Desmos Art 2.0

One of the hallmarks of the MTBoS is constant refinement and reflection – taking something of your own or someone else’s and making it better.

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:

  1. my students selected some very cool but also very challenging pictures to duplicate
  2. they needed massive amounts of support writing equations to match lines and curves
  3. 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.

Fingers crossed
Via Tenor

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.

 

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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.

Double Double
Making ’em hungry before lunch. Double Double, coming up.

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.

showtime


 

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:

 

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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:

 

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Oh, yeah, and this from a student as she turned in the assignment thru Canvas:

Desmos Student Comment
Yeah….

My big takeaways:

  1. I need to steer them towards reasonable images to duplicate. Avoid frustration and shutdown right from the jump.
  2. 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.
  3. 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.

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Linear Review Three Ways

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I’ve learned a few things about high school kids the last 14 years. One of those things is: they are not shy about telling you they need help. Might be verbal. Might be non-verbal. But the message is sent. So the question I have for myself is: You got the message. What did you do with this information, Mr. Teacher Man?

 

  • They need support.
  • They need a chance to collaborate and help each other.
  • They need to be able to think their way through a problem.
  • They need to see each other’s work
  • And they need reps. Lots and lots of self-checking reps.

We’ve got a quiz coming up on linear stuff. It’s all warmed-over Algebra I from their freshman year, but that was two years ago and for a lot of them at the beginning of the year it’s about as clear as mud. That’s a bad way to fly when we’re trying to rebuild a foundation for the rest of Algebra II.

I need a plan. Like Gerry Faust recruiting future Heisman Trophy winner and Pro Football Hall of Famer Tim Brown out of Texas:

Faust Recruits Tim Brown
The Golden Dream, by Gerry Faust and Steve Love

All the bases covered. And then some. Rapid fire.

I’m all-in for the gamified review favored by many members of my PLN. I like to have fun in class too. But my students in years past have also asked for a way to get more practice. Maybe even… a worksheet.

(Which, BTW, aren’t always as evil as they are made out to be. Depends on the worksheet. And the teacher, probably).

So I lined up a parade of varied review styles and methods for them this week:

We started with version 4.0 of my CCSD Enrollment activity on Desmos, because children must play. It had its ups and downs:

Next up is a review method promoted by Julie Reulbach known as One Sheets – all collaborative and student-centered. Plus it makes an excellent “as-needed” support on the quiz itself. The cleanup hitter is my very first MyMathLab assignment. The students can work on this online assignment over two days outside of class, getting multiple attempts at a problem, and able to access hints and help. That one’s targeted at my “give me a worksheet, please, Mr. Dull” people.

Differentiation, you guys. For real.

But not because it’s a buzzword (which it is), or because it’s a sub-domain on my evaluation rubrics (which it is). It’s a response to my students’ needs.

That’s a message I hear loud and clear.

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Piece By Piece

Image via giphy.

Last time we talked math in this space, I was trying to figure out a way to squeeze way too much content into the last five weeks of school, while still giving my students a chance to practice the skills and giving me a chance to assess their understanding, all while keeping a tiny sliver of their available brain cells focused on math stuff. Because it’s another fantastically gorgeous early May in The Region.

It's May In The Region
“Road Conditions: Wet”.  No kidding…

This week, I needed a performance assessment idea for Conic Sections. I also need to overlay final exam prep with new material in the finite time remaining before June 2.

And, I want to play with Desmos. Or rather, I want my students to play with Desmos.

Put all those ingredients in a blender, hit “Smoothie”, and you’ve got Piecewise Function Art!

Desmos piecewise staff picks

See everything up there labeled “Conics Project”? This project plan of mine is not a new idea, obviously.  I first came across it when Amy Gruen posted about her pencil/paper project back in the day. My co-teacher and I modified it for our Algebra II course that included several students with IEPs.

And then it sat in my back pocket for years until I changed schools and was assigned to Algebra II again this year.

The #MTBoS Search Engine tells me there are some awesome teachers getting cool stuff from their kids regarding this type of project. Check out Lisa Winer and Jessie Hester, to name two.

So I used their work as a starting point, customized it for my students, made up a packet with some sample art, my expectations for the project and the points scale, annnnnd away we go….

I insisted they did the pencil/paper planning first. I want them to make some fun & cool pics, yeah, but first and foremost I want them to get good at moving between representations of functions, and to get some reps on writing and graphing conics. I gave them two days to roll it around and plan at home, maybe sketch a quick picture or two. Then I planned for a pencil/paper Work Day in class Thursday, with the expectation (slightly unrealistic, it turns out) that they walk into class the next day with a list of equations. Then input equations to Desmos on Friday, with the project submitted via Canvas by the end of class.

Docs here:

Alg II (3) Conics Performance Assessment

Alg II (3) Functions one-pager


The initial reaction was… lukewarm: “Ugh”. “I’m taking the L.” “I can’t do this.”

Come on now. Don’t give up before you even try.

Most of them didn’t pick up a pencil before classtime Thursday, putting them in a hole to start. Fortunately I built in support, posting a Desmos Activity (via Stefan Fritz) to our page for them to play with, so they could see how to fine-tune an equation, and to restrict the domain. But the best progress was made in class on Thursday, when I convened some small groups, answered questions, walked through a couple of quick examples of drawing a graph and working backwards to its function rule, and also showing them how to translate a graph.

Next thing you know…

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Guys, for real. In my least interested class, I had 26 kids engaged, helping each other out, graphing, writing, struggling through the rough spots, cheering for each other and squealing with delight at themselves.

If they aren’t at home right now high-fiving themselves, they should be.

Then Friday, the Big Finish:


OK, in reality, my students needed a lot of support to bring this project in for a landing. A lot of them made a pencil/paper design that was way too ambitious to finish even with two days to work in class. Many were asking questions Friday that they should have brought to me on Wednesday or Thursday. Most got down to business in class on Friday, because it was the due date. But almost no one was remotely close to being done.

There’s two ways to handle that: 1) “Too bad, so sad, I told you guys to get started on Tuesday and you didn’t so now you’re out of time and out of luck. F.”

Or: 2) “Look, I can see you guys are making progress. How many of you are happy with your picture as it is right now? Not many, right? But you’re making good progress and probably could turn in something really fantastic with a little more time? Cool. The due date in Canvas is today, but with a time of midnight. Go home, finish it up, turn it in before you go to bed and we’ll call it good.”

In his autobiography “My American Journey“, General Colin Powell stated often one of his life’s guiding principles: “Never step on another man’s enthusiasm”. Good advice from a great man. I’m in, all the way. Why crush my students’ spirit just when they are hitting their groove with Desmos and putting together the equations for a whole big mess of functions? Math is happening here, people. I’d rather ride that wave, let them finish and give me something they can be proud of.

So, midnight it is. And we all get better, together, at teaching and learning.

Piece by piece.