The conics unit has come and gone in my Algebra II classes, and like last year I want to do a performance assessment. Back in the day this assessment was Amy Gruen’s piecewise functions picture. With the advent of Desmos it’s now a digital version of the same project. (I wrote about last year’s here). Then in early summer I saw the tweet that let me know how much better my project could be for my students.
Dropping the image into Desmos first, then creating the equations to match the image? Brilliant! That led to a pretty productive online conversation, and to me making some slight changes to my plan for this year. My big takeaways from last year were:
- my students selected some very cool but also very challenging pictures to duplicate
- they needed massive amounts of support writing equations to match lines and curves
- probably not everybody did their own work
Providing massive amounts of support is what Desmos does best. That scaffolding probably means less frustration, and less cheating. At least that’s what I’m telling myself.
Started before break with a functions review (Alg II (3) Functions one-pager), not only of conics but of all the functions we’ve learned this year. The day back from spring break we learned how to match equations with lines or shapes in a picture with this Desmos activity.
Then I introduced the project, and offered a carrot (it’s a quiz grade, you guys!). And away they went, seeking pictures.
They found standard-issue high-school-kid stuff: lots of cartoon characters, superhero or sports team logos, palm trees and flowers. I had them make a (rough) sketch of the image on grid paper, then try to identify equations of four functions that would be included in the final product. I wanted them to get used to the idea of seeing small sections of the larger whole, and finding ways to describe that section in math symbols. We also walked through the process of setting up an account in Desmos, opening a new graph and bringing in the image, and saving the graph so they could access it again.
By Day Two, we were ready to start getting serious about making some math art.
They were pretty excited about this project when they were googling around for images, finding their favorite characters or sports teams. They were less excited about this project when it came time to start writing equations.
A couple wanted to straight-up quit. I’m gonna use all my powers of persuasion to try to convince them otherwise. That, plus walking through the process, step by-step, of writing a general equation, then adding sliders and tweaking values until the curve matched up. I’m not sure it helped.
I did notice that very few of my students actually completed the reference sheet. And (in a related story) almost none had any recall of any function equations except y = mx + b. That is definitely part of the issue – a huge disconnect between a shape on a screen and the math symbols that represent it. And truth be told, that’s part of what I wanted this assignment to do – to cement that relationship.
Best-laid plans, right? I’ve got some work to do.
The morning of Day Three, the putative due date, one of my struggling students came in for extra help on the project. She left with a smile on her face, having made serious progress. Plus she agreed to act as a “resident expert” in class, helping out her tablemates when they got stuck. We made some halting progress as a class, but no one is close to done. Several of my students did say that they understood how to write an equation for a line or curve, and restrict the domain, just that it was going to take a long time and a lot of tedious work. So, similar to last year, with about 10 minutes left in class I offered a reprieve, shifting the due date to Monday. Then I’ll accept whatever they have and go from there. I set up the grading rubric in such a way that the points are weighted toward planning and less on the finished product, so the kids who laid down a foundation can still get a reasonable grade even if their final product is…. incomplete.
But I also want to be able to show them what their project could look like, with a little bit of persistence:
Just a little something I threw together over the weekend. 44 equations later…
The breakthrough for many came when they started to use vertex or intercept form for their parabolas. The ones who completed the functions reference sheet caught that first. I showed everyone on Monday, which of course was too late for many folks. Next year I’ll highlight that option earlier.
So, they begrudgingly turned in their paper/pencil planning work, along with a link to their Desmos creation, on Monday. Just like last year, some bit off way more than they could chew. Some got frustrated and quit. Some gave me a half-finished product. But the ones who stuck with it were able to turn in some pretty cool stuff:
Oh, yeah, and this from a student as she turned in the assignment thru Canvas:
My big takeaways:
- I need to steer them towards reasonable images to duplicate. Avoid frustration and shutdown right from the jump.
- I need to encourage my students to use the vertex form of quadratics. Anything that makes the movement of the curve more intuitive is good. I think eventually that will help cement translation of functions.
- I need to enforce the preparation steps that I built in: the reference sheet, the paper sketch, and the four function equations by hand. I need to help them draw the connection between curves on a screen and the associated math symbols.
The assignment is is a keeper. But I bet you it won’t look exactly the same three years from now as it did this week. In fact, I’m counting on it.