Yesterday after school our statistics teacher mentioned a conversation she overheard from 2 students about how my calculus class so far is easy and a review of precalculus. I agree with the "review of precal" statement. In our precalculus strand, we spend quality time on limits and even start a pretty thorough discussion on derivatives. Now in calculus, the first 10 days or so is spent on limits. Then we move on to derivatives which I believe only the first part will be a review. Now granted, this is only a total of about 15 or so days overlap .... 3 weeks .... but it got me to rethink things.
My initial intention at the start of the year, was to thoroughly hit limits, and then to throw AP exam type questions at them. ... I had to wait because the questions I found involved stuff we hadn't gotten to yet. Well, so today, I gave a brief discussion on our current limit topic: continuity and one-sided limits, and then gave them 5 really challenging problems to start on and finish for homework. I'm curious to see what I get back tomorrow. Based on some of the performance in class, I'm guessing that we'll have to discuss what are acceptable answers. It looked like lots of students had that "deer in the headlights" look.
I always find it fascinating that you can do the best job that you are capable of the first year you teach a subject, ... I mean, you really, seriously put thought into how you will teach something, and then after you've road-tested it, you see what problems the kids have, or you have a brainstorm in class about how better or different you could have done it, and you make notes for next year. I'm thinking that the 3rd year you teach a subject is when you really start to get your groove going.