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.
How do they pick these pictures?
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).
I have no explanation for this. I just like raptors. Rap-tors. Awesome.
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!
Competency-Based Education: Learn From My Follies Standards-Based Grading: Never “When”, but “How?”
My daughter is exactly in the same boat as your student…but I wonder what parents and students are to do in these cases. My kid is 14, 9th grade and in Algebra II. She gets A++ and is bored to tears..just like last year. It isn’t that it is all that easy but they move too slowly…she said she’d like to learn this stuff..but in one day instead of a week…she gets it and then they just keep repeating the same stuff. She is begging me to let her take PreCalc online this spring so she can take Calculus in 10th grade because she’s hoping that will be more of challenge for her. Her end goal is engineering or computer programming or some combo, thereof, in college..so I think it is good she loves math and wants to keep moving forward….It sounds like you think the way to slow them down is have them do more applied math along the way…..I think she’d be okay with that probably but the teachers here don’t do it. We’re looking at math and science camps for summer and they do applied activities..but honestly….since she’s been in science camps since she was 5-6…she looks at slides of these “advanced” camps and says, “I’ve done that bridge thing before, I’ve done that before, and that….”
So…what are we supposed to do? Tell them to take a year off math? BTW..I don’t think she’s brilliant or anything….this stuff is just easy for her the way they are teaching it. ?
That’s a great question. My inkling is that your daughter is really good at the math-ed pattern: learn processes, repeat process for tricky instances of process, show the teacher, forget, repeat with new process.
I have no doubt your kid is awesome, most are, but she’ll probably find out in college that she’s not actually good at math, or that she even likes it, what she’ll find is that she was good at the math-ed pattern, sadly.
What I would recommend, is putting her in situations where she creates some art using math. Processing.org is a great place to send kids like this, or ProjectEuler.
If she seems to like math for its own sake, but is also interested in programming and engineering, she could try working through a textbook like Gallian’s “Contemporary Abstract Algebra” or Cameron’s “Combinatorics”. I seem to remember that both are fairly accessible, would give her a flavor for what more-advanced math is like, and include non-trivial programming-project exercises in most chapters.
Alternately, she could take the material being taught in her math classes right now, and write programs to “do her homework.” She’ll learn a bit more this way than just going through the motions. If she documents her code well, she can come back to it later to relearn things that get rusty. She could even make it into interactive widgets, put up on a blog, and have a nice portfolio to show off when applying to college…
To me, it all depends upon the goal when this was set up. I assume there are some gaps that needed filling and you are working to fill those in before she hits calculus? Or maybe the goal is just to get her back to a place where she is motivated again? Bottom line is this: if you feel she’ll be in a place where she can succeed moving forward, I think you’ve done the job!
Incidentally, I just found out I am teaching a class called “Algebra III” next year. Another weird sandwich class that is designed for kids who passed Algebra II with a low grade but not ready for our IB equivalent precalculus classes. It’ll be interesting to see what the content expectations will be for a class like that.
@Marshall- I am doing the same class. My name for it was “Algebra 2 without the 12 weeks of Algebra 1 review”, which is essentially what our Algebra 2 looks like.
Doesn’t it just seem silly to call these things classes? I mean, what’s the point when we’re all just hitting at core competencies anyway? Why not just blow the whole schedule up, and let teachers just run with the kids in the wild? I’m sick of pretending that all my students are the same and that it takes them 18 weeks to learn everything.
Trite little activities? Yougottabekiddinme! That’s way better than any math class I ever had in school. 6 years of secondary math starting with pre-algebra, 20 credits in college, ONE project. Application problems in the book were the most fun I ever had, and they really didn’t teach me how to apply math. Cut yourself some slack.
As for the perceived need to delay a year, I suggest they take stats. I never had the class, but learned it by tutoring, and it’s way more useful to the average person than Calc. Imagine If the general public could actually understand and intelligently question the results of a scientific study reported in a magazine! I’ve read, from a medical researcher who wrote a stats book, that an alarming number of researchers don’t understand statistics well enough to use it properly.
+1 for the being-useful comment. I have NO IDEA why calculus is the end all for high school. ‘Tis ridiculous.
Well what SHOULD be the end all math course for high school? I know at our college the first math course we teach is Calculus…so students have to come with PreCalc done already. If they want to do Physics or harder math/sciences, it is considered better if Calculus is already done at high school level…where it moved slower…so they can take it again in college as review or jump right into their sciences with more confidence.