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Exploding Dots! Global Math Week 2017!

Hi all,

Life is getting away from me with some tough personal stuff. So I haven’t been as active with the online math teacher community/twitter/blogging/etc. for a while, and I sadly probably I won’t be for a while.

That being said, I really wish I could participate in this initiative that Raj Shah (no relation!) shared with me a while ago. But because of life stuff I might not be able to. But one of the biggest things I want to do is bring joy into the math classroom as a core value, and this does that. And I love the idea of a collective joyful math moment for students and teachers all around the world! I’ve done a bit of exploration with this initiative — exploding dots — and I think it’s fabulous and full of wonderment. What it takes? At minimum, 15 minutes of classtime! I highly recommend you reading the guest post I asked Raj to write (below), and joining in this worldwide effort to celebrate the interestingness of mathematics!

Always,

Sam

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The Global Math Project is an invitation to students, teachers, and communities everywhere to actively foster their sense of wonder and to enjoy truly uplifting mathematics. Math is a human endeavor: It’s about thinking creatively, exploring patterns, explaining structure, and solving real problems. The Global Math Project will share a unifying, joyful experience of mathematics with people all across the world.
Our aim is to thrill 1 million students, teachers, and adults with an engaging piece of mathematics and to initiate a fundamental paradigm shift in how the world perceives and enjoys mathematics during one special week each year. We are calling it Global Math Week.
This year, Global Math Week will be held from October 10–17. The focus of Global Math Week 2017 is the story of Exploding Dots™ which was developed by Global Math Project founding team member James Tanton, Ph.D.
Exploding Dots is an “astounding mathematical story that starts at the very beginning of mathematics — it assumes nothing — and swiftly takes you on a wondrous journey through grade school arithmetic, polynomial algebra, and infinite sums to unsolved problems baffling mathematicians to this day.”
The Exploding Dots story will work in any classroom, with a variety of learning styles. It’s an easy to understand mathematical model that brings context and understanding to a wide array of mathematical concepts from K-12 including:
  • place value
  • standard algorithms for addition, subtraction, multiplication, and long division
  • integers
  • algebra
  • polynomial division
  • infinite sums
  • and more!
Teachers routinely call Exploding Dots “mind-blowing”!
“I am still amazed by this. Exploding Dots has changed my fifth grade class forever!” – Jo Anna F.
 
“This makes me WANT to teach algebra!” – Kristin K.
 
“YES!” Hands up in the air in triumph! Decades of believing I couldn’t do math—poof! Exploded!”  – Jennifer P.
Join us for Global Math Week, October 10 – 17, 2017!
 
During Global Math Week, teachers and other math leaders are asked to commit to spending from 15-minutes to one class period on Exploding Dots and to share their students’ experience with the Global Math Project community through social media.
You can join the movement in four easy steps:
 
1) See Exploding Dots for yourself
Here’s a brief overview: https://youtu.be/KWJVAjONqJM
2) Register to Participate at globalmathproject.org
3) Conduct an introductory Exploding Dots experience with your students during Global Math Week
All videos, lesson guides, handouts are available for free at globalmathproject.org. Since everything is available online, inspired students (and teachers) can continue to explore on their own.
4) Share your experience on Twitter during Global Math Week using #gmw2017
That’s it!
The power of the global math education community is truly astounding. To date, over 4,000 teachers have registered to participate in Global Math Week (#gmw2017) and they have pledged to share Exploding Dots with over 560,000 kids from over 100 countries! We already over half-way to our goal
Help us reach and thrill a one million students!
The Global Math Project is a collaboration among math professionals from around the world. Spearheaded by popular speaker, author, and mathematician James Tanton, partner organizations include the American Institute of Mathematics, GDayMath.com, Math Plus Academy, and the National Museum of Mathematics.
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Bragging about my school

This is a milestone for me. I have been at my school for ten years, and this is the start of my eleventh. It’s the only school I’ve worked at. That’s a testament to my school, but more specifically, to my colleagues.

Last year, my school’s awesome director of communications contacted the math department to let us know that the one issue of the magazine she publishes four times a year was going to focus on math. And she wasn’t kidding! The cover of the magazine had most of my multivariable calculus kids on it (thinking deeply at the math-art show I helped put on last year)!

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One of my favorite things is that the feature article with an alliterative title, Making Math Meaningful, was simply the transcript of a roundtable discussion we had. A bunch of math teachers got in a room around a big table, and we were led by our director of communications who had done her research and come with some questions. There was a digital recorder in the center of the table. And through talking with carefully crafted prompts, we got to think deeply and collectively about our own practice. I can’t even tell you how interesting it was to listen to my colleagues during that facilitated conversation, and how proud I was to be in a school with such like-minded folks that I have the opportunity to learn from. (If you’re a department chair or academic dean, consider doing this!)

I wish I could just post a PDF of the article for you to read, but alas, the whole magazine is online but can’t be downloaded. Here are two quotations to whet your appetite:

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So if you want to read about a department that is doing strong work moving towards inquiry-based learning, and read the words of real teachers having a real conversation playing off of each other, I highly recommend you:

  1. Go to this site
  2. Make the magazine full screen
  3. Read pages 18 to 29

That is all!

A curriculum is more than a set of papers

I wrote, with my friend Brendan, an advanced geometry curriculum. I was insanely proud of some of it. For those of you who know me, you know I love writing curriculum. It takes time, so much time, but it flexes the best part of my teacher brain. I’m forced to think backwards (“what am I trying to really do here? what matters?”) and requires creativity (“how can I get kids from point A to point B by having them do the heavy lifting, but in that sweet spot where I’m not necessary but their collaboration is? where that moment of invention and surprise is real?”). It is tough, and a lot of what I do isn’t great. But even my worst is better than any textbook I’ve seen.

Back to geometry. A few weeks ago, I met with one of the teachers at my school who is going to be teaching advanced geometry. I shared all my materials with her electronically, but I met to talk through things in more detail. But this meeting reminded me of something I’ve felt acutely for a few years: a curriculum is more than a set of papers.

As I wrote each piece of the geometry curriculum (or as I worked with my colleague as he took the lead), I had so much whirring around in my mind. I knew the intentionality of the questions and their ordering. I knew where kids would stumble. I knew where I asked questions that had no answers — on purpose — to get kids to think. I knew that I included a particular question in order to prompt a class discussion. I knew there were placed I needed kids to call me over to have a discussion with each group individually.  I knew I had included questions which were designed for me to verbally ask follow up questions. And of course I knew which things were hastily designed and didn’t work out so well when teaching.

But as I was attempting to go through my materials with her, it struck me pretty hard how hidden and implicit all those things were in that collection of papers that she had.

A real curriculum needs so much more, if someone else is going to successfully use it instead of me. When creating materials for other people in my department, who are teaching the same material, I started writing comments/notes in Word when I had a teacher move that I had in mind when crafting the problems:

teacher notesteacher notes2teacher notes3

It’s also a good reminder for me in the future. These notes help me and my colleagues remember what I was thinking of when writing my stuff. When I started doing this, I realized how a curriculum is a set of problems/activities with the intentionality behind the problems and teacher moves spelled out

In the past few years, I’ve had the fleeting and recurring thought: hey, I should organize all my geometry, precalculus, and calculus files neatly, and put them online in a systematic order for anyone to access. Maybe all of it will be useful to someone, maybe bits and pieces. I still sometimes think that. But what keeps me back from doing it is that gnawing feeling in the back of my mind: things need to be spelled out so someone else understands the flow and intention of each thing. And how to use it in the classroom. Where to stop. How to start. If there were any important “do nows” that weren’t captured in the sheets. Or knowing that someone was written as extra practice or to reinforce an idea that a class in a particular year wasn’t getting.

Over the past two years, it’s become harder and harder for me to open my feedly app and read blogposts. (I find most of my blogposts through twitter now.) It’s just been hard to find the time, and I get overloaded. And I haven’t had time to blog much either. And that sucks. But one thing I love about blog posts — that you can’t get on twitter/facebook/ed research — is that they often illuminate hidden ideas and bring to life something inert. Like when I read a blow-by-blow about an activity/problem set/ worksheet. Something that shows me the thinking that went into creating it, or better yet, how things unfolded in a classroom. What teacher moves happened? What were students thinking? [1]

If I wrote materials… and had a blogpost about how each day unfolded with those materials… that would be a curriculum at its best in my eyes. Because life is breathed into it. It becomes three dimensional. It involves people. The teacher. The students. And it makes explicit what is happening and why. [2]

Note: Funnily enough, Sadie posted a great piece on the idea of “curriculum” the day after I started writing this one! It is definitely worth a read.

[1] I like writing these kinds of posts — though they take a long time. Here’s a recent one: https://samjshah.com/2017/04/28/multiple-representations-for-trigonometric-equations/

[2] Obviously I won’t ever have the time to do this. But it’s nice to fantasize about. An extensive 180 curricular blog. Writing this post also reminds me that I need to get back to regularly reading blogposts.

 

Bridge to Enter Advanced Mathematics (BEAM)

“Fundamentally, this is a question about power in society,” said Daniel Zaharopol, BEAM’s director. “Not just financial power, but who is respected, whose views are listened to, who is assumed to be what kind of person.”

***

My friend Dan said this to a New York Times reporter, in the context of an organization that he started called BEAM. It is a pathway for underserved middle school students to gain exposure, interest, and opportunities to see how amazing the world of mathematics can be. This is important. Why?

Guess how many math and statistics Ph.D.’s were awarded in 2015 to black students?

20.

***

So how do we change that? Dan and I were both at a lecture at Teachers College at Columbia yesterday given by Erica Walker. Her thesis? That you need mathematical socialization, spaces, and sponsoring (mentoring) to build positive, strong math communities.

Dan’s organization is doing that.

I highly recommend checking out the BEAM website to read about the ways it is trying to change the status quo.

But more than that, I recommend reading the article the New York Times reporter wrote about BEAM. She took an intimate, in-depth look at the program through the eyes of its participants — from riding the subway together to their discussion of the Black Lives Matter movement to their families. You may get welled up, as I did.

BEAM.png

 

Teaching is hard work. Election aftermath.

Yesterday, I told one of my precalculus classes how it was an exciting day. I was setting them up because it was election day, and kids at my school are heavily interested in politics, so I thought they’d say “yes! Election!” And I would say: “Actually, it’s because one of my best friends from college is having a baby.”

Of course that setup didn’t work, because of course a kid asked “why is today exciting?” Thanks, kid. But I told the class about my friend’s baby.

Yesterday evening, as the election results came in, I got more and more anxious. And when it was clear that Trump won, I was destroyed. I am not going to use this blogpost to explain my love for Clinton, or why Trump makes my blood boil. Instead, I want to just share how my day has gone.

I teach at an independent school in Brooklyn, and the population of kids and parents we serve are (for the most part) liberal. The kids are politically active and aware and interested. Today, I came to school and kids were destroyed.

In my first class, I talked to kids a bit, and then asked them what they wanted to do. After hearing them, I came up with the following plan. The kids who woke up to the news and wanted to learn more and get informed could read articles online. (There were about 4 of those kids.) I just asked that before they started reading, they take 3 minutes to type out all the questions that they have — so help them start processing. (Like “How could this happen? What was wrong with the polling? Who was voting for Trump? What does this mean for issue X?”). For the others, we formed a circle with the desks and I let kids talk. At points, kids cried. I didn’t join in — I wanted this to be a space for them. They expressed real sadness, hopelessness, optimism, anger, frustration, embarrassment, terror, empathy. I really heard my kids, and when talking about this election, they were speaking their truth, about their hopes and dreams (and how those hopes and dreams were altering). It destroyed me inside to hear them. To see how much this election has affected them. I guess I hated the fact that my kids are feeling what I’m feeling. I don’t want that for them.

I went to my second class, that precalculus class that I told about my friend’s baby. The first thing a kid said to me was inquiring about my friend’s baby. That small gesture — that this student would remember that — lifted my spirits. In this class, more wanted to read the news, and a handful of us talked. This discussion tended to a bit more political punditry — about the what’s and the how’s and less about their emotional state. I suspect they got many of their feelings out in their previous classes.

In my third class, we watched Hillary’s concession speech.I teared up twice during the speech. One kid left to gather themselves for a few minutes after the speech. I didn’t know what to do after. Kids said they didn’t feel like discussing things anymore — they were discussed out — but they also didn’t see how they could focus on work. I made the executive decision to spend the last 20 minutes of class having my kids watch the pilot of the West Wing. I hoped that some optimism in politics might help.

I have one more class to go. It’s a 90-minute block. I’m drained, right now. I don’t have much more in me. I suspect kids are also drained, but I don’t know. I’ll suss out how things are, and try to get through it.

I’m exhausted. Yesterday I woke up at 5:30am to vote. Yesterday I didn’t get to bed until very late (maybe 1pm), and then woke up at 3am to watch Trump’s victory speech. I then read articles until I forced myself to sleep from 4-6am.

Teaching is hard work. Yes, there are lesson plans and grading and meetings and a zillion other things. But days like today, days like today keep me in check. And reminds me how hard the hard work can really be. Because the hard work is being an emotional support. To let kids cry. To let kids know you cry. And to get through the hard times together.

Update: My last class came in with bags under their eyes. I was also tired. I asked them what they wanted to do. A few wanted to continue talking, a couple wanted to do some math and do some talking about the election (a mix), and one just wanted to do math. I decided we would go over the nightly work first, and then talk about the election.

When going over the nightly work, kids were actually focusing better than expected. They asked questions. They were able to answer questions. It was going well. I then ended up going on a fascinating tangent about fractals (related to one of the questions we talked about). And when I realized kids had never heard of fractals before, I showed them a youtube fractal video. Then they wanted to know how it was made. So I gave a short 10-minute lecture on the complex plane, and how the Mandlebrot set is formed. Kids were entranced by the video. I gave a 5-minute break before we sat down to talk about the election. (During the break, kids were in the hall watching more of the fractal video on one of their phones!) When we returned, everyone was silent. No one spoke. I just let it hang there. Eventually one voice. Then another. It wasn’t a rowdy discussion. Not everyone was in it. But most kids had something to say. And then when the day was close to ending, and there was a natural lull, I used a comment about “voting systems” to show a video about alternative voting systems. And then I let kids go home.

I just made the first four slides for class tomorrow. They’re not fancy. I’m tired. But I think they encapsulate what I’ve taken away from today.

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***

Now I must end. I now have to change all my lesson plans for the upcoming days, prepare for parent visiting day tomorrow, and write narrative comments. This feels impossible. But I needed to process today.

***

UPDATE: A student gave me a paper flower she made today, to thank me for facilitating a conversation about the election in our class on Wednesday. And that flower is going to stay on my desk all year to remind me of the other things we do as teachers that can be meaningful.

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Technically Beautiful

Last week, Technically Beautiful opened. It is a math-art show that I helped put together (with another math teacher and a museum educator) at our school. We have a small teaching gallery at my school, and we wanted to do something special for this space which capitalized on our expertise. That is how Technically Beautiful came into being.

Technically Beautiful Card Art Draft 4 - 640px.jpgThe poster for the show. The name, by the way, came from a #MTBoS tweep!

In this post, I wanted to share with you the gallery virtually. (In a future post, whenever I get a chance to breathe, I’d love to talk about the programming we made around the show and possibly a bit about how the show actually came into being.)

Here’s a walkthrough video of the gallery:

Here’s our vision statement for the show:

The website for the show is here. The five artists featured in the show are: George Hart, Edmund Harriss, Veronika Irvine, the Oakes Twins, and Paul Salomon.

And lastly, here are photos of many of the pieces:

 

 

Taking Stock

I spent 5 hours today cleaning out my desk, going through files, recycling mountains of paper. In concrete terms, it means school is over. Graduation is tomorrow. And then: I’m on summer vacation [1]. So now a bit of a brain dump as I take stock.

I’ve found this year to be an important transition point:

For the first time, I taught ninth graders, and for the first time, I taught geometry. And in order to do that, I worked an insane number of hours with my partner-in-crime and co-teacher BK in order to write an entire curriculum from scratch, from head to toe. Yup, you read that right. We — in essence — wrote a textbook. We sequenced the course, we wrote materials and designed activities for the course, and we had kids do all the heavy lifting. There are particular moments as a teacher which standout as “big moments.” Moments where we know we’ve developed immensely as a teacher. Transitioning from individual and partner work into total groupwork was one of those moments. Converting my non-AP calculus course into a standards based grading course was one of those moments. And writing a curriculum from scratch, in a single year, with an insanely thoughtful collaborator was the most recent of those moments [2].

The previous two years (before this school year) were two of the hardest years I’ve had as a teacher. We teachers were called on to do a lot in the wake of our school’s five year strategic plan — and it became overwhelming. I had no work-life balance. And  I became a bit curmudgeonly because of those tough years. But this year, things have been better. I still have no work-life balance, but the overwhelming onslaught of initiatives have subsided. One of the things I did to actively try to stay positive this year was to write down every single day one good thing that happened to me — big or small. From the first day of classes to the last. And those things are archived here. This was especially important because at the start of the school year, my mom was diagnosed with cancer (she is doing very well, fyi, no worries).

That being said, I am going to make a goal: that next year, I am going to just let the things that I can’t control go… There’s no point in getting worked up over something that you can’t do anything about. Instead, I’m going to stay loose, and bring back my frivolity and humor, and go off the beaten path in class more. While organizing today, I was looking through a number of old emails and cards from students, and saw so many inside jokes and fun times that they references… and then I thought about this year… and I came up blank. I couldn’t think of a time that I doubled over laughing in class. I couldn’t think of an ongoing joke that I had with a student. I could think of great lessons and a ha moments, but nothing frivolous and fun. So my vow is to make sure that next year involves more joy and laughter. For me, and for my studentsEvery day.

Wow, yes, this braindump led me to something big. With that, I’m out.

[1] That doesn’t mean I’m done with school. I have lucky 13 college recommendations to write. And two summer projects that each will take 25 hours each to complete (revise my multivariable calculus curriculum; plan for our new schedule next year with longer blocks).

[2] I’ve written entire course curricula before. Calculus, for example. But that took a few years to write and get added to. And Adv. Precalculus, which I did in a single year, but lacked the collaboration and innovation that I was able to do this year with BK.