Hectic times, low on sleep, high on things to think about. I like that even after 12 years of teaching I still have epiphanies. This last unit in AB calculus was derivatives and integrals involving e^x. In the past I've always grouped the derivatives and integrals on one day and was always amazed that my set of kids just confused everything and didn't know what to do and when to "go forward" and when to "go backward". I also used to just give them a brief intro to the basics and then start tossing challenging problems at them that I thought made them think, but apparently just confused them more. I also used to cut and paste from various sources and cobble together a presentation.
This year, I separated them into one day each. I also slowly and carefully picked my examples to build skills that gradually became harder with about 3 problems per skill .... thinking that I could semi walk them through the first one of each set and then they could practice on the next 2 before we built up difficulty. Also, I grouped the skills together, instead of mixing them up all higgeldy piggeldy. I also kept stressing: "The derivative of e to the box, is e to the box times the derivative of box". This seems to work better for my kids than "e to the u" which is just one more alphabet letter. I physically draw "e" with a blank box in the exponent.
This seems to have been MUCH more successful than in the past. Of course now I say to myself, "self .... DUH! What were you thinking??"