How I Teach Calculus: A Comedy (Opening Salvo)
The get-go of calculus can be a bit like that first time you meet someone you think you’re really going to like:
You like double tortilla burritos, too?
Yeah, who doesn’t?
Ha, nobody, you’re so funny. What else do you do? I mean, like, I mean. LOL!
I’m really into progressive education with a bent towards authentic questions and early childhood psychology.
Oh, cool. Want to spend the next 96 hours in uninterrupted eye contact?
Kinda like that, except there’s 30 of us, and I’m the only one who’s really excited about rates.
Here are the few ways I’ve started calculus that are worth mentioning:
The Radar Gun:
A simple, “How does this work?” usually does the trick.
I’ve gotten all sorts of answers, but it usually comes down to a competition between the squishy-returning-wave method and the pew-pew-pew-reflect-pew method. This can lead directly to the concept of infinitesimals.
The GO!Motion Probe:
Even simpler than the radar gun. Mess around with the samples per second of a typical Vernier Motion Probe.
The Distance Discrepancy:
Time the drop of watermelon–or any other significantly enjoyable thing to drop–from a height of greater than 6 meters.
Now ask for predictions for the time to fall for half (or double) that height.
So They Know All About Limits, Do They?
A lot of my students come to me with some cursory knowledge of limits.
Usually this knowledge is very much tied to math book problems.
Let them hang their limit hats on these:
Get out a fast camera. Capture anything:
Maybe not so many frames, but you get my drift.
My students dropped a rotten watermelon and took about 140 pictures using our high speed camera (at 60 fps). They then confirmed the results of the “falling equation,” as they called it from pre-calc, with times calculated from the close frames of the images.
Ask what the hell is the slope of a parabola?