One of the many reasons I put myself in a math PhD program is that it is an intense full-time laboratory in which for me to examine my own learning process, and my experience as a participant in math classrooms from the student side. I hope to record many lessons from this laboratory on this blog. Here is one.

As a teacher I have always strongly encouraged people to pipe up when they’re confused, whether working in groups or (especially) at the level of whole-class discussion. To encourage this, I do things like:

* I leave lots of wait time.
* I respond to questions (especially those expressing confusion) with enthusiasm when they are asked, and after they are discussed I point out concrete, specific ways in which the questions advanced the conversation.
* I give (very deeply felt) pep talks about the value of these questions.
* Sometimes I directly solicit questions from people whose faces make it seem like they have one.

I am behind all of these practices. However, in every class that I have taught, whether for students or teachers, including all those of an extended enough length so that the practices would have time to shape the culture, it has always seemed to me that participants are often not asking their questions. This has puzzled me a bit. I’ve generally responded by trying harder: leaving longer wait-time, making more of a point to highlight the value of questions when they happen, giving more strident and frequent pep talks. This hasn’t resolved the matter.

Now I am not about to pronounce a new solution. But I have what for me is a very new insight. I imagine some readers of this blog will read it and be like, “Ben, I could have told you that.” I’m sure you could have, but this wouldn’t have helped me: retrospectively, students have told me it many, many times. But I didn’t get it till I felt it. This is the value of putting yourself in their position.

What I’ve realized since beginning graduate school is that I had an incomplete understanding of why students don’t ask questions. I believed that the only reason not to ask a question is the fear of looking dumb. My approach has been entirely aimed at ameliorating this fear and replacing it with the sense that questions are honored and their contribution is valued.

Now one of the great advantages of going to grad school as an adult, rather than going fresh out of college, is that I have very, very little fear of looking dumb. (In the immortal words of my friend Kiku Polk, you get your “f*ck you” at 30.) To all my early-20’s people: your 20’s will be wonderful but if you make sure you keep growing, your 30’s will be better.

And one of the great advantages of going to grad school after over a decade as a teacher, is that I have a strong commitment to asking my questions, stemming from the value that I know they have both for myself and the class.

Perhaps as a consequence, I found that in all four of my classes last semester, I asked more questions than anyone else in the room.

Be that as it may, I frequently didn’t ask my questions.

What’s up?

As it turns out (and now, okay, maybe this is Captain Obvious talking, but a propos of all of the above, somehow I’ve been overlooking it for a decade), not wanting to hold up class is its own reason not to ask questions! Maybe it’s a basic piece of our social programming. If things are going one way in a room of 20 or 30 people, it feels sort of painful to contemplate forcing them in another direction on your account. Especially if you’ve already done it once or twice, but even if not. And more so the further your question seems to be from what the people around you (esp. the teacher) look like they want to talk about. All this is intensified if you’re not sure your question is going to come out perfectly articulate – not (necessarily or only) because of how this will make you look, but because you know that your interruption is going to take up more mental and social space if it has to start with a whole period of everybody just getting clear on what you’re even asking.

There is an added layer that it is often perceptible that the teacher desires for everyone to understand and appreciate what was just said as clearly as she or he understands and appreciates it. Last night I was in a lecture in which I was hyperaware of not always asking my questions, and part of the dynamic in that case was actually the professor’s enthusiasm about what he was saying! I did ask a number of questions, but one reason I didn’t ask more is that I sort of felt like I was crashing his party! My warm feelings toward this professor actually heightened this effect: messing up someone else’s flow is worse when it’s someone you like.

As I mentioned above, students have been trying to tell me this for years. I never got it, because on some level I always believed that the real problem was that they were afraid to look dumb. I remember a conversation with a particular student who was my advisee as well as my math student. When I pressed her on asking more questions in class, she said something to the effect of, “you know, you’re doing your thing up there, and I don’t want to get in the way.” I literally remember the voice in my head reinterpreting this as a lack of belief in herself. Now I think that that was part of it as well; but my response was all aimed at that, and so didn’t address the whole issue.

Now my process of figuring out how to operationalize this new insight in terms of teaching practice has only just begun, and one reason I am writing about this here is to invite you into this process. I am certainly NOT telling you to withhold your enthusiasm on the grounds that it might make kids not want to interrupt you with questions. Furthermore, evidently when I describe experiences from my graduate classes, I am describing a situation in which the measures you and I have been taking for years to encourage question-asking are mostly absent. I doubt most of my professors have even heard of wait time. Nonetheless, I am sure that this new point of view is fruitful in terms of actual practice. Below are my preliminary thoughts. Please comment.

If I want to really encourage question asking, what I have been doing (aimed at building a culture of question-asking) is necessary, but insufficient. It is also necessary to think about lesson structure with an eye to: how do I design the flow of this lesson so that (at least during significant parts where questions are likely to arise in students’ minds) asking their questions does not feel like an interruption? One model, which is valuable in other ways as well, is to have students’ questions be the desired product of a certain segment of class. For example, when the lesson arrives at a key idea, definition, or conclusion, ask students to turn to their neighbors and discuss the key idea and try to produce a question about it. Then have the pairs or groups report their questions. This way, the questions cannot be interruptions because they are explicitly the very thing that is supposed to be going on right then.

I like this idea but it has limited scope because it requires the point in the lesson at which the questions arise to be planned, and of course this can never contain all the questions I would want to have asked. Another thing to think about is the matter of momentum. I think my discussion of enthusiasm above really revolves around momentum. Enthusiasm generates momentum, but momentum is actually the thing that it hurts to get in the way of. Therefore I submit a second idea: the question of managing my/your own and the class’s momentum. Having forward momentum is obviously a big part of class being engaging, but perhaps it also suppresses spontaneous questions? Or under certain conditions it does?

(In a way this reminds me of the tension – one I am much more confident is an essential one of our profession – between storytelling and avoidance of theft – I discussed a particular case of this tension in the fourth paragraph here. Momentum is aligned with storytelling: a good story generates momentum. Avoiding theft is aligned with inviting questions.)

A last thought is that in a class of 20 or 30, having the class engage every question that pops into any student’s head at any time is obviously not a desirable situation. You might think I thought it was desirable based on the above. But the question is how to empower students to ask questions when we want them. I know that I for one have often known I wanted some questions so I could be responsive to them, and they weren’t forthcoming. The question is about how to change this. Part of the answer is about the culture, valuing the questions, encouraging the risks, and making everyone feel safe; but it’s the other part – how to structurally support the questions – that’s the new inquiry for me. As I said above, please comment.