On Thursday at #NCTMAnnual, four speakers urged teachers to reflect on their power not just to help students encounter mathematical knowledge but to change how students define themselves in relationship to math and to each other.

Video of each of their talks is online right now and each presenter invites you to join them in a follow-up conversation about their ideas over the next month. (More below.)

• Lauren Lamb told us about her experience learning mathematics as a young woman of color, how she often felt invisible in her classrooms and unrepresented in her textbooks. She described the ways her teachers did and didn’t involve her in her own mathematics education.
• Javier Garcia contrasted the ways we talk about students (as though they’re incomplete, fallible) and mathematics (as though it’s complete, infallible) and made a case that teachers should reverse those two descriptions.
• Nanette Johnson impressed upon the audience the fact that each of them will leave behind a legacy for their students, an indelible imprinting of their efforts, either positive or negative.
• Andrew Gael revealed the potency of our presumptions about student competence, and how students often live up and down to those presumptions. What we believe about student competence affects how we work with those students, which affects their opportunities to develop competence.

Great talks each one. Each one well worth your time.

But what happens to talks like these after they’re over? The ShadowCon Hypothesis is that the ideas from even great talks rarely survive contact with the reality of classroom instruction; that absent any kind of conversation or community organized around their implementation, those ideas are too easily put in a box labeled “Nice to Think About” or “Maybe Later.”

Each of our speakers agree with that hypothesis and each one wants to participate in a conversation with you over the next month. Sign up for a course you’d like to think and talk more about. We’ll place you on an email thread with a couple of random, interesting colleagues. Then you’ll receive a new discussion prompt once per week for the next four weeks, starting May 7. On a weekly basis, the speakers will summarize the most interesting ideas and answer the most perplexing questions from across all the groups.

It’s going to be a very interesting month.

[image via Cassie Sisemore]

The icon on my airplane’s wifi signal indicates I’m somewhere over Wyoming right now, en route to Washington, D.C., for collaboration and conviviality with thousands of math teachers from all around the United States. I’m looking forward to reconnecting with old colleagues and meeting new ones so let me tell you where we’ll find each other. If we’ve met, let’s catch up. If we’re just meeting, let me know what you’re working on or wondering about.

Wednesday

Desmos Preconference Workshop

My team will be running a morning workshop and an afternoon workshop on our newest, hottest technology and activities.

Also: Emdin’s opening session; NCTM Game Night.

Thursday

ShadowCon

Zak Champagne, Mike Flynn, and I have recruited four interesting speakers — Lauren Lamb, Javier Garcia, Nanette Johnson, Andrew Gael — each offering their own variation on a similar theme. The presenters and the organizers collaborated on these ten-minute talks for the last several months. The process was a joy and the resulting talks are really exceptional. We’ll also introduce a new way to continue the call to action of those talks long after they have ended.

Desmos Happy Hour & Trivia

Beep beep! Right after ShadowCon, I’m speed-walking straight to NCTM’s Top Rated Happy Hour Event. Then we’ll commence NCTM’s Highest Grade Trivia Competition. I can’t divulge any of the categories but if you were to brush up on your naughty words that rhyme with math vocabulary, I don’t think you’ll regret the effort.

Also: Sessions with Stiff, Rosen, Briars, Usiskin, Cirillo, Pelesko, and time at the Desmos booth, trying to convince people to buy our free calculators and free activities. (Pretend you don’t see me, friend. Pretend you’re on the phone with your mother. Pretend I didn’t invent those exhibitor-dodging moves. We are having this conversation, friend.)

Friday

Full Stack Lessons

I know my talk is at 8 AM. I know that. But I’ll be bringing coffee for at least me and one other person in the room. Maybe three more people if I can find one of those coffee carrier trays.

Here’s the description:

Two teachers can take the same idea for a lesson and experience vastly different results in class. This is often because one teacher taught from the full “stack” of questions and the other taught from just part of it. We’ll look at the contents of that stack and learn how to put the full stack of questions to work in your classes.

Also: Zager, Martin, United Airlines.

Here are three items that crawled into my head some time during the last few months and didn’t find their way out yet. This post is brain surgery.

Lesson Exploder

I have thought about this tweet from David Coffey at least once per week for the last five months.

I'm really enjoying @HrishiHirway's @SongExploder. His episode with @Lin_Manuel was especially informative.

I wish #MTBoS would do some Lesson Exploders – breaking down your process of making lessons.

— David Coffey (@delta_dc) November 26, 2017

The Song Exploder podcast interviews artists about the craft of songwriting. The artists describe their motivations for creating their songs, what they were trying to accomplish, and how they tried to accomplish it, all while the Song Exploder team teases out key elements of the song for illustration. I feel smarter about the craft of songwriting whenever I listen to it. Maybe not as smart as if I had spent a year at the Oberlin Conservatory of Music, but for how much smarter I’m feeling, it’s hard to argue with Song Exploder’s cost (free) and scale (internet-sized).

Now swap “teacher” for “artist” and “lesson” for “song.” I know what we can swap in for “Oberlin Conservatory of Music.” Classroom visits. Lesson studies. Problem solving cycles. Professional learning communities. Those are all very effective and also very expensive. I don’t know what to swap in for “Song Exploder,” though — an option that is less effective but basically free and scales with the internet.

What kind of digital media could we use to a) highlight something significant and useful about the craft of teaching b) as quickly as possible c) distributed as widely as possible d) in a form that’s replicable and episodic? (Song Exploder is up to 133 episodes right now.)

What current examples can we find? Teaching Channel videos? Blog posts? Lesson plans? Unedited classroom video? Marilyn Burns distills classroom anecdotes into really popular tweets.

What inspiration can we take from other fields? Delish videos? NFL Red Zone / Mic’d Up? Mystery Science Theater 3000? Twitch streaming?

New Jersey Turnpike

I can’t figure out the tolls on the New Jersey Turnpike.

If you don’t come from turnpike territory, how it works is you enter the turnpike somewhere and you exit the turnpike somewhere else. You pay depending on where you entered and exited.

My assumption is that the pricing would look pretty linear as a function of the miles traveled. Like this:

But it doesn’t. It looks like two linear functions with the second piece starting maybe at the Garden State Parkway. (Why?) And the Pennsylvania Turnpike exit is also way more expensive than a linear function would predict. (Why again?)

Here is the website that tells you the cost of different trips on the turnpike. Eric Berger, our CTO at Desmos, helped me type code into my browser’s Javascript console that returned all the data. Feel free to dig in. I’m looking for answers to my questions about pricing and I’m also interested in possible classroom applications of the data.

Cape Town’s Zero Day

Cape Town has a water crisis and a website that until recently calculated a “Zero Day” for their water reserves, a day when faucets will run dry and people will collect a daily allotment of water from central locations throughout the city.

That’s either terrifying or mathematically interesting, depending on which part of my brain I subdue while I’m thinking about it. How do they calculate that zero day? How can we put students in a position to appreciate, replicate, and even adapt those calculations for their own contexts?