As I was searching for "teaching polar coordinates" materials from an NCTM workshop I attended a while ago, I came across a packet that described scaffolding. I liked their 4 tier process they layed out:
1. I teach, you watch
2. I teach, you help
3. You do, I help
4. You do, I watch
I got me thinking about how I've been teaching lately, and about how different uses of these 4 steps work for different populations of students. I think lately my philosophy is more "2", then practice based on "4" with help if I see they need it. I teach preAP and AP classes that are supposed to be for students willing to try things on their own, but realistically has a whole range of abilities. I internally balk at running through all 4 steps because it makes me think of them learning math by seeing, "oh, this is THE method/way of doing things. I will memorize this technique and parrot it back when tested".
I want them to think for themselves. But then another part of me says, "well, they have to learn the basic skills first, and THEN you can throw in some harder thinking problems". And then a 3rd part of me is inundated with comments of "hard homework" and "you didn't teach us how to do THOSE types of problems". I, apparently, need to have more time to think through each lesson and map out my strategy of presenting concepts then mixing the types of problems effectively .... maybe with some warning about various problems and hints (?) and admonitions to actually put forth some effort on the more challenging ones.
Anyhow. Then that got me to thinking about how I store my teaching materials, and how my plan has evolved since I started teaching. I use those large plastic tubs (with tons of hanging files to store papers). I have 4 tubs currently: one for precalculus, 2 for calculus, and 1 I just started for algebra 1.
My hanging file folders used to be: "chapter 1", "chapter 2", .... because I shortsightedly thought I'd ALWAYS be teaching out of the same book and the same school and the same topic. Then I think I moved to large groups of topics in each hanging folder. I'd have to paw through all the papers each year when the time came to teach concepts. Then, for some reason, I moved to "first 6 weeks", "2nd 6 weeks", ... (what was I thinking). Maybe I was a masochist or liked to take tons of time to sift through the whole pile every time I had to teach something.
I finally wised up (at least it's working MUCH better for me) and added manila folders inside each large hanging folder, and the manila folders have concept titles: "vectors", "triangle area", "graphing lines". I've also used large sticky notes attached to lessons to make my reflections about how a topic went after I taught it the current time and possible suggestions for the future teaching of it. MUCH more convenient and time-saving for me.