One aspect of this exploration has been experimenting with explicitly framing mathematical knowledge building with students as a democratic process, analogous to being part of a democratic polity. In a democracy, at least according to the ideal, the direction of the polity is determined by its members, all having an equal say. In the same way, I’ve been striving to build a way of working with students in which they see the knowledge as determined by themselves engaged in a collective process in which they are all equal participants, substantially inspired by Jason Cushner and Sarah Bertucci’s Consensus Is the Answer Key.
My interest is in having students walk away from mathematical experiences knowing that math is nothing more mysterious than communities of humans trying to figure things out together; that the process that led to all mathematical knowledge is something they, and anyone, can participate in; that they can be the authors of such knowledge. That they are entitled to a say in what the community they are part of believes about math, and that their own sense of what to believe benefits by being part of a community thoughtfully working together to try to figure things out.
I hope these overall goals give you a sense of why I wanted to write about this as part of the Virtual Conference on Humanizing Mathematics: while math is often seen as some kind of disembodied and strangely history-less ancient wisdom handed down by specially-anointed priests (“math teachers”), themselves entrusted with it by an even higher priesthood (“mathematicians”), the truth is that it is nothing but the product of humans trying to figure things out together, and I want this to be what students experience it as.
While I do plan in the future on writing about the specific instructional protocols I’ve been exploring to accomplish this, I’m going to keep the scope limited here, and tell you just one story, about a time when the frame of “democracy” unexpectedly gave me a new resource in handling a situation to do with classroom culture that I priorly would have found challenging.
In 2017 I tried my first experiment building a whole learning experience around the math-knowledge-building-as-a-democratic-process metaphor. (It was a course at BEAM.) On the first day I explained that mathematical knowledge is democratic in character and that they would be working democratically as a community to decide what’s true. They bought in.
They were working through something, I no longer remember what. C asked a question or made an argument and A replied. A’s reply was mathematical and on topic, but his tone was a little condescending. Just a little, but it was there.
This is a type of situation in which I’ve historically found it a little hard to exercise my authority to move the classroom culture in a positive direction. I don’t want a room in which it’s okay for people to be condescending to each other. That’s a recipe for the class to start to feel emotionally unsafe. On the other hand, I’ve often had trouble finding a way of intervening in this type of situation that would have felt fair to A. If I said, “that was disrespectful,” well, perhaps it was, a little, but it was also on topic and advanced the conversation, and, well, “disrespectful” is a powerful word. Furthermore, this intervention would not have been very actionable for A: the thing I didn’t like was not located in his choice of words, but in a subtle tone thing. If he felt defensive at all (and who wouldn’t?), it would be difficult for him even to perceive what he had done that was being criticized; how would he correct it?
I think some teachers deftly handle this type of situation using light-touch humor, but that has always been a difficult tool for me to wield when being corrective. I’m too earnest; it’s hard for me to get that dial just right.
I’ve found myself in situations like this countless times, but this was the first time I had encountered it while teaching a class that had explicitly bought into the idea that they were a democratic community. I found myself, quite to my surprise, with a confident new move:
“A, you’re saying something very interesting, but your tone of voice is a little like you’re the teacher and C is the student. In a democracy, you’re equals. So can you try making that exact same interesting point except from one equal to another?”
And what was beautiful was that he completely, happily, undefensively took it on. In fact, he seemed excited to try. And, he did it! He said the exact same thing, except from one equal to another. The conversation proceeded with a new foundation of safety and mutual respect established.
I knew I wanted to teach them that math was something humans make by coming together as equals and trying to figure stuff out together. I didn’t know this would also give me new moves to support the development of a healthy mathematical culture. Retrospectively, maybe I should have.
 Sarah wrote an essay on this pedagogical principle which unfortunately has never been published, but the link above is a nice description of a session she and Jason and their students led at the Creating Balance conference in 2008.
I’ve been working to develop a community of educators interested in this “math-as-democracy” pedagogy. I facilitated a minicourse and a professional learning team at Math for America this past year on the subject, and James Cleveland, who was part of both, led a session at TMCNYC19. This fall I am co-facilitating another professional learning team on instructional routines, one of which is democracy-focused. If you’re interested in thinking about this circle of ideas with me, get in touch!