Nine hours over three days were required to complete the oral final. It was a test of stamina for me. Yet surprisingly pleasant.
One week in advance, students were given nine questions on which the examination would be drawn. They could use all resources available to prepare including but not limited to: each other, books, notes, and the internet. However, during the examinations students were limited to an 8.5 x 11 sheet of notes (or prepared material as allowed by the questions.)
Each student had 20 minutes to present two questions, the first question being their choice and the second was mine. Questions were graded holistically out of 50 points modeled on a rubric from Boedigheimer, Ghrist, Peterson, and Kallemyn in “Individual Oral Exams in Mathematics Courses: 10 Years of Experience at the Air Force Academy,” PRIMUS, Volume 25, 2015 – Issue 2.
Students could reject my chosen question for a four point reduction, twice. And at the end of the exam, I asked them for a self-assessment of their performance by question.
Some of the questions were borrowed directly from Francis Su’s 7 Exam Questions for a Pandemic. Others tried to encourage reflection and connection between topics in the course. Nothing required extensive computation—unless understanding was procedural rather than conceptual. Still others asked that students learn and prepare new material and connect it to fundamental ideas in the course. (With the first week of the quarter being a “soft start” and everything taking longer online, some topics had to be axed. Though it pains me to admit it, I let go of orthogonal complements in favor of spending more time on linear transformations, eigenvalues, and eigenvectors. At least I got to ask the students to read and prepare that material for the final exam rather than letting go of it entirely.) Here are the questions if you are curious.
You can download the question to see them more clearly.
- Everyone was nervous about this exam format—especially the English language learners. I reassured them this was not about the polish of the presentation but the quality of the content.
- Twenty minutes was enough time and because it was limited, it really kept everyone focused and on task. When there were technical difficulties it threw a wrench in the machine. The time overages added up and by the last appointment of the day I was frequently 7-10 minutes late.
- Student self-assessments were reasonable and reflected both the actual exam and their preparation. If anything, their scores were harsher than mine.
- It was obvious who had found answers online and were parroting solutions. All I had to do was keep asking clarifying questions to see if they really understood what they were saying.
- Things that surprised me:
- Questions 1, 7, and 8 were the most popular perhaps because they felt more traditional.
- Question 9 was the most commonly rejected question.
- No one chose to discuss mathematical beauty.
- Best part: once the examination interviews are done, so is the grading! I was probably too generous in my grading—but no one ever complains about that.
I will absolutely do this again. There are no worries about academic misconduct. Students spend time reflecting and synthesizing the course material rather than rote memorization of concepts. It could be even better with scaffolded activities to prepare for the oral examination or having the conversation in person. I will definitely add oral examinations to my toolbox whether teaching remotely or in person.