Toward a more comprehensive framework about questions

I love that this blog exists to help us teachers get a bit better with our questioning practices. Toward that end, I propose that we find effective ways to talk about our questioning practices with each other. I think it’s natural that we focus a lot of our attention on the phrasing of our questions and the thinking and responses that they elicited (or not), but I think that there are a lot of other subtle things that we can do differently to get different kinds of outcomes. By more completely describing the situations around our questions, perhaps we’ll be able to understand each other better and to learn from one another more effectively.

So here’s my proposed framework for talking about our questioning practices with each other. (Maybe “framework” is too fancy a word–I really just mean “categories of different things that we can refer to when talking about our questioning practices”.) This framework is intended to apply to both our general questioning practices and to specific instances of questions. This framework is mostly for our questions to students, and not questions from students to us or to each other.

1. the classroom culture and environment in which we operate

What norms and expectations do we set up around questions (teacher to student, student to teacher, student to student)? What do we do to help students feel safer to answer our questions or pose their own questions?

2. the context of the lesson that surrounds the question(s)

What are the goals of the lesson, and how do the questions at hand fit into that lesson? At the time of the question, what are students doing?

3. the purpose of the question(s)

Is the goal to probe students’ understanding, to push them father along in their thinking, or to invite curiosity and wonderment, or ..?

4. the non-verbal signals and body language that accompany our question(s)

Where are you physically located/positioned in the classroom relative to students to whom you are speaking to? How much wait time? If speaking to the whole class, how do you typically signal the kinds of responses you want (chorus response or hands raised or …)?

5. the actual phrasing and delivery of the question(s) itself

Besides the actual phrasing of the question itself, how is the question actually delivered? Is it delivered to the entire class, a group of students, or an individual student? Is the question only spoken, or is it printed on a page, or is it also displayed on a projector/screen?  If it is displayed, how long does it remain?

6. the mechanisms for eliciting student responses

What typically happens in your room if you don’t get a lot of responses? If students raise hands, how do you select someone to answer? Do you use some mechanism for ensuring more equity in who gets called on (like equity sticks, a roster, etc)?

7. how you use students’ responses to your question(s)

Do you anticipate certain responses to your question(s)? What happens if you don’t get the responses you anticipate? What do you do with the responses? How do you connect students’ responses with each other? Are there follow-up questions?

I’m sure this framework isn’t complete, but I hope it will help give folks a larger view of the kinds of things that could be discussed when talking about either (a) a specific question that you plan to use or that you used or (b) the general practices you employ when posing questions to students.

I’ll end this post with an example of (a) and (b).

---

I’m currently teaching a course in partial differential equations. Students in my class are advanced undergraduate and beginning graduate students studying mathematics and physics. On the very first day class, we started by talking through some definitions. As a group, we came up with a definition of a partial differential equation (PDE): an equation involving an unknown function and its partial derivatives. I wanted my students to dive into PDEs quickly so after that whole-class discussion, I posed this question both verbally and on the projector:

I had several goals: (1) I want students to realize that guessing and experimentation are perfectly good methods for solving PDEs; (2) I want students to remember that a function is a solution of PDE if it makes the equation true; (3) I wanted to set the stage for the method of characteristics. I announced that students had 60 seconds to think independently, then I gave them 3 more minutes to talk with others around them about the functions that they found. I tried to walk around as much as possible in those 4 minutes to observe students’ progress and make notes of who I would call on and in what order.

Students came up with “t-x” pretty quickly, but they also found things like 2t-2x and (t-x)^2. During those three minutes, if students exhausted polynomial solutions, I asked them to think of solutions involving trig functions or exponentials. I said this loud enough so that most of the class could hear this “push” question. Several groups realized that f(t-x) is the general solution to this PDE, where f is any differentiable function. One student got “sin(t)cos(x)-cos(t)sin(x)”, which was really interesting because it didn’t have the “t-x” explicitly. (It’s equivalent to sin(t-x) after using a trig identity.)

After the three minutes, I tried to sequence student responses. The “t-x” solution was first, followed by “2t-2x” and “(t-x)^2”. At that point one student yelled out the punchline that f(t-x) is the most general solution. That was a little earlier than I had wanted the general solution to have come out, but it was fine. Perhaps next time I could have been more careful about my sequencing. Three minutes was a very short amount of time to get around to 40 students and to sequence answers. Perhaps if I had some challenge questions prepared, I could have drawn out the activity longer so as to give me more time with individual groups.

Overall, I thought the question went pretty well. It set me up nicely for the method of characteristics (which is used to solve linear, quasi-linear and some non-linear first-order PDEs like this one).

---

Some thoughts about general questioning practices:

I’ve noticed that over the years, I’ve become much more prescriptive in how I pose questions to students. I am more explicit about how I want students to respond. For example, if I want a choral response, then I’ll preface/append my question with something like “Shout out the answer.” If I expect students to raise their hands, then I’ll raise my hand too near the end of my question and keep it up until someone raises her/his hand.  If I am waiting for several people to raise their hands before I select someone, then I’ll say “OK, Student X has an answer–I’m going to wait until [insert number] more people have a potential answer too.”

I am also way more explicit about my wait time with students too.  If a question that I’m posing requires significant independent think time, then I announce that I’m giving them [insert number] seconds of think time before I’m taking any responses.  I also tell students that it’s okay if there are awkward silences in class when people are trying to come up with their answers–that means they people are thinking.

I think it’s important to be clear about how you want students to respond to your questions because it removes some of the anxiety around questions, and it also creates a more level playing field for students to respond. I don’t want the students who are quick to raise their hands to always be the ones to speak. That said, I hope I strike a good balance being clear about how I want students to respond to questions, and allowing for some flexibility and freedom for students to go in a different direction if they want to.

I hope others will also post here about their questioning practices too, in addition to examples of super-awesome questions.