By Della Dumbaugh, Professor of Mathematics, University of Richmond

With the sudden shift to Zoom classrooms in the spring of 2020, I found it difficult to connect with students and uncertain of their understanding of critical content. On a whim, I resurrected and reconfigured a tool from graduate school: the oral exam. This assessment tool not only helped me address both of these issues but it also gave students an opportunity to improve their communication skills, conquer anxiety, and solve problems quickly and confidently.

How I Did It: Less is More

I started small and grew from there. Initially, I incorporated weekly five-minute oral quizzes on a precise topic. In my group theory class, one week I focused the oral quizzes on how to show a set is a subgroup. I advanced to twenty-minute tests where students worked five problems from various areas. For my Calculus II final, for example, students had one integral, one differential equation, one application of an integral, and two questions about series.

How I Did It: Scheduling

Students schedule their oral tests on a shared google document. They are responsible for creating an appropriate oral test-taking environment. They are creative: they tape paper to the wall to use as a makeshift blackboard, they position the computer to the side of their desk where I can see them working on their paper, or they present their work at a white board. They upload a pdf of their paper or a photo of their work on their white board to Blackboard (our class management system) once the exam is over.

How I Did It: Grading

I invest in a stack of legal pads at the beginning of the semester. I write out the time and a problem at the top of each page in advance of the oral exam. This strategy helps to prevent bias. When the oral exams begin, I open the google doc with the schedule. When the designated student appears in the zoom window, I greet them and give them their problem. I grade synchronously in the margin of the paper as I go along following the same system I would use on paper. For example, if a ten-point quiz problem is about showing where a function is increasing, I might assign three points for understanding that this problem is about setting the derivative greater than 0, four points for taking the derivative and three points for identifying the actual x-values where this is true. I do not discuss grades with the student during the oral exam. Later, I enter grades on Blackboard at the end of all of the exams. I often include comments with a student’s grade.

Secret to Success: Oral Exam Primer and Sample Oral Exams

I ask students to watch a six-minute “Oral Exam Primer” video I created to introduce students to the benefits of oral exams and how to prepare for them. The last part of the video includes two “sample oral exams.” Students watch these sample oral exams multiple times. They report that these sample oral exams give them confidence about what to expect and help them understand how to talk about mathematics.

What Students Gain: More than Mathematics

Students learn how to talk about mathematics. They practice by giving each other oral exams. When mathematical content drives social conversations, students gain a much stronger understanding of the material. As a faculty member with more than thirty years of experience in the classroom, I have discovered so many new insights from listening to students work problems out loud. When a student proves Lagrange’s theorem in an oral exam, for example, it is very clear whether or not they understand the role of equivalence classes and their properties and how they relate to cosets.

Students gain fast-paced problem solving skills. They identify the essence of a question, weigh various approaches to the problem and then make a decision about how to move forward. This collection of skills will serve them well in many professions. 

Real Time Feedback on Math and More

I use the waning seconds of an oral exam to affirm students. I often remind them of both the mathematical and broader skills they demonstrated in their oral exam. “You just proved Lagrange’s theorem,” I might begin, “which hinges on a solid understanding of subgroups and equivalence classes and their properties…this testifies to your ability to manage and organize layers of complex information. That skill will serve you well in the workplace.” If the student did not do as well as they would have liked, I might offer, “well, today was not your day. The good news is you did show a solid understanding of the derivative of a function, and we have another oral quiz next week.” I make sure to identify and celebrate their courage the next week when they pop back in the zoom window.

What Faculty Gain: Clearer Insights and Stronger Relationships

Oral assessments offer a more accurate understanding of what a student knows and does not know. They provide faculty with an opportunity to focus on the student and offer real-time feedback on their work. The time together also fosters stronger student-faculty relationships. I learned the strength of oral exams when I offered an extra credit assignment that could replace one weekly oral quiz. The first student who did the extra credit announced at the beginning of the next class, “I did the extra credit but I’d still like to take my oral quiz this week.” It turns out students like presenting mathematics to an attentive audience.

Variations on a Theme: Make Oral Exams Work for You

There are many ways to incorporate oral exams into your classes. One of my colleagues divides her large number of students into two groups and quizzes each group every other week on different problems. This approach allows her to maintain consistency for her students and a reasonable schedule for her. As a bonus, students in alternate groups quiz each other on “their” problems.

Another colleague posts six problems (without solutions) 48-hours before his oral quizzes. During the oral quiz, he asks students to present one of the problems with a solution (their choice) and then evaluate a possible solution to another problem. For the latter, the student determines the validity (or not) of the solution and identifies the steps (or lack thereof) involved. As one of the students in this class described it to me, “I have never studied so hard for any math class. As soon as the problems are released, I start working them. Once I have a solution, I go over it three or four times to make sure I know all of the steps. I love presenting my problem during the oral quiz. I have a fun time thinking about the one I want to do. The other one though? Those are tough. By working the problems multiple times I can usually recognize a solution or if it’s problematic.” This technique has the added benefit of teaching students the value of working and reworking problems.

Oral Exams for the Future

Going forward, I plan to incorporate oral exams in my classes even after the pandemic subsides (in person!). They do take time. The benefits, however, both in terms of understanding and conveying mathematical insights and cultivating life skills, are worth the investment.

For more on oral exams, see my “Revitalizing Classes Through Oral Exams” in Inside Higher Ed.