# Incorporating Writing Components in Applied Mathematics Courses

By Lina Sorg

STEM researchers seem to frequently overlook effective communication to focus their energy on the technical methods in their work. However, strong writing and oral skills are imperative when corresponding with people outside of one’s immediate fields, pitching projects and solutions to clients or industry partners, and securing a job. Catie Patterson, an assistant professor of mathematics at Austin College, has found a creative way to incorporate writing projects into her courses on mathematical biology and ordinary differential equations (ODEs). During a minisymposium at the 2018 SIAM Conference on Applied Mathematics Education, currently taking place in Portland, Ore., Patterson spoke about these projects, their benefits to students, and possible future improvements.

Austin College is a small liberal arts college in Sherman, Texas, with approximately 1,300 students and an average class size of 25. Patterson’s mathematical biology and ODE courses comprise mainly of juniors and seniors. The students complete either two or three open-ended projects per semester in teams of three to four, and spend two to four weeks on each project. “My first goal for these group writing projects is teamwork,” Patterson said. “Since it’s a writing project, I focus on written communication, especially for one’s targeted audience.” She drew preliminary inspiration from *Writing Projects for Mathematics Courses: Crushed Clowns, Cars, and Coffee to Go*, a book by Annalisa Crannell.

Patterson gathers information from the students on the first day of class to gauge their proficiencies, inquiring about their year/rank in school; major; reason for taking the class; comfort level with skills like modeling and computer programming; and confidence in soft skills like writing, communication, and managing a team. She then launches into the projects, which students are expected to complete outside of class time. For the initial mathematical biology assignment, Patterson designed a scenario in which a fishery wishes to establish itself in the students’ hometown. She provides them with a single equation that they must simplify (nondimensionalize), leaving the students to figure out the equation’s meaning, justify it, clarify the variables, and make an ultimate recommendation in the form of a cohesive letter.

Realizing that this level of vagueness was perhaps a bit much for the first project, Patterson introduced a “project 0” assignment in her ODEs class. This scenario involves two fictional parents that are having a baby in two weeks, and requires the students to create a savings plan for that child’s college education. “The problem here is that this letter is really short, so it’s missing a lot of information,” she said. Data about college preferences, saving vehicles and interest levels, and salary is all absent. Because they are not used to working with word problems of this degree, some students were dissatisfied with the lack of examples and vagueness. “It’s supposed to be open-ended, so mission accomplished,” Patterson said. “It also makes students use LaTex, and is thus an opportunity to become familiar with LaTex without using too much math.”

Another ODE project centers on the world of Harry Potter, and was thus fun for both Patterson to create and the students to solve. In the problem, a disease from the wizarding world is transported to the non-wizarding world. The wizards want to squash the disease before it exposes their covert identity to non-magical people, so students have to employ three ODE models to prevent the spread of disease.

For all three scenarios, Patterson gives students a simple instruction list of guidelines and a sample rubric, and encourages them to come to her with any questions. Each group is responsible for turning in a paper—in the form of a letter—that addresses and answers the problem and a reflection document that dictates how well the team worked together and what they learned. Patterson suggests that students use Overleaf and Latex, and found that many also use Excel and Wolfram Mathematica. 60 percent of the grade comes from the mathematical analysis; 20 percent comes from the writing, in terms of clarify, grammar, LaTax use, and so forth; and 20 percent is a reflection of teamwork.

Patterson shared an ideal response to the hospital problem with the audience. The students in question included the meat of the math work in an appendix and kept the actual letter to the hospital succinct. This is especially important when writing for a particular audience. “I want them to focus on the fact that if someone asks you to do a task, they may not be interested in any of the details,” she said. “They might just want to know the answer. I want them to be able to put math in the background if necessary.” In a way, this trains students to be consultants and explain complicated math to a more general audience; the letter is for their audience, and the appendix is for their records.

The teamwork component of these projects is especially valuable, as students quickly learn that they cannot do everything themselves and must collaborate with different personality types. “They’re going to have to work with people no matter what they do,” Patterson said. Despite the tasks’ success, she plans to continue tweaking them in future semesters with a stronger emphasis on proper letter formatting and a better division of content between the response letter and the appendix. “I want to emphasize a little bit more clarity in the information the students give in the appendix,” Patterson said, in terms of labeling all figures, axes, and legends; defining all variables; and assigning numbers to the equations for reference. She is also toying with idea of a team contract to clarify everyone’s obligations to one another. Nevertheless, her unique incorporation of writing and communication into mathematical curricula undoubtedly sets her students up for future STEM success.

Lina Sorg is the associate editor of SIAM News. |