Talking Circles and Math

Strange things happen when you go into a classroom and talk about something of which you’re very passionate. Sometimes, people take away something you had no intention of discussing. The same principle applies when giving a talk at a convention apparently.

When I was at NCTM talking about what I tried in my stats class, one of the slides I showed became an instant hit. It was posted on Twitter I think 5 times, making it one of the most popular tweets of all time.

So Geoff at Emergent Math asked me for a follow up explanation of tracking conversations. He flattered me, and I’ll oblige.

Last year around this time, I began to read Nate Silver’s The Signal and the Noise. As I read, I became more and more convinced that the narrative behind the book could drive my AP Statistics class. I set an intention to integrate the learning objectives of the stats class by reading parts of the the Signal and the Noise. For example, instead of introducing confidence intervals with a definition or an example, I really wanted to take the story of a flood plain in North Dakota to introduce the idea. This idea is what I presented at NCTM.

When I decided that I would assign actual reading to my class, I had an idea of how it would go. I would assign a reading, then at the next class I would begin a class with a simple question, “What did you LEARRRRNNNNN?” all mystical like, as if I was in one of those hoity-toity movies about … reading or whatever.

It turns out that when I framed the discussion this way, I didn’t exactly get the result that I was looking for. But, hey, this is coming from the guy who invented General Mutant Pancake Theory – no problem. I’ll just walk down the hall to my friends in the English and History departments and steal all of their ideas. One idea they had for me was tracking conversations.

The basic structure is this: Before class starts, I have students read and I give them some leading questions. Questions like:

  • What are the differences between an observation and an experiment?
  • How were correlation and causation discussed?
  • What is a lurking variable that came up?
  • How do we “prove” causation?

During class, students sit in a circle. We put up all the names on the board. Either a student or I are in charge of “tracking the conversation”. My job is to listen and ask questions. Their job is to make the conversation awesome.

In the diagram below, A(dam) makes a point about how causation can be confused with correlation, then D(enise) follows up with something she heard on NPR that relates to the pregnancy study. F(reddie) asks how one can prove causation and then A(dam) reminds him of a problem in which we talked about proving causation. C(eara) asks another questions about how this relates to confidence intervals, and the conversation continues.


We don’t really need arrow heads for any of these lines, we just need to see who’s involved and to what degree. G(reg), E(than) and B(etsy) haven’t chimed in yet, but everyone sees that, and at times I might direct the conversation at one of them if they still have no lines connecting them to the rest of the conversation. But usually, another student will call them out, which I think is super empowering.

What makes this work? First, no matter how advanced the students are, they are still amateurs in the subject area. Even though they may be great symbol manipulators or really understand what we’ve done so far, I intentionally gave them material that is new and just outside of their knowledge base.

Second, by taking myself out of the circle and being a guide, it takes the sense of agency away from me and gives it to them – again, then idea that I’m trying to empower them. I rarely correct any incorrect interpretation, but if it seems to pervade the conversation, I might ask some clarifying questions.

Caveat: this system probably isn’t working if you have a class of 30. I have only tried it with ~15. However, it’s totally possible to break the kids into smaller subgroups and do the same kind of thing.

I’ve been interested in Socratic-seminar-like conversations in math class for a long period of time. All knowledge is socially constructed, so when I see students being active agents in that process, it models what learning outside of the false environment of school looks like. Not to get all Vygotsky on you, but constructing a situation like this makes different neurons fire in young brains than just having them work independently.


Takeaways from #NCTM14

Nothing is rejuvenating like spending a few days with like-minded people. I feel incredibly fortunate that I was able to speak with many innovative, passionate, and engaging math educators.

And… there’s more to it than that. Obviously, the people who are able to attend NCTM either have districts who are willing to foot part of the bill, received some kind of grant, or paid their own way. That is, the attendees are not representative of the larger math education population. But it seemed that I talked to two kinds of people: those who were content being there and those who were super hungry to connect.

I teach at a super small private school. We have about 220 kids in 6th – 12th grade. I don’t hear bullshit acronyms like “KWLM” – literally “kids we love the most” when talking about children who have not had success at school. I don’t hear kids being called “low” or “high.” I don’t hear these false classifications of children that have nothing to do with how they learn. Even a casual label like “lazy” is describing a behavior, not a person. I encourage you, if you hear a child being called by a label, call them on their shit. It can be awkward, but it can’t be a practice that continues or ignored.

End rant. Here’s a collection of takeaways I had.

The sessions by Christopher Danielson and Michael Serra respectively were the only two where I actually had to think mathematically. I think that it’s such a rich experience for math teachers to be able to be back in a learning environment with novel material. Students do it every day.

What I loved about Danielson’s presentation is that he didn’t know where it would lead: when students come up with their own classification system of hexagons, he doesn’t have a pre-defined notion of what we would create (unless he’s already come up with every possible way to classify his set of 14 or so hexagons.)

Michael Serra had created inquiry based materials which can be found here. We worked together in groups on some of his pre-created materials. I highly endorse the donut polygon problem set.

Recurring theme: Few people have a clear vision of what to do with technology in the classroom. I heard so many stories of computers, iPads, smart boards and other gadgets being stuck in storage because they were being used improperly or didn’t foster student learning (or both).

This was the first year I went to a talk on math and social justice. Rochelle Gutierrez’s sessions focused on the “unearned privilege” that those who can do math have in society. Math typically is heralded as the highest form of intelligence, and presents a high barrier to some. I really dug her point that “math needs people” as a converse to the traditional “everyone needs math.”

People I met put up with a lot of pressing questions. I don’t know how no one told me to shut the hell up all weekend. When asked about your craft, you people are much less defensive than I think I would be.

Steven Leinwand gave the sermon of the week. Among other items, he mentioned the “devastating impact of teacher isolation”; how standards and assessments are the bookends – necessary but not sufficient; and plugged the new Practice to Action text. I’m still confused why Practice to Action isn’t a free text, supported by NCTM, the Dept of Ed or some other professional organization. If the document is so important, why not put it in the hands of everyone? Maybe I’m naïve here.

“Don’t read off your slides. Don’t read off your slides. Stop it. Don’t read off your slides.” – me talking to myself and about half of the presenters.

Dan Meyer had a great presentation on lessons we can take from how video games are structured. He’s got a summary here. But what I really took away was a line at the end of his presentation. He pointed out that so many people are vying for kids’ attention: video game developers, shoe creators, wanna-be teen celebrities, musicians, etc. etc. etc. But what teachers are given (by law no less) is a captive audience. Students are “forced” to be with us for 180 days out of the year, and it’s a time that should be treasured and honored. It’s a time to innovate and connect kids with mathematical thinking instead of mechanical procedures.

I couldn’t have been more grateful for everyone who stopped by for my presentation. I was literally in the hallway grabbing anyone who looked at my sign in an act of shameless self-promotion. It was my first one, and I didn’t really feel nervous – it seemed like all who attended really wanted me to succeed.

I think that’s the vibe that should be supported by NCTM: we want you to be a badass and you can do that here at our conferences. Other than that, I’m still not sure why people come.

NCTM 2014 Slides

I embedded my slides from my talk about using non-traditional texts in my AP Statistics class. They might not be clear if you missed it. Feel free to hit me up on Twitter if you have any questions.

(I tried to embed this about 10 different times, but the heights were all wrong. Forgive the extra click)

Bringing the (Signal and the) Noise

Notes from #SXSW

Inspired, ignited and discombobulated describe best my mindset. I feel like I’ve travelled here from another planet even though SXSW is approximately 6 miles from my house. Big thanks to the Khabele School for getting a ticket for me. I have just recently discovered the vast bucket-turning-into-an-ocean that is the educational blogging/tweeting community. To call it rich is an understatement. SXSW Edu was also my first educational conference (not relegated to just math), and I wanted to share my thoughts from a novice perspective. All of the talks can be found here. Below are some of my initial assessments (no pun intended) of the event.

On Conference Life

First, I had an incredible time on twitter seeing what everyone was talking about. More often than I would like, I wanted to go to more than one presentation at a time. However, I gathered a lot of good information just by the hashtag of various talks. On the other hand, I was shocked to see how much blatant self-promotion and product hocking went on. Color me naïve. Even the Lego’s Robotics program gave a presentation regarding their latest/great work the EV3 would enrich schools, but very little evidence of what that really looked like.

On Big “Ed Tech”

Here’s a primer:

Keeping in mind what Audrey Watters called “the corporate-driven conference agenda and the lack of educators”, I was floored how few panels actually included real life teachers. I know we are an elusive species and difficult to find in the wild, but damn. With the influx of app developers, venture capitalists, and “non-profit learning companies”, I would have loved to see more actual teachers sharing best practices. I could not find a mission statement on SXSWedu’s site, but in their about page they mention creativity and innovation. Creativity and innovation seemed to be relegated primarily to developers of a platform, app or environment.

The ideas of divergence rarely came up – especially in the “personalized”, “just-in-time”, “adaptive” educational technology secret sauces. But Alfred Solis of the “8 Elements of Project Based Learning” asked a very simple and intriguing divergent question: When does 1 + 1 not equal 2?

Bill Gates keynoted the event. I understand he didn’t get famous for his speeches, but it was pretty hard to watch. He began his talk by comparing education to polio. The basic premise of all of these ed tech talks is that Schools are broken and therefore we must (something really cool with flashing screens). Half of the talks began with showing some graphic or another showing Finland and Singapore’s superiority w/r/t Math scores. I understand: you can’t get funding without painting a bleak picture, but that doesn’t make their case necessarily valid.

I’ve heard of NBA draft drinking games, but I’m worried if anyone starts one during an educational conference. Any of the following words would have caused SXSW to look like Jonestown: personalization, seamlessly, point of instruction, adaptive, or standards based.

One last point: “Content agnostic” should be a bad word when it comes to learning environments. To think studying Mathematics looks anything like studying History is a gross simplification. Yet “content agnostic” seemed to be a real swell idea.

I will post next week my comparisons of many of these ed tech companies to the work of B. F. Skinner.

On Classroom Life

But the conference had some extremely useful speakers. I’ll try to be brief

Jeff Sandefer at the Acton Academy might have changed my life forever. He started with flatly saying that most standards taught were useless – that’s pretty strong counter point to almost every other panel at the conference. He had 7 outstanding principles that guided his school (two of my favorites: Every child is a genius; Never answer a question, ever).

Karen Fasimpaur gave many technology specialists and teachers some great resources on OER’s (Open Education Resources). They might change what education looks like or they might be ignored completely. The biggest challenge for OER’s is the quality control issue: Who is going to manage this beast? This could be solved by giving grants out to young, tall enterprising people from Austin to write one.

Wesley Fryer dropped a reference to Seymour Pappert! I’m guessing constructivism would be viewed by technology specialists like the ancient Wiccans would be viewed by modern agnostics. But I appreciated that students should be given support to construct their own knowledge at some level.

Speaking of obscure references, Tomas Riley of the Children’s Creativity Museum dropped a reference to Paulo Freire and how he wanted his museum to be “of the streets” vs. “on the hill”. If there had been a panel dedicated to critical pedagogy, how many ed tech people would have shown up? The idea of access was dismissed by several panelists.

One of the most powerful lessons I learned was from Elisabeth Soep of Youth Radio at her “Making Apps with Youth” panel. She compared the decision to give students access to open-ended platforms as similar to the canonical Jimmy Wales “steak knife” story. I teach in a very loving, yet traditional environment. I still operate under a very basic pretense: the possible costs of using computers/laptops/phones outweighs the potential benefits of those modern devices. This is an **extremely** difficult transition for many teachers to make. Especially when students who are classically trained without calculators might fare better than those without on certain assessments.

And coming full circle, the tension between power and quality control is still at the heart of most educational conferences. I’m refreshed and ready to join the larger internet community in searching for best practices.