So the question I ask myself before I give any calculus lesson is: “Why on Earth would anyone actually go through the trouble of doing it this way?” There really is a rich set of useful problems that can only be solved using differential calculus, so why not present them (or, God forbid, let the kids think of them) to students and work your way out?
My rhetoric here is getting a bit lofty, and I hope my actual lessons don’t end up being a let down, but they sometimes are for me, too. It turns out that it’s hard to come up with real things for math to do when you’ve only been modeled the most sterile way of learning math.
I find this kind of exuberant, confident, loose-limbed classroom introspection pretty much irresistible. It’s rare you find an edublogger this prolific who also works full-time in a classroom.
Put your money in Shawn Cornally, Inc., while his stock price is low.