Teaching Pre-Calculus to One Kid All Semester: The Dance of the Sallies
Is Sallies the plural of Sally? It is now.
Thank GOD I can write about math again. I’ve come through my blue period (being obsessed with grading reform) and I’m back to actually teaching math.
Right now I have one math student; she’s a refugee from the Pre-Calc II class down the hall, and I’ve taken her on as an independent study.
Oh, what’s Pre-Calc II you ask? It’s a class my school created to prevent sophomores and freshmen from taking Calculus. Yes, we had that problem. No, it’s not a good problem to have.
Pre-Calc II is basically an annoying amount of trig that no one ever uses (I was a physicist) and a bunch of stuff about conics precariously teetering on a dearth of orbital mechanics.
Let’s think for a second what it means to have a plentitude of sophomores ready to take calculus. It means that you had students get through Algebra, Algebra II, Geometry, and some sort of Pre-Calc (srsly, what is that?) in 3 academic years or less. This was possible at my school because of block scheduling and the way our middle school accelerates kids, but I kind of think it’s kind of bonkers.
Which leads me to the question, is there such a thing–before I try to invent it and waste my whole summer–as a mental abstraction aptitude metric that people don’t balk at? Seriously, is there? I’d love a link.
Well, back to the action, my little refugee came to me bruised and battered from scheduling issues and mismatched pedagogy. It kind of felt like nursing a sulking falcon back to health (which I’ve done, in a figuratively literal sense).
The process went like this:
Fugee: What chapters should I learn and how many days should I spend on each?
Me: I don’t know, it depends on what we can motivate properly.
Fugee: So, like one per week with quizzes on Fridays?
Me: Ha, ok, sure.
Fugee: Why are you laughing at me?
Me: Oh, I’m not, sorry. Here, roll this iron ball by this magnet and come up with a model for its motion…
Here’s what we’ve done so far:
- My little Fugee has built a parabolic oven from a directerix and focus (you’d be surprised how little they really understand when they read those little definitions in the book about how these things are constructed)
- She has dealt with the square dartboard.
- She has learned to use GeoGebra to find relationships between arbitrary measures on ellipses, hyperbola, and whatnot.
- I had her build a tethered-cow-and-barn system and optimize the grazing area.
- She has surveyed and found the altitude of nearly ever lamp post on campus.
- She has created a unit circle and divined such things as tangent, cosecant, and versine.
- And now she’s messing around with shapes that have more than two foci. I honestly have no idea where this is going.
Here’s my thought-knot. This is an independent study, so I have very little time to devote to her proper math education; hence all the trite little activities above. Although she claims to like math again, and she’s excited to take Calculus next year (which will be all about sailboats, btw), I can’t help but feel like I basically reached half-a-knuckle deep into my bag of cheapest tricks.
Is it progress that she thought this was awesome, even though I feel like I’m short changing her?
Oh, and by the way, I’m a Phoenix! FML!