I'm not sure if you know about Taylor Mali, but you need to. He is an outstanding poet whose work usually deals with teaching. As I was sitting here, grading my calculus homework and thinking about today's lesson, I thought I wanna teach like that, like the first snow, falling.
There are moments now when I think the students are really intrigued and on the edge of their seats, but there are also so many days when I'm just working to push through what needs to be covered next in the book. And that's where my problem is. I follow the book too closely. I am a slave to the next section, to the order they present things in. If we start a conversation about graphing derivatives and it's not talked about for two more sessions, I follow the conversation for a few minutes until their interest is semi-satisfied, then I say, "More on this in two days." Why not follow the topics they want to talk about and go back to today's lesson some other time?
I think that simply making that change, to actually teaching on what's relevant at the moment and not what comes next, is the change that my teaching is looking for this year. Something needs to change. I'm flat lining. Modesty aside, I'm good teacher but I'm no where near a great teacher.
I'm afraid. What if we don't have enough time to cover everything that we need? What if I skip over a concept or a theorem that they were supposed to know, but I just missed it somehow by not following the book? I think I've been teaching my calculus material long enough now that I'm familiar enough with it to know about skipping things. And maybe I will have to take days where I cram a bunch of "book facts" at them instead of concepts. I know I can find a balance and it won't destroy my students.