Often, I have students ask me insightful questions that are not within the scope of the current discussion, but none the less offer to provide a deeper understanding of the material. The difficulty lies in the fact that these questions are not traditionally taught or covered in the classes. I have taken to recording the questions and incorporating them into future discussions. This provides two benefits to the students: 1) It brings student participation and interest in the material up, and 2) It provides alternative ways to explain the same material.
As I discussed in my teaching philosophy, I center my teaching around making sure students are involved and not just passive listeners. This has led to many interactions that have ended up deepening the understanding of the material for all students in the class, and not just the student who originally asked the question. In addition, as evidenced in the video teaching sample, I make sure to ask students to answer conceptual questions throughout the instructional period to increase participation and understanding.