Dan Meyer at dy/dan just posted about teacher-student analogies. His analogy is that the student is like a weight lifter and the teacher is the spotter. I like this. It is similar to my usual analogy that the teacher is like a trainer and the student doing some exercise. Another analogy I often use is a person learning to ride a bike. The learner is the one doing stuff, not the "helper" or "facilitator". I am really not sure what to call the helping person. Maybe the Yoda would be a good term. I like that.
Look at a person learning to ride a bike (btw, here are my tips for learning to ride a bike). Could you imagine teaching "bike riding 101" in a lecture class? I could make some awesome power point slides about bike riding techniques, rules for bikes, the history of bikes, and bikes and the environment. If I were really motivated, I could actually demonstrate bike riding for the class.
No. This would not work. None of those students would know how to ride a bike after the course (assuming they didn't already know). Instead, they need to get on a bike to learn. Yes they will fall some. Maybe I will hold on the back of the bike a little (no, I promise I won't let go. Ooops, I lied).
The thing I like about the weightlifter-spotter, after the workout the weightlifter is sore. If you are going to get stronger, the lifting of weights is going to hurt a little. The same is true for real learning, it will make you sore in the head (confused). This is a natural part of learning. I like to tell my students, if you don't get confused you either didn't do anything or you already knew it.
Let me end with my favorite part of Dan's post about weightlifter-student analogy. Talking about how the spotter is the teacher:
"And, my word: we're spotting thirty people at once"
There was a session at AAPT- I think it was LF: Good Teaching Ideas- in which a teacher - I think it was Diane Riendeau- who gave a great example. She explained to us how to knit. Could we knit, after listening to her explanation? Well, I couldn't. Then her helpers passed around skewers and yarn, and we all REALLY learned to knit. Anyway, it was a really cool teaching demonstration. It feels a bit overwhelming to me to be a spotter for 30 people at once, but I think I could teach 30 people to knit at once. Or maybe not knit, but I think you know what I mean.
I think rather than trying to spot 30 kids at once, I'd like them to be able to spot each other. By becoming the teachers, they will learn that much more!