I'm a math grad student, and next semester I start TAing a calculus class for the first time. We all know about the standard recitations: instructor gives short lecture on some more difficult topic from class, then spends the rest of class solving homework problems on the board. I personally find such recitations extremely boring, and I have a hard time seeing how students (who often don't even take notes!) can learn anything useful from a recitation like this. Most students I know just show up because the problems the TA solves are free marks on the homework.
I'm wondering about more interactive ways to run a recitation. Right now I'm thinking about making the students attempt all problems using think-pair-share. Students get to work for a few minutes, then pair up and talk about their solutions with someone else, and then we work through the problem together on the board. We might not get through as many problems, but it should make the students more involved in class.
Would this be a good way to run a recitation? What are some other ways to run a recitation to encourage student participation?