I always struggle during the days spent going over differentiation rules. The mathematician in me says the students need to see where the rules come from so that they aren't just a recipe. On the other hand, I see students glazing over a bit with notation and getting lost in the midst of the overall goal: how do we find shortcuts for finding derivative functions outside of using the limit definition every time?
I have also tried going through the derivations in class and having them just watch and see the progression on their own, without copying things down. Some compulsively copied despite my repeated requests not to do so - I think it was a situation of seeing copying notes down as an alternative to really digging in to what was actually going on. It's mindless to copy down notes, a great alternative to actually going through the steps of understanding.
Last year I made videos of the derivations and asked students to watch them outside of class in a one-off attempt at flipping. That didn't work - students said they watched but 'didn't get it', so my attempt to quiz them when they arrived in class was a bust.
This is my compromise this year: for finding the derivative of a constant, a constant times a function, and the power rule, students will be guided through what has essentially my lesson plan for previous lessons. Sums of functions, products, and quotients will be given first as applications of the limit rules, but the details of getting from the start to the finish will be kept as an exercise for later.
See my handout for today here:
03 - CW - Differentiation Rules