The Mathematical Language of Change: Teaching calculus during the pandemic

Editor's Note: Reda Ansar is a columnist on The Collegian.

On a Thursday evening in a normal summer, Dr. Della Dumbaugh's house would be full of students chatting together and finding derivatives on a giant chalkboard. After attending class on campus during the day, they would reconvene at her house for an evening of calculus review and community building. This summer, however, the giant chalkboard and abundant seating in Dumbaugh's home went unused.

Dumbaugh, the assistant chair and professor of mathematics, did not let the closure of campus nor inability to teach in person from creating a unique learning experience for her students. For her first time ever, Dumbaugh held an entirely online Calculus I course at the University of Richmond. Dumbaugh, who has taught calculus at UR most summers since 2011, said this five-week course in May and June received significant interest from students compared with recent years.

"With the pandemic, we had an extraordinary number of students who wanted to take Calculus this summer," Dumbaugh said. "I would estimate three to four times the number of students who ordinarily want to take Calculus were interested, at least.

"I think students realized their other opportunities — their internships, their jobs — were canceled, and they wanted to move themselves forward toward their degree or towards their career goals. And calculus is probably part of that."

This was the case for rising sophomore Reda Ansar. Although she was already planning on taking classes this summer, the cancellation of her job and internship plans made it possible for her to take more classes than she originally planned, she said. Of the three classes that she took remotely this summer, she said Calculus was her favorite. 

"I think the class was the best class out of all of them to take online," Ansar said. "I think it was a little bit more difficult for the discussion-based classes, whereas calc is just 'Here are problems' and then you solve them."

The class included brief lecture videos for each lesson, with homework assignments due daily, Ansar said. Students did oral quizzes on Wednesdays, review sessions on Thursdays and had a test each Friday, Dumbaugh said. 

Listening to students work through their problems aloud during oral quizzes was beneficial to her as a professor, Dumbaugh said. 

"I will have oral quizzes and tests as an integral part of all of my classes this fall and probably going forward. I did that this summer and it was so successful," she said. "In an oral quiz, I give feedback right at the end. Instantaneous feedback is really helpful for students and for me as a teacher because it helps me see real-time what they do and don't understand."

Some students, including rising sophomore Serena Pollard, were concerned about oral quizzes at the start of the course. But, as the class continued, her attitude changed, she said.

"Initially, I was quite hesitant about performing oral quizzes, but as I took more and became comfortable with them, I began to enjoy them," Pollard wrote in an email to The Collegian. "For me, as the semester neared the end, I began to prefer the oral quizzes rather than the written quizzes, as verbally explaining math made more sense to me than writing it out."

Beyond the benefit of helping students understand concepts, Dumbaugh said that the oral quizzes ended up being a successful way of building relationships in a remote class.

"I love working with students, so I had to figure out a way to make that happen as part of the class," she said "[Using oral quizzes] was really rewarding for me, because even though it took a lot of time, I got to be with students."

Relationship-building is an important part of teaching mathematics, Dumbaugh said. In an effort to create community within her class, she created a class Facebook page, offered extra credit opportunities for group work and hosted regular Zoom meetings open to the whole class, she said.

Despite these efforts, rising sophomore Whitney Clark acknowledged the difficulty of building relationships in a virtual class.

"I found it hard to build relationships with classmates that I didn’t know prior to taking this course," she wrote in an email to The Collegian. "This is probably because we weren’t all together in a classroom setting trying to get to know each other."

Other students did not feel a loss in relationship building because of the class' remote format.

"Although building relationships was different, as I was not seeing my classmates face-to-face, I don’t think it negatively affected my ability to create relationships with classmates or my professor," Pollard wrote. "Honestly, I believe I created a better relationship with my professor than I would’ve having been in the classroom."

For Ansar, the social elements that Dumbaugh added to the course made it possible for her to get to know her classmates, she said. 

"After the test was finished, we would just sit and talk about the homework, about what this week was like," Ansar said. "There were a lot of opportunities to meet each other, ask questions, so I think that most people enjoyed it."

The importance of building relationships in her classes ties to Dumbaugh's value of using math as a way to go beyond the classroom. 

"One of our extra credit opportunities was to read an article in the New York Times and post something interesting about it," Dumbaugh said. "Some students found lots of interesting articles — that's how we learned about each other. I mean, this was never just about calculus. That was required content. But I'm teaching calculus so that my students will be stronger and better prepared for the workforce."

And as that workforce morphs in the face of our current global health crisis, Dumbaugh sees value in learning calculus specifically.

"You have to remember, calculus is the mathematical language of change," Dumbaugh said. "So it's a great class to take during the pandemic. I mean there's so much changing uncertainty around us right now, why not take the mathematical discipline that studies how to talk about that? And that's what these students were doing."

For Dumbaugh, creating an entire course in the midst of a pandemic was not an easy feat, but she attributed much of the course's success to her students, she said.

"I have to give the students a lot of credit, because the students were willing to try new study techniques and meet with each other," Dumbaugh said. "I don't know what their expectations were on the front-end, however, they rose to the occasion."

As we begin a new semester in which many students will be adapting to remote learning in their classes, Dumbaugh provided encouragement for students to take initiative.

"My students made friends, they worked together, I think we had a class spirit and community," she said. "My main encouragement for students taking classes remotely is if you invest in the class, if you take the lead, other students will follow you. And that will help your class and will just enhance the learning."

Ansar, admittedly terrified about the possibility of having all remote classes, also sees the potential for students to make this semester positive, she said. 

"I think with virtual, the main thing is it's what you make out of it," she said. "Even on campus, I took some classes that just did not work for me. I think it's quite the same thing online, really. There has to be a lot of self-motivation, but it's doable."

Adapting to a remote format is easier said than done, Ansar said. But after practicing online learning this summer, she remains positive that it can be a valuable experience.

"I had a few professors who had never done remote work before, but they handled it like a champ. And genuinely, now that all my classes are over, I really do feel like I got something out of all of them."

Contact multimedia editor Nina Joss at nina.joss@richmond.edu.