The oral exam is not just for graduate school. Surprisingly, I found that teaching mathematics online during COVID-19 infused the seemingly antiquated tactic of oral exams with fresh purpose.

With solutions and other resources readily available online, students can gain a false sense of security about content, and faculty members can have a difficult time assessing what a student knows. Oral exams provide a way to deal with both issues simultaneously. Updating oral exams for the 21st-century virtual classroom helps students improve their communication, conquer anxiety, solve problems quickly and think creatively. They also give students an opportunity to articulate layers of sophisticated thinking in an organized fashion, a skill they can take with them to any workplace.

I’ve used oral exams to assess student understanding in mathematics classes from calculus to upper-level theoretical courses. I’ve also used them to build relationships with students. They were a huge success for the students and for me. Below I outline some strategies for using oral exams in the classroom and associated benefits for students.

**Nuts and Bolts**

Some of the basics for conducting effective oral examinations include the following:

**Less is more. **Set specific, discrete content for each oral assessment. For oral quizzes, I typically focused on a single topic -- say, applications of the derivative. For the exam, I asked students to tackle five problems covering precise topics.

**Sample exams.** Students are often unfamiliar oral exams of any kind, and I don’t want that unfamiliarity to interfere with their ability to succeed in mathematics. So I asked two students to take their oral quizzes a day early and allow me to post them for other students to view. Students reported that these practice oral quizzes gave them confidence about what to expect and helped them understand how to articulate the steps in solving problems. It was a win-win.

**Student scheduling. **Create a Google Doc with specified times and make students editors so they can each schedule their exam.

**An investment in legal pads. **Consider writing out questions for students in advance of their oral exam on a legal pad, which I found allowed me to move from one student to the next with ease. I used the left-hand margin to grade synchronously. I entered the grade and comments on our Blackboard system after I finished all of the quizzes or tests.

**What Students Gain**

Students learn much more than just the subject matter of their oral exams. They also gain:

**Communication skills.** The students were responsible for communicating sophisticated mathematics in a timed setting. As one student reported later, “At first, I was afraid of the oral quizzes. After I took one, however, I realized how much I liked to talk about math. I started meeting with a friend after that so we could talk about problems together.” When your course content drives social conversations, students gain a much stronger understanding of material. And, in many ways, the oral exam provided far fewer distractions than a paper exam in a classroom with students coughing, drinking from water bottles and so on.

**Skills for conquering anxiety.** A talented 6-foot, 7-inch basketball player would appear in his rectangle on Zoom visibly nervous at the start of his oral quiz. After I gave him his problem, he would repeat it back to me and then take a deep breath. Those 17 seconds seemed to help him gain his focus and direction. Then he would begin, “This is a problem about a derivative …” This student was fully prepared to sink a three-pointer with 1.8 seconds left on the clock to win a basketball game but found himself challenged by a question about where to find the horizontal tangent line of a function. Expertise in both areas will help him find success off as well as on the court.

**Fast-paced problem-solving and creative skills. **Students had a short time to solve a demanding problem. They had to identify its essence, weigh various approaches and then act -- skills that will serve them well in many professions. For students who aspire to a career as a physician, for example, they will evaluate patients, consider this information to make a diagnosis and, finally, outline a treatment or medication, often while a patient is waiting. I hope an oral exam in calculus will begin to build the necessary skills to complete this multipart task with finesse. In my course, students created elaborate testing environments at home where they could capture and convey their ideas with available technology. One student taped paper to the freezer portion of her refrigerator and presented her work like a teacher.

**Presentation skills. **Although these students regularly attended our remote class in sweats and T-shirts, they took showers, brushed their hair and put on button-down shirts for their oral quizzes. I did not include dressing appropriately as part of the instructions, but the old adage of "dress for success" is alive and well. Students recognized that looking professional made them feel better about presenting their work.

**Real-time feedback. **In a typical in-person classroom, students take some sort of exam or other form of assessment on paper in class and submit it. Even if faculty members grade such assessments promptly, students will still have to wait several days for feedback. With an oral exam, in contrast, you can see immediately what a student understands or not and point them to particular areas for further study.

One student, for example, worked a derivative problem beautifully but could not evaluate a trigonometric function at the end. I responded along the lines of: “You just did beautiful, sophisticated work that showed a solid understanding of how a derivative works and what it tells us about the function. Your last calculation hinges on a firm understanding of an important trig function. I’m going to schedule you for a follow-up discussion at 5:30 p.m. By then, I’d like for you to have learned the graph of that function and some basic values.” At the scheduled time, the student reappeared on Zoom and demonstrated a stronger understanding of the function.

**Harnessing the Power of Oral Exams Elsewhere in the Classroom**

The success of the oral quizzes led to the creation of an entirely new approach to studying for the final exam. Individual students *volunteered *to work one important problem to prepare for the exam. I met with them over Zoom and recorded each student working through their problem and then collected those videos in a folder on our Blackboard site titled “Video Final Exam Review.” I encouraged students to use even three minutes of their free time to view one of the videos and work through a problem that would help prepare them for the final.

Students absolutely loved this collection of problems and reported that, indeed, in the moments before dinner, right before bed or in an afternoon lull, they would go to the folder, click on a video and work a problem. “Sometimes I watched the same video a few times just so I could get down all the steps,” one student commented.

**Benefits for Faculty Members**

Oral exams provide an accurate assessment of what a student knows -- and does not know -- about the material. Surprisingly, it only takes five or 10 minutes to gain insight into a student’s understanding of mathematics. As a thought experiment, try to talk about mathematics -- or any academic discipline -- for five straight minutes. That’s a long time for one person, especially an 18-year-old in a calculus class, to talk about their knowledge without interruption.

Students cannot hide in an oral exam, which also allows faculty members to grade more efficiently. You can grade on the spot. Most important, oral exams can bring joy to you as the instructor. When my institution went online, I had struggled to find the same delight in the remote setting of a classroom consisting of 1-by-2-inch rectangles on my computer screen as I had in the classroom. An oral exam with each student reminded me of why I got into this business in the first place -- to advance students through scholarly pursuits, in particular, mathematics.

**Beyond the Remote Classroom**

Looking forward, I will certainly make more extensive use of oral exams in my classes this fall. Currently, my institution has adopted an “aim for in-class but be prepared to move remote” frame for the fall. I plan to incorporate oral quizzes from the start of the semester, even when we return to a more traditional classroom setting.

In the first days, I will have students use their oral quiz time to introduce themselves. From there, I will begin weekly content-based oral quizzes. Yes, oral quizzes take enormous amounts of time. The benefits, however, in both mathematics and in life skills are well worth the investment.

*Della Dumbaugh is professor of mathematics at the University of Richmond.*