I know this isn't an original idea, but it seemed like a good fit for the end of Precal (for juniors: my classes had both juniors/seniors, and seniors needed some time to review for their final, which was two weeks earlier than the juniors'). Here's how my version of a Desmos Art project went this year.
This semester, we studied polynomial, rational, and trigonometric functions. Use these functions (plus any other functions or relations you want) to create an original piece of art using Desmos.
This is an Awesomeness project, which means there are 5 points available. To earn them, make sure your creation:
1. Uses domain and/or range restrictions
2. Uses inequalities for shading
3. Uses all three function types studied this semester.
4. Uses three or more functions or relations not studied this semester and/or not studied in this class.
5. Is awesome! Convince me on the last slide by discussing any struggles you had, anything new you learned, what your creation means to you, etc.
Pretty good results: some kids got into it, and I'm trying to stay positive about things at the end of the year so I won't get into those who didn't (you can probably tell), or those who borrowed a little too heavily from stuff you can find online (or right on the staff picks page, ffs- if you see anything down there that bothers you, please let me know). Some of these are great! The sword and the mosques, the war/peace, the mountain scene: pretty sure all of these were original, and noticed these students putting in some effort.
I read a lot of science fiction
I struggle sometimes to come up with good contexts for problems
= Alien Math
My first escapade into alien math was a problem about alien units, the point of which was to understand conversions without getting hung up on feet/meters/etc. I wrote it a few years ago, and it works pretty well. I use it when the opportunity presents itself.
This year, I wanted to do something with my Geometry classes for the final modeling unit after we talk about volume, density, etc. There are lots of problems about surface area and volume and density, making comparisons, maximizing, etc. But I wanted to have a little fun with it, so I came up with
The Flerkus Miners of Gleep!
Introduced it to the ss after our last assessment. There was some satisfying (for me) confusion, then people got to work!
Step 1: Make sense of the problem
Step 2: Plan and calculate
Turned out to take a couple of class periods for most kids to get a handle on this, which was a very interesting process to watch. And I did my best to JUST watch, not giving clues or hints or judgement, just observing their thinking and how they got into it.
Step 3: Build it!
Things were messy and chaotic, but it was pretty fun. Couple of days on this, running out of class time, then we were ready to start
Step 4: Product Testing
A. I made a submission form for students to check off requirements and write down measurements. Mostly, this gave some students a bit of time to frantically add last-minute touches.
B. Blamium distribution ended up taking entirely too much time, and was kind of hard to judge, so I scrapped it after these first few gave it a try.
C. The Flerkus Weigh Station was tons of fun! Rice everywhere, students fighting to be the one who got to pour the flerkus, be the scale expert, make predictions, etc.
Step 5: Awesomeness!
(Yes, I'm focusing on the positive here)
The kids came up with some great stuff for their "Awesomeness" point.
This was fun, and a great way to end the year. The whole points thing needs some work, and the logistics of the testing, too. I think it was worth the time we spent, got more out of the students than anything else would've the last few weeks of school, and left them with a good "taste in their mouth" as they leave my class for the year.
So, when I made up my grading scale in August, I left 5 points for "awesomeness", which I didn't define very well. Here's my description from my assessment document:
Part 1: Graph My Room!
Senior "Foundations" class ended up on 3D graphing at the end of the year, and ss had a really hard time visualizing and conceptualizing 3D spaces. We did tons of activities, made 3D coordinate planes, even installed semi-permanent x/y/z axes in my classroom. When we were getting ready for our last summative assessment, one of the students, being a senior, asked, "can we just, like, do a project or something instead of a test for this?" So I, after a little bit of mwahaha, said, "OF COURSE WE CAN!!!" Then I came up with this:
Final Awesomeness Project- Graph My Room!
Using isometric graphing paper, make an accurate scale drawing of my classroom. Use your drawing to find the following.
A. The distances PQ and RT (These points will be posted around the classroom).
B. The equations of all of the planes that make up the walls, floor, ceiling.
Prepare all of this in a poster.
There are 5 awesome points available.
1-2. Distances are within 50 cm of the actual distance
3. Plane equations are accurate
4. Working for the above is clear
5. The poster is awesome!
About 4-5 class periods to get this done, with varying levels of success. A few notes on the process:
I've spent this year really focusing on summative assessment. For the last few months, I've been thinking a great deal about formative assessment, and changing the way I introduce students to concepts, figure out what they know and what they need some help with, and move towards a goal.
In hindsight, this project feels to me like it could have been THE UNIT rather than something we did at the end. I have dreams of one day having a good, meaty problem to START. Create the headache, etc.
I'm really starting to think this is going to be my focus for next year, and I'm pretty excited about it.
Back in January, I was wracking my brain about how to make assessments go better in my classes; there was too much stress, too much concentration on the wrong things: it felt too much like a big bad test that everyone should be stressed out about. So I thought to myself, what if they could take a break, take a walk, talk about the test, get rid of misconceptions and jitters, etc.
And that's what we did.
I didn't really have a good idea about how to do this the first time, so I was kind of loose with everything.
"Work on the test for 10 minutes, then we'll take a walk. Come back, work for another 30, we'll do it again. then 20 minutes to finish."
The idea here was to have some time to get into it, then ask questions that might have come up, then some more work, then final questions.
I didn't talk or answer any questions. I let students take notebooks and pencils with them, and bring them back into the room.
After each class's first test walk, I asked for some feedback about the process:
Ok, nothing really shocking there. I used the "cheating" results to have some conversations about why I write assessment questions the way I do, why I ask for so much from one question, why my assessments are only 1-2 questions.
The next few questions on the survey gave me some more interesting feedback (summarizing and cherry-picking some results here).
Did anything bother you about taking a break during the test?
Describe any suggestions you have for how we can make tests less stressful.
Teachers with more foresight than me probably know exactly what went wrong with this: some students used the breaks, especially the last one, to just copy each others work. Of course they did!
The process with the rest of the classes in this first round of tests allowed us to have some great discussions about how to show your understanding (and how to show that it's YOUR understanding).
I pretty quickly stopped letting students take notes or any paper with them, instead sending a basket of whiteboards and markers with them that got erased before they came back into class. I also got rid of the second break: work 10 minutes, 10 minutes to discuss, 40 minutes for the rest of the test.
I don't have really good data on this. Visual modeling increased, but also paragraphs of writing where some good algebra steps would do just fine. "Less tell, more show!" became my most often used comment on assessments.
I think it "felt" better, at least to me. At least most of the time. It also gave me some more freedom (along with some more directed test-prep on my part) to ask more open-ended questions: "Make up your own triangle and solve it to show me you understand trigonometry".
Then there was
The oblique asymptote incident:
So, one of my precal sections, my "difficult" class, last period of the day, test over rational expressions and functions, Illustrative Math question about fuel efficiency...
In this class, I have one student who's way ahead of everyone, a transfer this year from another school where his algebra 2 class covered most of what I have to cover to meet the needs of the students here. He's the "go to guy" during test walks, the one the other students crowd around. He and I had had a discussion about a similar problem, and and how to tie the idea of an oblique asymptote to the context and the solution. It wasn't something that most of the students were ready for, but he was. Here's some of the nonsense I got back on this test:
I threw these and a few others into a presentation (yes, along with some positive things, too) and used it to have a very pointed discussion about cheating. I also found ways to remove this student from the conversation during walks (by having my own conversation with him) so that the others wouldn't get distracted by things they're not ready for.
I settled on a 3 minute reading period (look over the test and strategize: no talking, no writing, no calculators) followed by a 10 minute walk before each test, with whiteboards if students want to use them. Some students still try to memorize the entire problem and get classmates to give them the "answer" (whatever that means), but this is where I think I can feel comfortable. This is what I did for the rest of the year.
Reflection: Why do this?
Test walks are a pain in my ass, mostly because they cause me to spend so much time thinking about and watching for academic dishonesty. I'm not sure if they really help with assessment results because I'm too lazy to do a real look into the scores, and my records aren't good enough to call this useful data yet. I still have assessments where the majority of students miss the mark completely and/or give nonsense answers to questions.
I do this, and I'm going to continue to do this, because of the mathematical discourse it produces. The "pressure" of these discussions produces the best mathematical discussions I ever get to witness, even from the students who are the most disengaged in the classroom. Students argue their case, critique the reasoning of their classmates, ask questions, and don't stop asking until they get it. On one of the last walks this year I tried to capture this in a video. It's kind of hard to hear what they're saying, but you could probably get the idea with the sound off.
So, the question I'm working on now is: How do I get this kind of engagement as a normal part of my classroom... without having to give a test every day!