My appreciation for unusual teaching methods began as an undergrad, with my favourite teacher of all time, Warwick Armstrong. A radical Romantic inspired by Paulo Freire, Warwick would make a point of dispensing with the usual classroom trappings. Before each session of his fourth-year geography class, Warwick would clear all the chairs or desks out of the room, to create a completely flexible space. We would typically begin by sitting on the floor in a circle for conversation; soon we would divide into groups to work on projects and - just as often - create dramatic performances to get across points made in the course. Warwick had strong opinions about the material he discussed in class, much of which I disagreed with, but open debate was a centrepiece of the class environment, and fifteen years later his ideas have stayed with me far more than most other professors'.
I have not yet been quite bold enough to follow that sort of method in the classes I taught myself; I think that, like a jazz musician, one needs to be better versed in the conventional scales before one can improvise well. If at some point I had been teaching the same material for five years, I might well move to something like that. But having such an ideal to aspire to left me with an active interest in experimenting with teaching. I did teach a course on the model of Warwick's graduate course, which he set up as an Oxford-style tutorial: the class was based above all on student projects, so that in the second half of the semester class the readings were recommended by the students themselves based on their work.
I've also used dramatic role-playing exercises in several religion classes. Having students act out the roles of participants in a conflict is useful both in situations where they might feel too distant from the subject matter (say, the partition of British India) or where they might feel too close to it (exploring theological differences between Catholicism and Protestantism at a Catholic school). It gives students a way to relate to the material directly but without raising the personal stakes.
I've experimented a lot with interteaching as a way to get students learning actively in peer discussion. It was particularly helpful for my classes at Stonehill, where students were often reluctant to participate or ask questions in large-group discussions. And, of course, I regularly experimented with teaching technologies including discussion forums, grading rubrics and Facebook communities.
In my course on Indian philosophy, I experimented further with innovative teaching. Drawing on Blau and Caspi's pedagogical research, I fostered student collaboration through in-class cooperative research, using Google Drive to help students work together and comment on each other's papers. I also had the students discuss their reading before class on a WordPress blog, and asked the students to post their final papers on a Google site so their research could be shared with the wider world.