My students and colleagues all know how much I love Desmos, and how much I rely on it in my classroom. I've been playing around with doing an art project using Desmos for awhile, trying to find the right time, the right content connection, the right group of students, etc. I've thrown the idea out to different groups of students as an alternative or enrichment in a couple of cases, but never really prepared for it or made it an intentional goal. The way I presented and assessed it over the last couple of weeks with my 9th grade Integrated 2 class is the closest I feel like I've come (yet) to doing it right. I also feel like a lot of other teachers must do something like this, but I couldn't find anything that really fit what I wanted to do (although Jon Orr's Beautiful Functions was kind of an inspiration).
I've got a growing love affair with "functions" as a specific area of focus in my instruction, and a growing understanding of how they fit into all the other areas, and how they fit into the grades 8-10 currriculum I've been working on for the past 4 years. Grade 9 is the first time we really dig into function transformations, and we're also at a point where we've had some experience dealing with functions that are a little more "interesting" than linear and exponential (mainly quadratics, but we also dabble in radicals and cubics).
Tech and Prep
Working up to this assignment included the following desmos activities.
1. Transformations Review by Suzanne Von Oy
This worked as a nice intro, with answers students could check. Also, the "library" of functions used matched up nicely with where we were.
2. Match My Function by Jon Orr
This was nice because it asked for the functions in function notation, something I was shooting for in the project. It also let students play around with unfamiliar function types, and drove home the idea that transformations are universal, and apply to all functions, even ones we don't know yet.
3. Make a Face! by Me!
I'm still in the process of finding the right balance between spending my time making my own materials and spending my time searching for existing materials. This was fun to make, and focused in on some of the main aims of the project. I think it got the kids ready pretty well. Building it also gave me a better idea of the time and effort it would take for the students.
Part of the "success" of this project, I think, was that I put some thought into the requirements, and into how I would assess it. Not perfect (I'd like to find a way to make it a little more "mathy"), but at least it's clear. Here's the Google Doc of the assignment and rubric.
Providing a model
I remembered to do this this time! It always helps, especially with the language I was looking for at the end.
This is a recreation of the mask of one of my favorite comic book characters, Grendel. I used an image from this link for a guide: https://www.redbubble.com/people/bighairmonkey/works/3126293-grendel. For the nose, I used two transformations of the quadratic parent function, one of which was a vertical reflection so that the parabola opened down. I shaded between them using the top function as a restriction for the shading on the bottom function. For the eyes, I used exponential, quadratic, and absolute value functions, which I dilated, reflected, and translated, then used inequalities to shade. I found some of the shapes in the mask difficult to reproduce using functions, because they curve back in on themselves. This would make them fail the vertical line test, so they couldn’t be functions. In order to reproduce these shapes correctly using functions, I would have had to write many different small functions. Instead, I decided to simplify the shapes to make them easier to draw with fewer functions."
I gave the students two 90-minute class periods to work on this so that I could make sure they got off to a good start, and then two weeks outside of class to put in whatever amount of effort they wanted. I'm really happy with what they came up with. (The one on the top left's supposed to be me, BTW :)
To take care of a 40-minute Friday class, students showed off their work to the class, practicing their academic language. Fun way to finish off the week.
I had a really rough class last week with my 8th graders. They'd been using a Chinese word pretty regularly in class that I suspected was a swear word. So I decided to call them out on it. When I heard a student using the word, I'd ask them what they said. And what did they do? As you can probably imagine, they totally lied to me. Then their classmates backed them up.
I left that class pretty furious and went directly to the Mandarin teacher to confirm my suspicions (it's like the worst word you can say in Mandarin). Then I started stewing... Losing sleep... Plotting my revenge...
Because of the schedule, it turned out that I didn't see this class again for a week, which was probably a good thing. I asked a colleague for five minutes with them at the end of her class the next day, and I let them know that I knew what they were saying, and I was really disappointed with them. I tried to make sure they understood that it wasn't the profanity that really bugged me (I use profanity, although I don't throw it around in public), it was the dishonesty. Also, that this was an indicator of a bigger problem with this class: the lack of academic language in our daily discourse.
Silence... Blank stares... Some guilty looks... Some grins...
So then we all had a week to think about it. I spent a lot of mental energy on it, although I doubt they did. I got an email from one of the students involved apologizing for the profanity, but didn't hear anything else.
The next time I had them in class, I started out by making sure they understood the problems:
I sat at my desk in the corner and left them to have a conversation. Slow start... leaders emerge... They ended up having a pretty decent conversation for 8th grade students.
After about 45 minutes, I stepped in and gave a little direction to solidify and wrap things up, and then led them through some roleplaying scenarios (1 plays teacher and 2 play students).
The school trip is coming up, so again, we have a long period of time until our next class. I feel like they did some good work today, and I hope it sticks. At least it got them talking and thinking about this.
Take-aways, Lessons Learned:
Let's see if I can keep up with a blog!