How I Teach Calculus: A Comedy (Rates & Gas Tanks)
It seems that cars are just the best context generators ever. Lots of people use one, they cost us giant piles of money, we even start wars over getting gas for them. Working cars into math lessons is like an EpiPen for the the anaphylactic reaction that most students have to school.
By this, I do not mean the type of drudgery that gets passed off as application. You are not generating context or interest by providing all of the information about a toy system that has never and will never actually happen.
I was driving my new car and I noticed — perhaps fallaciously — that my gas gauge seemed to drop faster when the needle was below 50% than when it was more full.
I decided to take pictures of the gas gauge and odometers. I spliced them together into a kind of stop-motion video, but the timing isn’t quite right.
[This is also an experiment to see if Metallica will sue a teacher for fair educational use of their product. Anyone want to take the over-under on 5 days until a cease-and-desist order?]
There are a thousand questions that could arise from this, which is why I love the rich media technique (WCYDWT), and this video isn’t even that interesting really.
The point is not to teach the specific curriculum, but to trust that the important curricular points will arise through creative questions and actual thinking. All of that planning that we do (and bitch about) is actually hamstringing our students. The planning is where the thinking is, folks.
- The obvious question: What if you drive differently? Like stop-and-go vs. highway? That questions shows a lot of thinking, and requires us to go and get data that is much cleaner.
- What shape is the gas tank and how does the gas gauge work? This questions requires a lot of genuine related rates (hallelujah!) and some useful understanding of geometry (Bonjour, Canards!).
- Is it psychological, because you start worrying about running out of gas as you get less? This question is an awesome combination of psychology and math.
- There are a million more that students will come up with, both more advanced and rudimentary than these. This is called real differentiation. This is called being interested. This is called everyone freaking drives a car.
The point here is that my kids totally bought into this, and, like I said before, it’s really not that interesting. The model here is that when the teacher shows some interest in generating good prompts, the kids respond with a heightened awareness beyond what “school” normally requires.
I suppose the only thing I’ve learned in my short years is that students respond genuinely to a teacher who is invested, interesting, and totally willing to ignore the normal mode of school.