written. If students arrange a good editor, they will learn from the editor’s suggestions for revision. Furthermore, given the subject of the essay, it’s doubtful that an editor could write the paper and, when I see these essays, I’m generally confident that students have written the initial draft.

There are very few essays that go to the 70 percent maximum. This is likely because students understand my feelings about the importance of writing and hence know the 70 percent threat is credible. But when I find errors, I don’t automatically impose the 30 percent penalty. I’ll take into account the severity of the errors before deciding whether to penalize. I’m lenient but not too lenient.

So, does my approach work? The only direct evidence I have is the feedback I receive from students in their post-course evaluations. Most of them point to my approach to their writing as different, refreshing, and useful. Some go as far as to suggest that all courses need to take the same approach.

What about grammar courses?

In conversations about how to deal with student illiteracy, I often hear the suggestion that students need to take a grammar course and learn how to diagram a sentence. My feeling is that grammar courses are useful but a little goes a long way. You can teach students a lot about rules with my approach, either directly or in the Mr. Fixit exercises. In addition, a student who embarks on a strong reading program will internalize the rules of grammar without explicit instruction, much the way a child learns to use irregular verbs.

Changing the curriculum emphasis

About 15 years ago, I was sitting in my office having just marked some of the worst case write-ups I’d ever encountered. The writing has horrible, and I was thinking about what to do. I soon decided I would devote some time to their writing skills. I felt that teaching students to write a decent sentence would be more valuable to them than explaining why the Traveling Salesman Problem is NP-hard. In today’s climate, when high school educations are not what they used to be, spending a bit more instructional time on fundamental skills makes a lot of sense. And for me, it was fairly easy to take time away from some of the elective topics I normally presented toward the end of the course.


I believe that all professors in all disciplines have a responsibility to try to develop the writing skills of their students. In this piece I’ve presented the approach I take to try to get students to get to the ignition point, the point where they decide they’ll learn to write.

All of us aspire to be that passionate caring teacher who, through sheer force of personality, inspires their students to the ignition point. But I’m not that kind of teacher. What I can do, though, is work hard with students individually to improve their writing abilities. If you do it with respect and compassion, students see your efforts, and some will experience the change of heart required to get to the ignition point.


Clark, Andy, and David Chalmers. 1998. “The Extended Mind.” Analysis 58, no. 1 (January): 7–19. https://doi.org/10.1093/analys/58.1.7

Donald, Merlin. 2010. “The Exographic Revolution: Neuropsychological Sequelae.” In The Cognitive Life of Things: Recasting the Boundaries of the Mind, edited by Lambros Malafouris and Colin Renfrew, 71–79. Oxford: The McDonald Institute Monographs.

———. 1993. Origins of the Modern Mind: Three Stages in the Evolution of Culture and Cognition. Cambridge: Harvard University Press.

Hutchins, Edwin. 1995. “How a Cockpit Remembers Its Speeds.” Cognitive Science 19, no. 3 (July): 265–288. https://doi.org/10.1016/0364-0213(95)90020-9

King, Stephen. 2000. On Writing: A Memoir of the Craft. New York: Scribner.

National Center for Educational Statistics. 2012. The Nation’s Report Card: Writing 2011 (NCES 2012-470). Washington, DC: Institute of Education Sciences, US Department of Education. https://nces.ed.gov/nationsreportcard/pdf/main2011/2012470.pdf

Rose, Mike. 1989. Lives on the Boundary: The Struggles and Achievements of America's Underprepared. New York: Penguin.

Sheils, Merrill. 1975. “Why Johnny Can’t Write.” Newsweek, December 8, 58–65.

W. J. Hurley, PhD, is a professor in the Department of Mathematics and Computer Science at the Royal Military College of Canada.