The Teaching Muscle I Want to Strengthen in 2018.

[a/k/a 3-Act Task: Suitcase Circle]

It’s the muscle that connects my capacity for noticing the world to my capacity for creating mathematical experiences for children. (I should also take some time in 2018 to learn how muscles work.)

By way of illustration, this was my favorite tweet of 2017.

Right there you have an image created by Brittany Wright, a chef, and shared with the 200,000 people who follow her on Instagram. Loads of people before Ilona had noticed it, but she connected that noticing to her capacity for creating mathematical experiences for children. She surveyed her Twitter followers, asking them to name their favorite banana, receiving over one thousand responses. Then on her blog she posed all kinds of avenues for her students’ investigation – distributions, probability, survey design, factor analysis, etc.

That skill – taking an interesting thing and turning it into a challenging thing – is one of teaching’s “unnatural acts.” Who does that? Not civilians. Teachers do. And I want to get awesome at it.

But Ilona ran a marathon and I want to run some wind sprints. I need quick exercises for strengthening that muscle. So here are my exercises for 2018:

I’m going to pause when I notice mathematical structures in the world. Like flying out of the United terminal in San Antonio at last year’s NCTM where I (and I’m sure a bunch of other math teachers) noticed this “Suitcase Circle.”

Then I’ll capture my question in a picture or a video. Kind of like the one above, except pictures like that one exist in abundance online.

Civilians capture scenes in order to preserve as much information as possible. That’s natural. But I’ll excerpt the scene, removing some information in order to provoke curiosity. Perhaps this photo, which makes me wonder, “How many suitcases are there?”

In order to gauge the curiosity potential of the image, I’ll share the media I captured with my community. Maybe with my question attached, like Ilona did. Maybe without a question so I can see the interesting questions other people wonder. You may find my photos on Twitter. You may find them at my pet website, 101questions.

I want to get to a place where that muscle is so strong that I’m hyper-observant of math in the world around me, and turning those observations into curious mathematical experiences for children is like a reflexive twitch.

(Plus, that muscle will be more fun to strengthen in 2018 than literally any other muscle in my body.)

BTW. Check out the 3-Act Task I created for the Suitcase Circle. It includes the following reveal, which I’m pretty proud of.

BTW. The suitcase circle later turned into Complete the Arch, a Desmos activity, which has some really nice math going on.

[Suitcase Circle photo by Scott Ball]

Featured Comment

Ilona Vashchyshyn :

I would just add that we shouldn’t forget that the classroom is a world within a world for us to notice, and that while many great, unforgettable tasks are based on interesting phenomena that we’ve observed or collected outside of school, on a day-to-day basis, high-impact tasks are probably more likely to be rooted in our observations and interactions with our students (in fact, even the banana tweet and post were sparked by a conversation with a student who was eating what was, to me, an exceptionally green banana). They tend not to be as flashy, but can have just as much impact because they’re tailored to the kids, norms, relationships, and histories in our classrooms.

About 
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.

8 Comments

  1. Reply

    Dan, thanks for this unexpected shout-out and your kind words. I’m still very much working on connecting these muscles myself.

    Featured Comment

    I would just add that we shouldn’t forget that the classroom is a world within a world for us to notice, and that while many great, unforgettable tasks are based on interesting phenomena that we’ve observed or collected outside of school, on a day-to-day basis, high-impact tasks are probably more likely to be rooted in our observations and interactions with our students (in fact, even the banana tweet and post were sparked by a conversation with a student who was eating what was, to me, an exceptionally green banana). They tend not to be as flashy, but can have just as much impact because they’re tailored to the kids, norms, relationships, and histories in our classrooms.
  2. Reply

    Everybody knows music is the same as mathematics, but I invite you to listen to song´s lyrics (which are a human production) and create teaching material out of them. In my particular case, my ears must be closer to my teaching muscle than my eyes.

  3. Reply

    Hi Dan, Following your talk at the AMTNJ, I created a Desmos activity with this picture. I had originally given it as a picture in my challenges folder for my students and asked the specific question “How many suitcases?” But following your great suggestions on creating more agency and interest in math investigations, in doing fake math for real world contexts or real math for fake contexts (I cannot quite remember the formulation on that), I thought I should instead ask the students to come up with “math” questions about the picture (I wanted to limit it to “math” questions to try to set some parameters for my students, but the hide-student-response button on Desmos will work too for that). Other interesting questions, like you note, include the radius size or the area contained by the ring or many other items that might come as questions. I’d really love a blog post about that real math fake math and non-routine cognitive skills we could all be driving at in each of our classes. I’m not there yet, but I feel like that focus would be a good one for me. Thanks so much for your thoughtfulness on our craft of teaching and for always soliciting feedback on ways we use your ideas or ways we try to improve our own craft. I learn so much every time I read your materials and your readers’ comments and although I’m 23 years into this game of teaching math, I still find it exciting to improve what I am giving the students and so appreciate having all these great materials you share so I can get better.

  4. Reply

    Thanks for your feedback, Dianne. So fun to hear about people putting those principles to work so quickly after a talk. If you want to read more about the real world v. real work, please have a look at this post.

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