I have had the tremendous good fortune to meet and get to know Karim Ani and Dan Meyer in the last couple of years. The three of us have gone back and forth on blogs, Twitter and email. I have learned an awful lot from the conversation.
Last winter I watched the two of them in action at a conference organized by Keith Devlin. I found it really interesting. But I also got frustrated by the lack of critical questioning. The audience wasn’t asking any hard questions and they weren’t asking any hard questions of each other. These minds are way too sharp not to push back on each other a bit.
And if there’s one skill I have developed in my work in higher ed, it’s asking critical questions.
So I hounded these gentlemen and got them to sit down for a conversation at the NCTM meeting in Philadelphia. I compensated them with beer and cupcakes. As I get time, I’ll transcribe the recording of our conversation and post excerpts here.
Up first is a question Dan and Karim have debated a few times. Where do questions come from in math class?
Today we’ll hear from Dan. I’ll get Karim’s response up soon. The questioning is pretty softball here too. Later installments will be different.
NOTE: The people have spoken. They demanded editing so that conversational speech is more easily read as prose. I have done that with a light hand. The original, less edited version is available as a pdf.
Christopher: Traditionally, questions in math classrooms come pretty much exclusively from two places. They come from the teacher in which the teacher asks students questions with a known answer and students are expected to, either in unison or individually when called upon, provide an answer.
The other place questions come from is from students. When the teacher stops and says, “any questions”? Which is what I think you were playing with with your “anyqs” hashtag that turned into 101 questions, Dan.
But I think…those are sort of stereotypical…opportunities for questions to arise in math classrooms. I think we would each chafe against those as being particularly productive. And if that’s what math classrooms continue to be, I don’t think that produces a particularly productive math classroom and each of us has a vision of what questions should look like in math classrooms. So if you could just say a couple of words about-in your mind-where do, or should, questions in math classrooms come from?
Karim: The stork brings ‘em, huh?
Dan: I guess I would take that large question-it’s a good question-and start carving things off from it. Something I’ve dealt with a lot that is just tough to deal with is the idea that we should take a concept and that students should come up with their own questions for it. [This] has been a persistent critique that always bums me out. It bums me out because anyone who makes the point that students should have more control over their learning instantly occupies the moral high ground.
There’s…you asked at the very start about what compromises we’re willing to make for implementation’s sake. Having every student working on a question of their own device. Logistically, I might on my best day be willing to manage that. It’s not something I would construct for a national policy on teaching, or state or local or whatever.
So carving that off…the business of today’s class will not necessarily be on whatever question you the student just kind of came up with. So if you guys want to take that one on, I would love to… That’s been a tough one for me for a while now.
What I would say is this-that all things being equal-if the day has an objective; if there’s something on the agenda today that came from a standards sheet or the natural progression of the mathematics from previous days-all things being equal I would love for that to emerge from a question that the student came up with, or alternatively feels a lot of investment in. And you can gin up investment different ways.
But ideally I know that if I’m asking a question that students don’t care about, I can get them to work on it, and even answer it. But it’s gonna be at the expense of administrative managerial capital. It means I am putting my currency on the line insanely. You guys need to do this; it’s your grade, or you like me or whatever.
All things being equal, I would rather not have to spend that capital. That’d be a start, I suppose, on questions.
Christopher: So you made me think of your Eric the sheep post. You had a graduate course, or someone who came and spoke in your graduate program who came and had you work on the Eric the sheep problem and I remember reading that post and you were writing about the really quite wide variety of questions that people came up with in response to this really open task that had been posed.
I remember reacting, thinking about trying to understand what the person who brought the task to the class, like…what were they hoping to teach a collection of graduate students about problem posing or teaching mathematics or research or cognition, like I didn’t get at all what…
I saw that the lesson would be completely unmanageable if I were teaching in high school, so I couldn’t imagine that it was modeling Here’s what we should be doing. And I struggled to understand what the point of the lesson for graduate students was.
Dan: Yeah. That was an interesting day.
I would say I’m referring to an even more Montessori, constructivist sense. Those questions came from a prompt; a very specific direct prompt about the sheep who cuts ahead in line.
I’m thinking more of like, why are you suggesting sheep? What if the student doesn’t want to deal with sheep? You know, let the student pose their own problem.
So there’s a spectrum here of student agency. And I’m saying I get that at some point the teacher’s going to have to say, This is what we’re going to do today. And I would love for that moment to be as closely aligned to what the student would like to do today as possible, acknowledging that isn’t ever going to be the case in a world that includes Call of Duty.
One last thing…this is the absolute best form of session feedback, as far as I am concerned—getting to read someone else’s notes on the session speaks volumes about what participants experienced (in contrast sometimes to what I think we did).
Overthinking my teaching 