I am lucky enough to be teaching a course on Galois Theory that only has five students in it. The set-up of the course is this: we are working out of Pinter (which I really like due to its ease of reading, great problems, and price of $12; I don’t like that he defines subgroups/subrings/etc in a weird way and is sloppy with defining variables), and students present problems from the textbook to each other.

This will be obvious to people who do IBL, but: holy cow do you get a sense of what students understand and what they don’t. A large part of this is the small class size, but this IBL-like format helps. What students understand (or not) is often not what I would expect.

Because I only have five students, I am doing oral exams. The format is this: I give them four problems the week prior to the exam. Students are allow to work together to figure out the answers. They come to the oral exam having written one of the four problems up nicely in LaTeX. The oral exam starts by the student choosing one of the remaining problems and explaining it. I then (randomly) pick one of the two remaining problems. The session ends with me presenting a problem they haven’t seen before (I try to make these easy enough that the student should know what to do immediately). We will do these exams four times during the semester, and they take 30 minutes per student.

Once again: this testing format makes it crystal clear to me what (and how well) students understand things, and it is clear how I should adjust the in-class work based on the information I get from the exams.

I am wondering if this could scale: could I give a class of 25 students, say, 4 questions, have them write up one, and then have them *write* the solutions to a subset of the remaining problems? I like that this is a learning opportunity for the students, since they get to learn from each other in an exam situation, but they are still individually accountable. However, I am wondering how much is lost if the exams aren’t oral.

Thoughts?