I started something new this week. I’m not entirely sure where it will end up, but I like how things are shaping up after just one challenge.
Here’s what I presented to my students:
Age-appropriate for Precalculus and Calculus? Not exactly. With a slight nudge, this is something a group of Desmos-equipped 6th graders could tackle.
But… Oh. My. The blank stares. The confused looks. The surprisingly non-isolated bewilderment.
I could write a post about how students “get rusty” with things they don’t practice, et cetera, but I think something else is going on here. Many students struggled in such a way that I suspect—rather, I’m convinced—they never learned much of anything about linear functions at any depth. (I shudder to think about how deep their understanding of exponential and logarithmic functions goes, even as we’ve been working with these functions all throughout the year.) Presented with a problem in a format just slightly askew from what they’re used to, they struggled and stalled.
I could write a blog post lamenting the quality of the students passed along to me by various colleagues. But there’s more to the story, especially since I’ve taught most of these students in two, three, four, or even five other classes. An indictment on their former teachers is an indictment on myself.
So what’s my next move? How do I address the current state of graphing affairs in my own classroom and in our department as a whole? With a few resolutions:
- Resolved, never to treat a particular mathematical topic in isolation when valuable connections are readily available.
- Resolved, to present students with tasks which demand that they make connections between numerical, graphical, and algebraic representations.
- Resolved, to allow key topics to spill over across the confines of individual lessons, chapters, and units.
- In particular… Resolved, to develop a series of “match my graph” challenges to develop students’ “function sense” (or “graphing sense”?) over the course of the entire year.
- Better yet… Resolved, to collaborate with my colleagues (in real life as well as online) to develop a series of thoughtfully sequenced/coordinated “match my graph” challenges for every course in the 7-12 sequence.
For now, I’ll create two or three challenges per week to share with my Precalculus and Calculus classes. They’ll gradually grow in difficulty, and we’ll soon shift from linear to quadratic, to power and exponential and logarithmic, to conic, to parametric, to trigonometric, and even to polar. Eventually, I hope to tag the challenges by grade level (with some challenges receiving multiple tags) so we can more easily integrate them into the rest of our courses in the department.
I’ll report back on our progress later this semester. In the meantime, if you want to create a few challenges of your own, I’d love to see them!
In fairness to my students, some solved the challenge rather easily (as they should have). I’ll soon provide them with a more demanding challenge, but for now, I’m interested in seeing how I can address the blank stares and confused looks that popped up on more than a few faces earlier this week.
One of my students brought a huge smile to my face with an email this weekend. Read about it here.