So there's an argument for going into the classroom (as a teacher) completely unprepared, stumble through the material, reason things out in fron of the students, go down hopeless calculations for a while, then say "scratch that", "let's see....hmmmmm", etc....Nothing should be clear, the students would have to make huge efforts just to find out what's on the hw. I know some people like this (not by design). I wonder if their students learn some important life-skills though.
I sort of unintentionally had this happen to me. When I was 13 I moved to a new school which was a little less competent than my previous school. In my previous school all the information was packaged and delivered to us to memorize. In this new school the teachers would just roughly go over the topic and it required a lot of independent effort on my part to understand the subject matter.
This led to this mini explosion of clarity in my head. While in my previous school I was bored of learning and depended almost exclusively on rote memorization, this new school forced me to think about why I know what I know. This transformed me into an incredible math/science nut. Just taking the information into your own hands and thinking about it turned me into someone who constantly raved about the beauty of mathematics.
In my own experience, this can work well in a small group with engaged students. I had an excellent optics class where we would try to derive a known result as a group: the professor would explain the experiment, draw a picture, and then ask us to help. If we got him going, he would take a few steps, then ask again. Now, I remember next to nothing of equations for optics, but I have a very good idea of how to go about figuring out the outcomes for various experiments theoretically.
On the other hand, I've had professors stop referring to notes partway thro... (read more)
So there's an argument for going into the classroom (as a teacher) completely unprepared, stumble through the material, reason things out in fron of the students, go down hopeless calculations for a while, then say "scratch that", "let's see....hmmmmm", etc....Nothing should be clear, the students would have to make huge efforts just to find out what's on the hw. I know some people like this (not by design). I wonder if their students learn some important life-skills though.
In my own experience, this can work well in a small group with engaged students. I had an excellent optics class where we would try to derive a known result as a group: the professor would explain the experiment, draw a picture, and then ask us to help. If we got him going, he would take a few steps, then ask again. Now, I remember next to nothing of equations for optics, but I have a very good idea of how to go about figuring out the outcomes for various experiments theoretically.
On the other hand, I've had professors stop referring to notes partway thro... (read more)