You only have 30 minutes so they can't expect this to be too deep. I would break the demonstration into two parts.
- 20 minute teaching demo
- 10 minute discussion of teaching methods
Actions speak louder then words so I would show them how I teach first. If you start with a discussion of your teaching methods, the committee will probably interrupt with a bunch of questions and use up all the time. If time matters this could be a serious problem.
For the demonstration, it's best to stick to a topic that I have complete mastery over and need no notes or textbook to teach anymore. I will already be nervous and don't need the cognitive overload of trying to teach a topic I do not totally own.
The actually teaching method that I would use would be a conservative one because I am trying to show mastery of teaching. I would not try to teach in a new experimental way unless I have already thoroughly mastered such a method. Better to lecture with perfection than to try cooperative learning with utter failure. Below is a sample lesson plan that would work for a statistician.
- Explain what the students are going to do today (2min)
- Demonstrate the new skill (7min)
- Practice the skill together (5min)
- Allow the students to practice the skill individually or in small groups (5min)
- Correct together (1min)
For the discussion on teaching methods, I think they want to know more than just what methods I used because they just saw that. I think what the may want to know is about my philosophy, which is why do I teach or use the methods that I use. So this provides me with an opportunity to explain what I was trying to do during my demonstration. Why did I explain to the students the purpose of the lesson? Why did I demonstrate instead of lecture? Why did I do practice problems together? etc. Please keep in mind that teaching methods are derive from various philosophical positions about teaching/learning so understanding your philosophy of teaching is providing a deeper explanation of the methods you use.
Again, putting the discussion at the end assures that I have time to demonstrate my teaching and allows the committee to ask questions during the discussion.