In my Transition to Proof course last fall, I began building concept questions to supplement the regular proofs, and using them to target specific misconceptions or difficulties that students are having (or that I expect based on past experience). By concept questions, I mean short questions, usually multiple choice or true/false, that are designed to draw out students’ thinking and generate productive disagreement. Every time we had one of those discussions, I was exhilarated by the amount of discourse in the room. This practice evolved because I promised myself that I would focus on getting more discussion out of students in that class, since, in the past, I felt that there were too few students able to comment or question the proofs presented by their peers at the board. With the concept questions, I felt like I was seeing what the students were getting or missing from those proof presentations. In particular, the questions really helped to draw out the main points of proofs, points that I thought they would have gotten from a direct discussion of the proof, but which may have been less apparent than I had assumed. I almost feel like students in previous iterations of the course were shortchanged because they did not get this added layer of discussion to push their thinking forward. That’s when tinkering pays off.
As a result, I have planned some form of concept questions into both of my courses for this fall. Accompanying this change, I have also included the concept questions into the course grade. In addition to using the concept questions as a teaching tool, I am curious as to: (a) whether simply participating in the concept questions correlates with performance in the course, and (b) whether answering questions correctly on the first try correlates with performance in the course. Most of all, I would like to know whether using the concept questions as a tool in class improves the class’ understanding of the key concepts, but this will be hard to measure. I am thinking that I may have some items on some exams in one of the classes that I will reuse from prior years, so that I can compare performance. That’s not as good as an experiment, but at least I will have a basis for comparison.
The larger message is that it is healthy to revisit one’s goals for a course, to think about personal goals for improving one’s teaching, and to be willing to try new ideas that show promise of bringing students closer to the learning goals, and to measure the impact of the changes so that what works remains in place, and tactics that don't work are revised or edited out of the course.