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How I Welcome Newcomers to Online Teacher Professional Development (a/k/a the #MTBoS) and How You Can Too

Here is the promise:

There is a community of math educators that meets online at all hours of the day. They trade support and resources and many of the educators who meet there will tell you it is the most indispensable professional development they have ever experienced. If you lack support in your school or district, this community might actually get you through. I’m referring to the the Math Twitterblogosphere, or the #MTBoS, an abbreviation that is as unwieldy and charming as the community it names.

Here is the reality:

Where am I? Who are all these people? Is it rude to just say something to somebody? These conversations look interesting but do I just … jump in?

Here is an ugly bit of unexamined privilege:

Loads of people informed me immediately that, nope, Twitter only works that way if you already have lots of followers, if you’re already in the community, and that it also helps to belong to a demographic that is accustomed to being listened to all the time.

People informed me that their first leap into this teaching community was scary, that getting “shot down” was bad, but bad also was simply getting ignored.

I decided I didn’t want to ignore a tweet from a newcomer to the Math Twitterblogosphere. So about a month ago I wrote up the designs for a Chrome extension and hired a freelancer to build it. The extension highlights tweets from users that meet any criteria I choose.

Here is my “Welcome to the #MTBoS” rule. It highlights tweets from anyone with fewer than 100 tweets, people who are likely new in town, so I can make sure they hear from somebody.

The results have been a blast. I don’t break much of a sweat on these welcome wagon tweets. “Never stop tweeting” is my standard greeting, after a more personal remark. Other times I try to connect newcomers to the resources they’re after. Regardless, people are generally really excited to receive these quick tweets.

That’s someone whose day got made because this little Twitter extension made it easy for me to make sure she didn’t get ignored.

You can make someone’s day too. Loads of these newcomers aren’t following me. Many of them are looking for classroom teachers to follow. Many of them are looking for people who are only a couple of years ahead of them in their careers, not ten or twenty.

You’re welcome to install the same extension, without any warranty, and with only the most meager set of instructions. (If I start hearing that a bunch of you want to install it, I’ll give it a proper download page with a proper set of instructions. 2017 May 25: Updated with that page.)

Hey. Good work, everybody. People are writing dissertations about us. People from outside mathematics education are looking in at us as a model for professional community. This place is special. Let’s keep expanding it – its numbers, its representation, and its heart. This is one idea I had recently. What’s yours?

Featured Comment

Michael Pershan offers his work towards community building: comment on more blogs.

RIP Malcolm Swan

In trying to explain to family and friends what Malcolm Swan meant to the field of math education, I’ve been putting him in the same category as Michael Jordan – talents that come along once in a generation in disciplines that are as much art as science. In Swan’s case, he designed experiences that endeared students to mathematics, and endeared teachers to students, more effectively than anyone I know. You can pick up his The Language of Functions and Graphs, now thirty years old, and wonder, “What have we been doing all this time?” Swan drew math out of the world and thought out of our students in ways that feel challenging and new even today.

Malcolm was uncommonly humble and generous for someone of his talent. He was willing to spend time and trade ideas with me long before I had anybody’s name to drop, or any name of my own. He was also uncommonly dedicated to the field of math education, writing articles, giving talks, and hosting workshops, and all throughout you knew he believed completely that you too can do what I do, that math education isn’t art or science so much as it’s design. And he believed that design could be taught and learned.

That’s why I’m sad for everyone who knew Malcolm personally, for his family and his colleagues at the Shell Centre, but I’m not as sad for our profession as I thought I would be. Malcolm’s talent was generational and unique, but he did more than any of us could have hoped to explain it. Over his career, he added to our profession in permanent ways far more than his death now subtracts. I know we will still be learning from Malcolm for decades. And throughout those decades, the best day of my week will be any day I get to introduce a new teacher to his work, and pass along his conviction that “you too can do what he did.”

The Difference Between Math and Modeling with Math in Five Seconds

Jim Pardun sent me a video of a dog named Twinkie popping balloons in the pursuit of a world record. How you train a dog to do this, I don’t know. How there is a world record for this, I don’t know either.

What I know is that this video clearly illustrates the difference between math and modeling with math.

You can’t break math. Some people think they broke math but all they did was break ground on new disciplines in math where, for example, triangles can have more than 180° and parallel lines can meet.

Our mathematical models, by contrast, arrive broken. “All models are wrong,” said George Box, “but some are useful.” And we see that in this video.

Twinkie pops 25 balloons in 5 seconds. How long will it take her to pop all 100 balloons? A purely mathematical answer is 20 seconds. That’s straightforward proportional reasoning.

But mathematical modeling is less than straightforward. It requires the re-interpretation of that answer through the world’s imperfections. The student who can quickly and confidently calculate 20 seconds may even be worse off here than the student who patiently thinks about how the supply of balloons is dwindling, adds time, and arrives at the actual answer of 37 seconds.

Feel free to show your classes that question video, discuss, and then show them the answer video. Or if your class has access to devices, you can assign this Desmos activity, where we’ll invite them to sketch what they think happens over time as well.

The difference between the students who answer “20 seconds” and “37 seconds” is the same difference between the students who draw Sketch 1 and Sketch 2.

You might think you know how your students will sort into those two groups, but I hope you’ll be surprised.

That difference is the patience that modeling with math requires.

BTW. I’m very interested in situations like these where the world subverts what seems like a straightforward application of a mathematical model.

One more example is the story of St. Matthew Island, which dumps the expectations of pure mathematics on its head at least twice.

Do you have any to trade?

2017 May 19. Steve Rein asked for the data set. Right here.

The Bureau of Non-White Dude Math Education Keynote Speakers

At a workshop in New York City yesterday, I was complimented in the morning for my In-N-Out Burger activity (which was actually created by Robert Kaplinsky) and in the afternoon for my File Cabinet activity (which was actually created by Andrew Stadel). This mix-up will come as no surprise to either Andrew or Robert or anyone who has ever seen the three of us presenting at a conference together. This happens all the time.

Also this week I received an email from May-Li Khoe, a researcher at Khan Academy, reflecting on her experience seeing Fawn Nguyen keynoting CMC-North. Both May-Li and Fawn are Asian-American.

I did not expect to be so affected by having Fawn speak during the keynote. Obviously the content of her presentation made an impression on me, but reflecting back later, I realized that I have never seen anyone remotely resembling myself as a keynote speaker, at any conference, ever.

We want all students to see themselves as people who can do mathematics, regardless of their race, ethnicity, gender, or any other variable. The power of mathematical thinking is good for everybody, and nobody should feel like their identity excludes them from that power.

The project of extending that access will require a diverse corps of teachers, which will require that a diverse corps of teachers sees teaching as a career full of advancement possibilities. Which means, among other efforts, that we need a more diverse corps of teachers speaking in front of large rooms of teachers.

So if you’re organizing a conference, I’m asking you to consider inviting any of the names below to give a talk before you consider inviting another tall, white dude. I’ll personally vouch for all of their abilities to deliver outstanding talks to large rooms of people. I have included Twitter contact information for each of them, along with websites and sample talks. I’m also happy to connect you with any of them personally. Let me know.

  • Maria Anderson. Applying research to instruction. [Twitter, Web, Sample]
  • Harold Asturias. Teaching mathematics & academic language to emerging bilingual students. [Twitter, Sample]
  • Deborah Ball. Teacher development; mathematical knowledge for teaching. [Twitter, Web, Sample]
  • Robert Berry. Formative assessment; equitable experiences for all math students; #blackkidsdomath. [Twitter, Sample]
  • Jo Boaler. Cultivating a growth mindset in mathematics. [Twitter, Web, Sample]
  • Marilyn Burns. Helping students make sense of math. [Twitter, Web, Sample]
  • Ed Campos, Jr. Technology integration. [Twitter, Web]
  • Peg Cagle. Creating engaging mathematical experiences. [Twitter, Sample]
  • Shelley Carranza. Technology integration. [Twitter]
  • Rafranz Davis. Technology integration; creating equitable experiences for all math students. [Twitter, Web, Sample]
  • Juli Dixon. Teaching students with special needs. [Twitter, Web, Sample]
  • Annie Fetter. Mathematical thinking and problem solving. [Twitter, Sample]
  • Kristin Gray. Creating engaging mathematical experiences. [Twitter, Web, Sample]
  • Rochelle Gutierrez. Creating equitable experiences for all math students (and their teachers). [Twitter, Sample]
  • Shira Helft. Instructional routines that promote discourse and sensemaking. [Twitter, Sample]
  • Ilana Horn. Cultivating a student’s mathematical identity. [Twitter, Web, Sample]
  • Elham Kazemi. Understanding a student’s mathematical thinking. [Twitter, Sample]
  • Jennie Magiera. Technology integration. [Twitter, Sample]
  • Danny Martin. Creating equitable experiences for all math students. [Sample]
  • David Masunaga. Mathematical inquiry, particularly in geometry.
  • Fawn Nguyen. Mathematical thinking and problem solving. [Twitter, Web, Sample]
  • Cathy O’Neil. The powerful and sometimes pernicious effect of algebraic models in the world. [Twitter, Web, Sample]
  • Carl Oliver. Integrating social justice and mathematics education. [Twitter, Web]
  • Megan Schmidt. Integrating social justice and mathematics education. [Twitter, Web]
  • Marian Small. Creating engaging and productive mathematical experiences. [Twitter, Web, Sample]
  • Joi Spencer. Integrating social justice and mathematics education. [Twitter, Sample]
  • Lee Stiff. Technology integration; creating equitable experiences for all math students. [Sample]
  • John Staley. Teaching mathematics for social justice. [Twitter, Sample]
  • Greg Tang. Creating engaging and productive mathematical experiences for elementary students. [Twitter, Web, Sample]
  • Megan Taylor. Creating engaging and productive mathematical experiences. [Twitter, Sample]
  • Kaneka Turner. Cultivating a student’s mathematical identity. [Twitter, Sample]
  • Sara Vanderwerf. Creating equitable experiences for all math students. [Twitter, Web]
  • Jose Vilson. Creating equitable experiences for all math students. [Twitter, Web, Sample]
  • Audrey Watters. Analyzing technological trends and their effect on education and society. [Twitter, Web, Sample]
  • Anna Weltman. Integrating creativity, art, and mathematics. [Twitter, Web, Sample]
  • Talithia Williams. Statistics; diversity in higher education. [Twitter, Sample]
  • Jennifer Wilson. Helping students make sense of mathematics; #slowmath. [Twitter, Web, Sample]
  • Cathy Yenca. Technology integration. [Twitter, Web, Sample]
  • Tracy Zager. Literally anything – have her read the tax code. (Also once her book comes out, your probability of getting her for your conference decreases asymptotically to zero. Buy now.) [Twitter, Web, Sample]

Add someone deserving or promising in the comments. Attach the same information you see above.

[Photos by Cathy Yenca and Kristin Hartloff.]

2016 Dec 14. The commenters have already caught a bunch of my really embarrassing omissions. Thanks for picking up my slack, everybody.

2016 Dec 16. In response to this critique from TODOS, I’d like to clarify that, yes, this list is incomplete, and my hope was that it would be made more complete in the comments. Additionally, my process in constructing the list is inherently biased towards a) speakers who have already given addresses to large rooms, which likely reflects the institutional biases of organizations who rent large rooms, b) speakers I have already seen, many of whom probably don’t challenge my privilege in ways I’d find uncomfortable, c) speakers who address secondary educators on themes of technology and curriculum design, themes reflective of my own disciplinary interests, d) speakers whom I could remember, which reflects my own lousy memory.

In spite of all those biases, I decided it was better for this list to exist than to not exist. I’m interested in hearing from TODOS (or anybody else) how this project could have done a better job advancing the interests of students and teachers of color.

Featured Comment

Elham Kazemi:

I was in graduate school before I had my first Persian teacher (if you exclude my education in Iran). It was an amazing experience, and I did every ounce of work possible in that class.

Shock and Disbelief in Math Class

Reader William Carey via email:

Last year I realized that Pre-Calculus is really a class about moving from the particular to the general. We take particular skills and ideas students are comfortable with — like solving a quadratic equation — and generalize them to as many mathematical objects as we can — solving all polynomial equations. As we worked our way through polynomials, we wanted to move from reasoning about particular quadratic equations like y = x2 + 2x + 1 to reasoning about all quadratic equations: y = ax2 + bx + c. For homework, the students had to graph about twenty quadratics with varying a, b, and c.

Then we got together to discuss the results in class. They remembered that a controls the “fatness” or “narrowness” of the parabola and sometimes flips it upside down. They remembered that c moves the parabola up and down. They weren’t totally sure what b did. A few students adamantly maintained that it moved the parabola left and right (with supporting examples). After about fifteen minutes of back and forth, we decided to go to Desmos and just animate b.

Shock and disbelief: the vertex traces out what looks like a parabola as b changes. Furious math and argument ensue. Ten minutes later, a student has what seems to be the parabola the vertex traces graphed in Desmos. Is it the right parabola? Why? Can we prove that? (We could and did!)

Previously: WTF Math Problems.